id
stringlengths 14
117
| description
stringlengths 29
13k
| code
stringlengths 10
49.8k
| test_samples
dict | source
class label 3
classes | prompt
stringlengths 391
104k
|
|---|---|---|---|---|---|
313_C. Ilya and Matrix_28319
|
Ilya is a very good-natured lion. He likes maths. Of all mathematical objects, his favourite one is matrices. Now he's faced a complicated matrix problem he needs to solve.
He's got a square 2n × 2n-sized matrix and 4n integers. You need to arrange all these numbers in the matrix (put each number in a single individual cell) so that the beauty of the resulting matrix with numbers is maximum.
The beauty of a 2n × 2n-sized matrix is an integer, obtained by the following algorithm:
1. Find the maximum element in the matrix. Let's denote it as m.
2. If n = 0, then the beauty of the matrix equals m. Otherwise, a matrix can be split into 4 non-intersecting 2n - 1 × 2n - 1-sized submatrices, then the beauty of the matrix equals the sum of number m and other four beauties of the described submatrices.
As you can see, the algorithm is recursive.
Help Ilya, solve the problem and print the resulting maximum beauty of the matrix.
Input
The first line contains integer 4n (1 ≤ 4n ≤ 2·106). The next line contains 4n integers ai (1 ≤ ai ≤ 109) — the numbers you need to arrange in the 2n × 2n-sized matrix.
Output
On a single line print the maximum value of the beauty of the described matrix.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
1
13
Output
13
Input
4
1 2 3 4
Output
14
Note
Consider the second sample. You need to arrange the numbers in the matrix as follows:
1 2
3 4
Then the beauty of the matrix will equal: 4 + 1 + 2 + 3 + 4 = 14.
|
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
################################
n=int(input())
from math import log
l=list(map(int,input().split()))
l.sort(reverse=True)
a=int(log(n,4))
if n==1:
print(l[0])
else:
ans=l[0]*(a+1)
i=1
c=0
while i<n:
if a>1:
for j in range((4**c)*3):
ans+=l[i+j]*a
a-=1
i+=(4**c)*3
c+=1
else:
ans+=l[i]
i+=1
print(ans)
|
{
"input": [
"1\n13\n",
"4\n1 2 3 4\n",
"16\n521848329 105907607 414661942 473600423 264555612 186332345 774233687 736918178 456150336 216550357 568433949 135218174 18789799 324141005 617635501 149674864\n",
"1\n6\n",
"16\n666766712 653140033 670637874 170909587 210382562 358152171 128926299 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n612095723 222321386 616933999 386488979 943748076 902598472 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 60225467 969809069\n",
"1\n8\n",
"4\n963662765 272656295 383441522 477665112\n",
"4\n7 9 6 9\n",
"4\n423654797 623563697 645894116 384381709\n",
"1\n9\n",
"4\n791725034 812168727 528894922 479977172\n",
"16\n978618343 473608041 799158564 800910753 461479363 520477481 780529176 678879534 118274424 720632652 639921017 582019792 143353286 537373229 944668919 758615621\n",
"4\n437587210 297534606 891773002 56712976\n",
"16\n521848329 105907607 414661942 473600423 264555612 186332345 590809843 736918178 456150336 216550357 568433949 135218174 18789799 324141005 617635501 149674864\n",
"1\n3\n",
"16\n666766712 653140033 670637874 170909587 210382562 25750657 128926299 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n612095723 145843797 616933999 386488979 943748076 902598472 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 60225467 969809069\n",
"1\n5\n",
"4\n23621909 272656295 383441522 477665112\n",
"4\n7 9 3 9\n",
"4\n423654797 623563697 645894116 509847407\n",
"1\n2\n",
"4\n791725034 812168727 209136028 479977172\n",
"16\n978618343 473608041 799158564 800910753 461479363 520477481 780529176 678879534 118274424 720632652 639921017 582019792 225578081 537373229 944668919 758615621\n",
"4\n437587210 297534606 891773002 90968561\n",
"1\n10\n",
"4\n1 0 3 4\n",
"16\n521848329 105907607 414661942 589564275 264555612 186332345 590809843 736918178 456150336 216550357 568433949 135218174 18789799 324141005 617635501 149674864\n",
"1\n4\n",
"16\n666766712 653140033 670637874 170909587 210382562 19693664 128926299 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n612095723 145843797 664397551 386488979 943748076 902598472 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 60225467 969809069\n",
"1\n1\n",
"4\n38604083 272656295 383441522 477665112\n",
"4\n7 9 3 17\n",
"4\n423654797 1222650212 645894116 509847407\n",
"1\n0\n",
"4\n791725034 1195357211 209136028 479977172\n",
"16\n978618343 473608041 799158564 800910753 461479363 520477481 780529176 678879534 118274424 720632652 1126830014 582019792 225578081 537373229 944668919 758615621\n",
"4\n437587210 297534606 1253109584 90968561\n",
"1\n15\n",
"4\n1 0 3 5\n",
"16\n521848329 105907607 414661942 589564275 264555612 186332345 590809843 1432894221 456150336 216550357 568433949 135218174 18789799 324141005 617635501 149674864\n",
"1\n11\n",
"16\n666766712 653140033 670637874 170909587 210382562 23183657 128926299 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n946198983 145843797 664397551 386488979 943748076 902598472 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 60225467 969809069\n",
"1\n7\n",
"4\n38604083 272656295 279502460 477665112\n",
"4\n7 9 2 17\n",
"4\n423654797 1222650212 645894116 215946008\n",
"4\n791725034 96765278 209136028 479977172\n",
"16\n978618343 473608041 799158564 800910753 461479363 520477481 780529176 678879534 118274424 720632652 1126830014 573380639 225578081 537373229 944668919 758615621\n",
"4\n437587210 297534606 249536246 90968561\n",
"1\n26\n",
"16\n521848329 105907607 414661942 589564275 264555612 186332345 590809843 1432894221 456150336 191962312 568433949 135218174 18789799 324141005 617635501 149674864\n",
"1\n18\n",
"16\n666766712 653140033 670637874 170909587 210382562 23183657 157294306 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n946198983 145843797 664397551 386488979 943748076 1489357863 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 60225467 969809069\n",
"4\n38604083 272656295 279502460 914052332\n",
"4\n7 9 2 12\n",
"4\n423654797 1222650212 101983880 215946008\n",
"4\n791725034 96765278 209136028 778089277\n",
"16\n978618343 473608041 799158564 800910753 450679529 520477481 780529176 678879534 118274424 720632652 1126830014 573380639 225578081 537373229 944668919 758615621\n",
"4\n437587210 297534606 249536246 24697671\n",
"4\n1 1 1 5\n",
"16\n521848329 105907607 764822457 589564275 264555612 186332345 590809843 1432894221 456150336 191962312 568433949 135218174 18789799 324141005 617635501 149674864\n",
"16\n666766712 653140033 670637874 170909587 210382562 23183657 102273902 750686139 315428350 607830667 363710774 325047228 570196776 38425426 438601514 634274054\n",
"16\n946198983 145843797 664397551 386488979 943748076 1489357863 681820298 449949990 359507903 613063462 437031953 902348579 697631196 99280352 26941545 969809069\n",
"4\n59245506 272656295 279502460 914052332\n",
"4\n7 9 2 7\n",
"4\n423654797 1222650212 101983880 87459381\n",
"4\n791725034 96765278 7995926 778089277\n",
"16\n978618343 473608041 799158564 311159005 450679529 520477481 780529176 678879534 118274424 720632652 1126830014 573380639 225578081 537373229 944668919 758615621\n",
"4\n437587210 297534606 249536246 28551054\n",
"1\n84\n",
"16\n521848329 105907607 764822457 589564275 264555612 186332345 590809843 1432894221 456150336 191962312 568433949 26261067 18789799 324141005 617635501 149674864\n",
"1\n17\n",
"4\n1 1 3 5\n",
"1\n52\n",
"1\n12\n",
"4\n1 1 1 1\n"
],
"output": [
"13",
"14",
"9436107110",
"6",
"10395033063",
"13643168169",
"8",
"3061088459",
"40",
"2723388435",
"9",
"3424934582",
"14440495117",
"2575380796",
"9031943913\n",
"3\n",
"10062631549\n",
"13566690580\n",
"5\n",
"1635049950\n",
"37\n",
"2848854133\n",
"2\n",
"3105175688\n",
"14522719912\n",
"2609636381\n",
"10\n",
"12\n",
"9169038091\n",
"4\n",
"10056574556\n",
"13614154132\n",
"1\n",
"1650032124\n",
"53\n",
"4024696744\n",
"0\n",
"3871552656\n",
"15485512030\n",
"3332309545\n",
"15\n",
"14\n",
"11256966220\n",
"11\n",
"10060064549\n",
"13992107796\n",
"7\n",
"1546093062\n",
"52\n",
"3730795345\n",
"2369328546\n",
"15476872877\n",
"1513213833\n",
"26\n",
"11232378175\n",
"18\n",
"10088432556\n",
"15685175372\n",
"2418867502\n",
"42\n",
"3186885109\n",
"2667440651\n",
"15466073043\n",
"1446942943\n",
"13\n",
"11757796872\n",
"10033412152\n",
"15651891450\n",
"2439508925\n",
"34\n",
"3058398482\n",
"2466300549\n",
"14974569106\n",
"1450796326\n",
"84\n",
"11648839765\n",
"17\n",
"15\n",
"52\n",
"12\n",
"5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ilya is a very good-natured lion. He likes maths. Of all mathematical objects, his favourite one is matrices. Now he's faced a complicated matrix problem he needs to solve.
He's got a square 2n × 2n-sized matrix and 4n integers. You need to arrange all these numbers in the matrix (put each number in a single individual cell) so that the beauty of the resulting matrix with numbers is maximum.
The beauty of a 2n × 2n-sized matrix is an integer, obtained by the following algorithm:
1. Find the maximum element in the matrix. Let's denote it as m.
2. If n = 0, then the beauty of the matrix equals m. Otherwise, a matrix can be split into 4 non-intersecting 2n - 1 × 2n - 1-sized submatrices, then the beauty of the matrix equals the sum of number m and other four beauties of the described submatrices.
As you can see, the algorithm is recursive.
Help Ilya, solve the problem and print the resulting maximum beauty of the matrix.
Input
The first line contains integer 4n (1 ≤ 4n ≤ 2·106). The next line contains 4n integers ai (1 ≤ ai ≤ 109) — the numbers you need to arrange in the 2n × 2n-sized matrix.
Output
On a single line print the maximum value of the beauty of the described matrix.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
1
13
Output
13
Input
4
1 2 3 4
Output
14
Note
Consider the second sample. You need to arrange the numbers in the matrix as follows:
1 2
3 4
Then the beauty of the matrix will equal: 4 + 1 + 2 + 3 + 4 = 14.
### Input:
1
13
### Output:
13
### Input:
4
1 2 3 4
### Output:
14
### Code:
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
################################
n=int(input())
from math import log
l=list(map(int,input().split()))
l.sort(reverse=True)
a=int(log(n,4))
if n==1:
print(l[0])
else:
ans=l[0]*(a+1)
i=1
c=0
while i<n:
if a>1:
for j in range((4**c)*3):
ans+=l[i+j]*a
a-=1
i+=(4**c)*3
c+=1
else:
ans+=l[i]
i+=1
print(ans)
|
335_F. Buy One, Get One Free_28322
|
A nearby pie shop is having a special sale. For each pie you pay full price for, you may select one pie of a strictly lesser value to get for free. Given the prices of all the pies you wish to acquire, determine the minimum total amount you must pay for all of the pies.
Input
Input will begin with an integer n (1 ≤ n ≤ 500000), the number of pies you wish to acquire. Following this is a line with n integers, each indicating the cost of a pie. All costs are positive integers not exceeding 109.
Output
Print the minimum cost to acquire all the pies.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
6
3 4 5 3 4 5
Output
14
Input
5
5 5 5 5 5
Output
25
Input
4
309999 6000 2080 2080
Output
314159
Note
In the first test case you can pay for a pie with cost 5 and get a pie with cost 4 for free, then pay for a pie with cost 5 and get a pie with cost 3 for free, then pay for a pie with cost 4 and get a pie with cost 3 for free.
In the second test case you have to pay full price for every pie.
|
#https://codeforces.com/problemset/problem/335/F
h = [i for i in range(500001)]
t = [i for i in range(500001)]
ans = 0
len = 0
nw = 0
tot = 0
cnt = 0
a = []
def work(x):
y = x >> 1
while y and h[y] > h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x >> 1
def pop():
global len
h[1] = h[len]
len -= 1
x = 1
y = 2
if y < len and h[y + 1] < h[y]:
y += 1
while y <= len and h[y] < h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x << 1
if y < len and h[y + 1] < h[y]:
y += 1
def solve():
global cnt, len, tot, nw, a
n = int(input())
a = list(map(int, input().split()))
# print(a)
ans = sum(a)
a.sort(reverse = True)
a.insert(0, -1)
# print(a)
for i in range(1, n + 1):
if not nw:
nw = a[i]
tot = 1
else:
if nw > a[i]:
tot -= 1
cnt += 1
t[cnt] = a[i]
if not tot:
nw = 0
else:
tot += 1
if tot >= 2 and len and h[1] < a[i] * 2:
if h[1] < a[i]:
cnt += 1
t[cnt] = a[i]
cnt += 1
t[cnt] = a[i]
else:
cnt += 1
t[cnt] = h[1]
cnt += 1
t[cnt] = a[i] * 2 - h[1]
pop()
tot -= 2
if not tot:
nw = 0
if i == n or a[i + 1] != a[i]:
if nw == a[i] and len and h[1] < a[i]:
pop()
cnt += 1
t[cnt] = a[i]
for j in range(1, cnt + 1):
len += 1
h[len] = t[j]
work(len)
cnt = 0
for i in range(1, len + 1):
ans -= h[i]
print(ans)
solve()
|
{
"input": [
"4\n309999 6000 2080 2080\n",
"5\n5 5 5 5 5\n",
"6\n3 4 5 3 4 5\n",
"30\n3 6 3 8 6 4 4 2 4 10 8 5 9 6 7 7 9 4 7 4 10 1 9 10 4 7 7 4 2 3\n",
"1\n1\n",
"50\n4 2 6 7 2 6 3 8 8 2 4 8 4 4 1 4 5 2 2 5 6 4 3 3 3 6 8 2 1 3 1 8 2 3 7 4 7 5 4 8 3 5 7 8 6 7 5 8 7 1\n",
"40\n2 6 5 5 6 6 7 8 6 5 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 2 2 1 4 4 4 3 5 5\n",
"10\n1 1 1 1 1 2 3 4 5 6\n",
"2\n505072434 3351179\n",
"7\n10 9 5 5 4 3 2\n",
"1\n880460566\n",
"30\n3 6 3 8 6 4 4 2 4 10 8 5 9 6 7 7 9 4 7 4 10 1 9 10 4 7 7 4 3 3\n",
"1\n2\n",
"50\n4 2 6 7 2 6 3 8 8 2 4 8 4 4 1 3 5 2 2 5 6 4 3 3 3 6 8 2 1 3 1 8 2 3 7 4 7 5 4 8 3 5 7 8 6 7 5 8 7 1\n",
"40\n2 6 5 5 6 6 7 8 6 3 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 2 2 1 4 4 4 3 5 5\n",
"10\n1 1 1 1 1 2 3 8 5 6\n",
"2\n438883123 3351179\n",
"7\n10 9 5 10 4 3 2\n",
"1\n237338885\n",
"4\n309999 6000 2596 2080\n",
"5\n5 5 8 5 5\n",
"6\n3 4 5 3 6 5\n",
"30\n3 6 3 8 6 3 4 2 4 10 8 5 9 6 7 7 9 4 7 4 10 1 9 10 4 7 7 4 3 3\n",
"1\n4\n",
"50\n4 2 6 7 2 6 3 8 8 2 4 8 7 4 1 3 5 2 2 5 6 4 3 3 3 6 8 2 1 3 1 8 2 3 7 4 7 5 4 8 3 5 7 8 6 7 5 8 7 1\n",
"40\n2 6 5 5 6 6 10 8 6 3 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 2 2 1 4 4 4 3 5 5\n",
"7\n10 9 5 10 4 5 2\n",
"1\n98932919\n",
"5\n5 5 8 3 5\n",
"6\n3 4 5 3 3 5\n",
"1\n6\n",
"50\n4 2 6 7 2 6 3 8 8 2 4 8 7 4 1 3 5 2 2 5 6 4 3 3 3 6 8 2 1 3 1 8 2 3 7 4 7 1 4 8 3 5 7 8 6 7 5 8 7 1\n",
"40\n2 6 5 5 6 6 10 8 6 3 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 4 2 1 4 4 4 3 5 5\n",
"7\n10 15 5 10 4 5 2\n",
"1\n187720904\n",
"4\n309999 6000 4638 2194\n",
"1\n11\n",
"40\n2 6 5 5 6 9 10 8 6 3 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 4 2 1 4 4 4 3 5 5\n",
"7\n16 15 5 10 4 5 2\n",
"1\n32968143\n",
"5\n9 5 8 5 5\n",
"6\n3 2 5 3 3 9\n",
"30\n3 6 3 8 5 3 4 2 4 5 8 5 9 6 7 10 9 4 7 4 10 1 9 10 4 7 7 4 3 3\n",
"1\n9\n",
"40\n2 6 5 5 6 9 10 8 6 3 3 9 9 1 8 3 10 3 7 2 3 1 3 1 5 8 1 3 8 2 3 4 2 1 4 4 4 3 5 5\n",
"7\n16 15 5 10 4 5 4\n",
"1\n51648020\n",
"2\n438883123 2344125\n",
"4\n309999 6000 2596 2194\n",
"30\n3 6 3 8 5 3 4 2 4 10 8 5 9 6 7 7 9 4 7 4 10 1 9 10 4 7 7 4 3 3\n",
"2\n438883123 1317420\n",
"5\n6 5 8 5 5\n",
"6\n3 4 5 3 3 9\n",
"30\n3 6 3 8 5 3 4 2 4 10 8 5 9 6 7 10 9 4 7 4 10 1 9 10 4 7 7 4 3 3\n",
"2\n438883123 1209345\n",
"4\n309999 6000 4638 1266\n",
"2\n438883123 123767\n"
],
"output": [
"314159\n",
"25\n",
"14\n",
"96\n",
"1\n",
"130\n",
"100\n",
"16\n",
"505072434\n",
"22\n",
"880460566",
"96\n",
"2\n",
"129\n",
"99\n",
"19\n",
"438883123\n",
"26\n",
"237338885\n",
"312595\n",
"23\n",
"15\n",
"94\n",
"4\n",
"130\n",
"101\n",
"27\n",
"98932919\n",
"18\n",
"14\n",
"6\n",
"128\n",
"102\n",
"32\n",
"187720904\n",
"314637\n",
"11\n",
"103\n",
"33\n",
"32968143\n",
"22\n",
"17\n",
"93\n",
"9\n",
"105\n",
"35\n",
"51648020\n",
"438883123\n",
"312595\n",
"94\n",
"438883123\n",
"19\n",
"18\n",
"96\n",
"438883123\n",
"314637\n",
"438883123\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A nearby pie shop is having a special sale. For each pie you pay full price for, you may select one pie of a strictly lesser value to get for free. Given the prices of all the pies you wish to acquire, determine the minimum total amount you must pay for all of the pies.
Input
Input will begin with an integer n (1 ≤ n ≤ 500000), the number of pies you wish to acquire. Following this is a line with n integers, each indicating the cost of a pie. All costs are positive integers not exceeding 109.
Output
Print the minimum cost to acquire all the pies.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
6
3 4 5 3 4 5
Output
14
Input
5
5 5 5 5 5
Output
25
Input
4
309999 6000 2080 2080
Output
314159
Note
In the first test case you can pay for a pie with cost 5 and get a pie with cost 4 for free, then pay for a pie with cost 5 and get a pie with cost 3 for free, then pay for a pie with cost 4 and get a pie with cost 3 for free.
In the second test case you have to pay full price for every pie.
### Input:
4
309999 6000 2080 2080
### Output:
314159
### Input:
5
5 5 5 5 5
### Output:
25
### Code:
#https://codeforces.com/problemset/problem/335/F
h = [i for i in range(500001)]
t = [i for i in range(500001)]
ans = 0
len = 0
nw = 0
tot = 0
cnt = 0
a = []
def work(x):
y = x >> 1
while y and h[y] > h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x >> 1
def pop():
global len
h[1] = h[len]
len -= 1
x = 1
y = 2
if y < len and h[y + 1] < h[y]:
y += 1
while y <= len and h[y] < h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x << 1
if y < len and h[y + 1] < h[y]:
y += 1
def solve():
global cnt, len, tot, nw, a
n = int(input())
a = list(map(int, input().split()))
# print(a)
ans = sum(a)
a.sort(reverse = True)
a.insert(0, -1)
# print(a)
for i in range(1, n + 1):
if not nw:
nw = a[i]
tot = 1
else:
if nw > a[i]:
tot -= 1
cnt += 1
t[cnt] = a[i]
if not tot:
nw = 0
else:
tot += 1
if tot >= 2 and len and h[1] < a[i] * 2:
if h[1] < a[i]:
cnt += 1
t[cnt] = a[i]
cnt += 1
t[cnt] = a[i]
else:
cnt += 1
t[cnt] = h[1]
cnt += 1
t[cnt] = a[i] * 2 - h[1]
pop()
tot -= 2
if not tot:
nw = 0
if i == n or a[i + 1] != a[i]:
if nw == a[i] and len and h[1] < a[i]:
pop()
cnt += 1
t[cnt] = a[i]
for j in range(1, cnt + 1):
len += 1
h[len] = t[j]
work(len)
cnt = 0
for i in range(1, len + 1):
ans -= h[i]
print(ans)
solve()
|
359_A. Table_28325
|
Simon has a rectangular table consisting of n rows and m columns. Simon numbered the rows of the table from top to bottom starting from one and the columns — from left to right starting from one. We'll represent the cell on the x-th row and the y-th column as a pair of numbers (x, y). The table corners are cells: (1, 1), (n, 1), (1, m), (n, m).
Simon thinks that some cells in this table are good. Besides, it's known that no good cell is the corner of the table.
Initially, all cells of the table are colorless. Simon wants to color all cells of his table. In one move, he can choose any good cell of table (x1, y1), an arbitrary corner of the table (x2, y2) and color all cells of the table (p, q), which meet both inequations: min(x1, x2) ≤ p ≤ max(x1, x2), min(y1, y2) ≤ q ≤ max(y1, y2).
Help Simon! Find the minimum number of operations needed to color all cells of the table. Note that you can color one cell multiple times.
Input
The first line contains exactly two integers n, m (3 ≤ n, m ≤ 50).
Next n lines contain the description of the table cells. Specifically, the i-th line contains m space-separated integers ai1, ai2, ..., aim. If aij equals zero, then cell (i, j) isn't good. Otherwise aij equals one. It is guaranteed that at least one cell is good. It is guaranteed that no good cell is a corner.
Output
Print a single number — the minimum number of operations Simon needs to carry out his idea.
Examples
Input
3 3
0 0 0
0 1 0
0 0 0
Output
4
Input
4 3
0 0 0
0 0 1
1 0 0
0 0 0
Output
2
Note
In the first sample, the sequence of operations can be like this:
<image>
* For the first time you need to choose cell (2, 2) and corner (1, 1).
* For the second time you need to choose cell (2, 2) and corner (3, 3).
* For the third time you need to choose cell (2, 2) and corner (3, 1).
* For the fourth time you need to choose cell (2, 2) and corner (1, 3).
In the second sample the sequence of operations can be like this:
<image>
* For the first time you need to choose cell (3, 1) and corner (4, 3).
* For the second time you need to choose cell (2, 3) and corner (1, 1).
|
n,m=map(int,input().split())
l=[list(map(int,input().split())) for _ in range(n)]
for i in range(n):
if (i==0 or i==n-1) and sum(l[i]): print(2); break
elif l[i][0]==1 or l[i][-1]==1: print(2); break
else: print(4)
|
{
"input": [
"4 3\n0 0 0\n0 0 1\n1 0 0\n0 0 0\n",
"3 3\n0 0 0\n0 1 0\n0 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"4 3\n0 0 0\n0 0 0\n0 0 0\n0 1 0\n",
"3 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 1 0\n",
"3 5\n0 0 0 0 0\n1 0 0 0 0\n0 0 0 0 0\n",
"3 3\n0 1 0\n0 0 0\n0 0 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 0\n0 1 0\n0 0 0\n",
"13 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"3 3\n0 0 0\n0 1 1\n0 0 0\n",
"3 5\n0 0 0 0 0\n0 0 0 0 1\n0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 0\n0 0 0\n0 0 1\n0 0 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n",
"3 3\n0 0 0\n0 0 1\n0 0 0\n",
"5 5\n0 0 0 0 0\n0 1 0 0 0\n0 0 0 1 0\n0 0 0 0 0\n0 0 0 0 0\n",
"3 3\n0 0 0\n1 0 0\n0 0 0\n",
"5 3\n0 0 0\n0 0 0\n1 0 0\n0 0 0\n0 0 0\n",
"5 3\n0 0 0\n0 1 0\n0 0 0\n0 0 0\n0 0 0\n",
"4 4\n0 0 0 0\n0 1 1 0\n0 1 1 0\n0 0 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"3 5\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 0\n0 0 0\n0 0 0\n",
"3 3\n0 0 0\n0 0 0\n0 1 0\n",
"3 4\n0 1 0 0\n0 0 0 0\n0 0 0 0\n",
"4 3\n0 0 0\n0 0 0\n0 1 0\n0 0 0\n",
"4 3\n0 1 0\n0 0 0\n0 0 0\n0 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n0 1 0\n0 1 0\n0 0 0\n0 0 0\n",
"3 5\n0 0 0 -1 0\n0 0 0 0 0\n0 0 0 1 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 0\n0 1 0\n0 1 0\n",
"5 3\n0 0 0\n0 0 0\n0 1 0\n0 0 1\n0 0 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n0 1 0 0\n",
"5 3\n0 0 0\n0 1 0\n0 0 0\n0 0 1\n0 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 1\n1 0 0\n0 0 0\n0 0 0\n",
"4 3\n0 0 0\n1 0 1\n1 0 0\n0 0 0\n",
"3 5\n0 0 0 -1 0\n0 0 0 0 0\n0 1 0 1 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 0\n1 1 0\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n0 0 0 0\n0 0 0 1\n0 1 0 0\n",
"5 3\n0 0 0\n0 0 1\n1 0 0\n1 1 0\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 1\n0 0 0 -1\n0 0 0 0\n0 0 0 1\n0 1 0 0\n",
"5 3\n0 1 0\n0 0 1\n1 0 0\n1 1 0\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 1\n0 0 0 -1\n0 0 0 1\n0 0 0 1\n0 1 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"4 3\n0 0 0\n0 0 0\n0 0 -1\n0 1 0\n",
"3 5\n0 0 -1 0 0\n0 0 0 0 0\n0 0 0 1 0\n",
"3 5\n0 0 0 1 0\n1 0 0 0 0\n0 0 0 0 0\n",
"3 3\n0 1 0\n0 0 0\n0 -1 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"5 3\n0 0 0\n1 0 1\n0 0 0\n0 0 0\n0 0 0\n",
"3 3\n0 1 0\n0 1 1\n0 0 0\n",
"3 5\n0 0 0 0 0\n0 0 0 0 1\n0 0 0 -1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n0 0 0 0\n0 1 0 0\n",
"3 3\n0 -1 0\n0 0 1\n0 0 0\n",
"5 5\n0 0 0 0 0\n0 1 0 0 0\n0 0 0 1 1\n0 0 0 0 0\n0 0 0 0 0\n",
"4 4\n0 0 0 0\n0 1 1 0\n0 1 0 0\n0 0 0 0\n",
"3 5\n0 0 1 0 0\n0 0 1 0 0\n0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 1\n0 0 0\n0 0 0\n",
"3 3\n0 1 0 0\n0 0 0 0\n0 0 0 0\n",
"4 3\n0 0 0\n0 0 0\n0 1 0\n0 1 0\n",
"4 3\n0 0 0\n0 0 1\n1 -1 0\n0 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 0\n0 1 0\n0 0 1\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n0 0 0 0\n1 0 0 0\n0 1 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n0 0 1\n1 0 0\n1 0 0\n0 0 0\n",
"3 5\n0 0 0 -1 0\n0 -1 0 0 0\n0 1 0 1 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 -1\n1 1 0\n0 1 0\n",
"5 3\n0 0 0\n0 0 0\n1 0 0\n1 1 0\n0 1 0\n",
"7 4\n0 0 0 0\n-1 0 0 0\n0 0 0 1\n0 0 0 -1\n0 0 0 0\n0 0 0 1\n0 1 0 0\n",
"5 3\n0 2 0\n0 0 1\n1 0 0\n1 1 0\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 1\n0 0 0 -1\n0 0 0 1\n1 0 0 1\n0 1 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0\n",
"3 5\n0 0 0 1 0\n2 0 0 0 0\n0 0 0 0 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n1 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"5 3\n0 0 0\n1 0 1\n0 0 1\n0 0 0\n0 0 0\n",
"3 3\n0 1 0\n1 1 1\n0 0 0\n",
"5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 1 1\n0 0 0 0 0\n0 0 0 0 0\n",
"3 5\n0 0 1 0 0\n0 0 1 0 0\n0 0 0 -1 0\n",
"5 3\n0 0 0\n0 0 1\n0 0 1\n0 0 1\n0 0 0\n",
"4 3\n0 -1 0\n0 0 1\n1 -1 0\n0 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 1 0\n0 0 0\n0 1 0\n0 0 1\n0 1 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n0 0 0 0\n1 1 0 0\n0 1 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n1 0 1\n1 0 0\n1 0 0\n0 0 0\n",
"5 3\n0 0 0\n0 0 1\n0 1 -1\n1 1 0\n0 1 0\n",
"5 3\n0 0 0\n0 0 0\n1 0 0\n1 1 0\n0 2 0\n",
"7 4\n0 0 1 0\n-1 0 0 0\n0 0 0 1\n0 0 0 -1\n0 0 0 0\n0 0 0 1\n0 1 0 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 1\n0 0 0 -1\n0 1 0 1\n1 0 0 1\n0 1 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n1 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 1 1\n0 -1 0 0 0\n0 0 0 0 0\n",
"3 5\n0 0 1 0 0\n0 0 1 0 0\n0 0 1 -1 0\n",
"5 3\n0 0 0\n0 0 1\n0 -1 1\n0 0 1\n0 0 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0\n",
"5 3\n0 1 0\n0 0 0\n0 1 0\n0 0 1\n0 2 0\n",
"7 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 -1\n-1 0 0 0\n1 1 0 0\n0 1 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 0 0\n1 0 0\n1 0 0\n1 0 0\n0 0 0\n",
"5 3\n0 0 0\n0 0 0\n1 0 0\n1 2 0\n0 2 0\n",
"4 32\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 1 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n1 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"3 5\n0 0 1 1 0\n0 0 1 0 0\n0 0 1 -1 0\n",
"5 3\n0 1 0\n0 -1 0\n0 1 0\n0 0 1\n0 2 0\n",
"7 4\n0 0 0 0\n1 0 0 0\n0 0 0 0\n0 0 0 -1\n-1 0 0 0\n1 1 0 0\n0 1 0 0\n",
"5 50\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"5 3\n0 -1 0\n0 0 0\n1 0 0\n1 2 0\n0 2 0\n",
"50 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 1 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n1 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n",
"3 5\n0 0 1 2 0\n0 0 1 0 0\n0 0 1 -1 0\n",
"5 3\n0 1 0\n-1 -1 0\n0 1 0\n0 0 1\n0 2 0\n",
"50 4\n0 0 1 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 1 0\n0 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n1 0 0 0\n0 1 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n",
"5 3\n0 1 0\n-1 -1 0\n0 1 0\n0 0 0\n0 2 0\n"
],
"output": [
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"4\n",
"4\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Simon has a rectangular table consisting of n rows and m columns. Simon numbered the rows of the table from top to bottom starting from one and the columns — from left to right starting from one. We'll represent the cell on the x-th row and the y-th column as a pair of numbers (x, y). The table corners are cells: (1, 1), (n, 1), (1, m), (n, m).
Simon thinks that some cells in this table are good. Besides, it's known that no good cell is the corner of the table.
Initially, all cells of the table are colorless. Simon wants to color all cells of his table. In one move, he can choose any good cell of table (x1, y1), an arbitrary corner of the table (x2, y2) and color all cells of the table (p, q), which meet both inequations: min(x1, x2) ≤ p ≤ max(x1, x2), min(y1, y2) ≤ q ≤ max(y1, y2).
Help Simon! Find the minimum number of operations needed to color all cells of the table. Note that you can color one cell multiple times.
Input
The first line contains exactly two integers n, m (3 ≤ n, m ≤ 50).
Next n lines contain the description of the table cells. Specifically, the i-th line contains m space-separated integers ai1, ai2, ..., aim. If aij equals zero, then cell (i, j) isn't good. Otherwise aij equals one. It is guaranteed that at least one cell is good. It is guaranteed that no good cell is a corner.
Output
Print a single number — the minimum number of operations Simon needs to carry out his idea.
Examples
Input
3 3
0 0 0
0 1 0
0 0 0
Output
4
Input
4 3
0 0 0
0 0 1
1 0 0
0 0 0
Output
2
Note
In the first sample, the sequence of operations can be like this:
<image>
* For the first time you need to choose cell (2, 2) and corner (1, 1).
* For the second time you need to choose cell (2, 2) and corner (3, 3).
* For the third time you need to choose cell (2, 2) and corner (3, 1).
* For the fourth time you need to choose cell (2, 2) and corner (1, 3).
In the second sample the sequence of operations can be like this:
<image>
* For the first time you need to choose cell (3, 1) and corner (4, 3).
* For the second time you need to choose cell (2, 3) and corner (1, 1).
### Input:
4 3
0 0 0
0 0 1
1 0 0
0 0 0
### Output:
2
### Input:
3 3
0 0 0
0 1 0
0 0 0
### Output:
4
### Code:
n,m=map(int,input().split())
l=[list(map(int,input().split())) for _ in range(n)]
for i in range(n):
if (i==0 or i==n-1) and sum(l[i]): print(2); break
elif l[i][0]==1 or l[i][-1]==1: print(2); break
else: print(4)
|
452_C. Magic Trick_28336
|
Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.
The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.
You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.
Input
First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.
Output
On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.
Examples
Input
2 2
Output
0.6666666666666666
Input
4 4
Output
0.4000000000000000
Input
1 2
Output
1.0000000000000000
Note
In the first sample, with probability <image> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.
With the remaining <image> probability he took two different cards, and the probability of pulling off the trick is <image>.
The resulting probability is <image>
|
import sys
import os
n,m = map(float, sys.stdin.readline().split())
res = 0
if (n == 1):
res = 1
else:
res = (1+(n-1)*(m-1)/(n*m-1))/n
print(res)
|
{
"input": [
"4 4\n",
"1 2\n",
"2 2\n",
"1000 1000\n",
"998 1\n",
"999 999\n",
"555 543\n",
"2 987\n",
"1 999\n",
"321 123\n",
"1 1\n",
"987 123\n",
"678 231\n",
"10 10\n",
"2 1\n",
"461 1000\n",
"2 3\n",
"998 2\n",
"999 504\n",
"555 907\n",
"3 987\n",
"1 1435\n",
"614 123\n",
"6 10\n",
"723 1000\n",
"4 3\n",
"975 504\n",
"555 671\n",
"6 987\n",
"433 123\n",
"4 2\n",
"9 10\n",
"3 3\n",
"975 884\n",
"555 142\n",
"433 147\n",
"3 2\n",
"15 10\n",
"3 4\n",
"555 19\n",
"736 147\n",
"3 1\n",
"13 10\n",
"3 6\n",
"995 19\n",
"13 7\n",
"4 6\n",
"13 12\n",
"6 6\n",
"811 543\n",
"321 230\n",
"678 211\n",
"17 10\n",
"6 2\n",
"2 4\n",
"999 809\n",
"240 907\n",
"4 987\n",
"214 123\n",
"11 10\n",
"379 1000\n",
"4 5\n",
"975 660\n",
"628 671\n",
"12 987\n",
"466 123\n",
"7 3\n",
"9 19\n",
"312 884\n",
"555 279\n",
"820 147\n",
"5 1\n",
"15 2\n",
"555 16\n",
"736 52\n",
"13 15\n",
"5 6\n",
"995 12\n",
"13 2\n",
"9 12\n",
"7 6\n",
"725 543\n",
"176 230\n",
"678 126\n",
"17 15\n",
"5 2\n",
"2 6\n",
"19 907\n",
"13 987\n",
"1 3\n",
"1 987\n",
"1 232\n",
"1 4\n",
"1 2112\n",
"1 5\n",
"1 6\n",
"1 712\n",
"1 38\n"
],
"output": [
"0.399999999999999967\n",
"1.000000000000000000\n",
"0.666666666666666630\n",
"0.001998001998\n",
"0.001002004008016039\n",
"0.002000000000\n",
"0.003597050814\n",
"0.749873289406994381\n",
"1.000000000000000000\n",
"0.006195654284\n",
"1.000000000000000000\n",
"0.002017095387\n",
"0.002941310918\n",
"0.181818181818181795\n",
"0.500000000000000000\n",
"0.004331529575\n",
"0.700000000000\n",
"0.0015027548831996296\n",
"0.0019990178729991604\n",
"0.003598377748537914\n",
"0.5554054054080817\n",
"1.0\n",
"0.0032414781922363548\n",
"0.2937853107344667\n",
"0.002762959403995896\n",
"0.3863636363636359\n",
"0.0020481992847883354\n",
"0.0035976814697341567\n",
"0.30543827056532813\n",
"0.004594914105134589\n",
"0.35714285714285693\n",
"0.20099875156055844\n",
"0.49999999999999933\n",
"0.0020490722862806076\n",
"0.003587713891540386\n",
"0.004597965565268134\n",
"0.4666666666666661\n",
"0.12304250559283719\n",
"0.5151515151515145\n",
"0.003505857906402178\n",
"0.002706327432897783\n",
"0.3333333333333333\n",
"0.14132379248657706\n",
"0.5294117647058848\n",
"0.0019562475943176723\n",
"0.1384615384615468\n",
"0.4130434782608637\n",
"0.1424317617865711\n",
"0.2857142857142855\n",
"0.0024623056248673065\n",
"0.006207364163559469\n",
"0.0029407074901903934\n",
"0.10894535328926226\n",
"0.24242424242424276\n",
"0.7142857142857137\n",
"0.001999765155818707\n",
"0.008311416499745612\n",
"0.4373574866980806\n",
"0.009286320185745576\n",
"0.16597164303586806\n",
"0.005267458463709973\n",
"0.4078947368421082\n",
"0.002048679314554324\n",
"0.0031798121788180075\n",
"0.15965127079119892\n",
"0.0042698684766458855\n",
"0.22857142857142856\n",
"0.20522875816994487\n",
"0.006396381075935155\n",
"0.0035939222527534937\n",
"0.0024292613322545653\n",
"0.2\n",
"0.09885057471264365\n",
"0.0034881373095397537\n",
"0.0026894867600867436\n",
"0.14353687549564498\n",
"0.3379310344827622\n",
"0.0019254493422968463\n",
"0.11384615384615392\n",
"0.2024922118380185\n",
"0.24738675958188583\n",
"0.002754184985788407\n",
"0.01130692907277928\n",
"0.0029360057021668834\n",
"0.1106993978693947\n",
"0.2888888888888883\n",
"0.7272727272727267\n",
"0.10244099106703383\n",
"0.14786258169204705\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n",
"1.0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.
The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.
You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.
Input
First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.
Output
On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.
Examples
Input
2 2
Output
0.6666666666666666
Input
4 4
Output
0.4000000000000000
Input
1 2
Output
1.0000000000000000
Note
In the first sample, with probability <image> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.
With the remaining <image> probability he took two different cards, and the probability of pulling off the trick is <image>.
The resulting probability is <image>
### Input:
4 4
### Output:
0.399999999999999967
### Input:
1 2
### Output:
1.000000000000000000
### Code:
import sys
import os
n,m = map(float, sys.stdin.readline().split())
res = 0
if (n == 1):
res = 1
else:
res = (1+(n-1)*(m-1)/(n*m-1))/n
print(res)
|
475_A. Bayan Bus_28340
|
The final round of Bayan Programming Contest will be held in Tehran, and the participants will be carried around with a yellow bus. The bus has 34 passenger seats: 4 seats in the last row and 3 seats in remaining rows.
<image>
The event coordinator has a list of k participants who should be picked up at the airport. When a participant gets on the bus, he will sit in the last row with an empty seat. If there is more than one empty seat in that row, he will take the leftmost one.
In order to keep track of the people who are on the bus, the event coordinator needs a figure showing which seats are going to be taken by k participants. Your task is to draw the figure representing occupied seats.
Input
The only line of input contains integer k, (0 ≤ k ≤ 34), denoting the number of participants.
Output
Print the figure of a bus with k passengers as described in sample tests. Character '#' denotes an empty seat, while 'O' denotes a taken seat. 'D' is the bus driver and other characters in the output are for the purpose of beautifying the figure. Strictly follow the sample test cases output format. Print exactly six lines. Do not output extra space or other characters.
Examples
Input
9
Output
+------------------------+
|O.O.O.#.#.#.#.#.#.#.#.|D|)
|O.O.O.#.#.#.#.#.#.#.#.|.|
|O.......................|
|O.O.#.#.#.#.#.#.#.#.#.|.|)
+------------------------+
Input
20
Output
+------------------------+
|O.O.O.O.O.O.O.#.#.#.#.|D|)
|O.O.O.O.O.O.#.#.#.#.#.|.|
|O.......................|
|O.O.O.O.O.O.#.#.#.#.#.|.|)
+------------------------+
|
def main():
n = int(input())
print("+------------------------+")
b1 = 0
if n == 0:
b1 = 0
elif 1 <= n <= 4:
b1 = 1
else:
b1 = (n + 1) // 3
if 0 <= n <= 1:
b2 = 0
elif 2 <= n <= 5:
b2 = 1
else:
b2 = n // 3
b3 = 0
if n < 3:
b3 = 0
else:
b3 = 1
b4 = 0
if n <= 3:
b4 = 0
else:
b4 = (n - 1) // 3
print("|", end = '')
for i in range(1, 12):
if i <= b1:
print('O.', end = '')
else:
print('#.', end = '')
print('|D|)')
print("|", end = '')
for i in range(1, 12):
if i <= b2:
print('O.', end = '')
else:
print('#.', end = '')
print('|.|')
if b3 == 0:
print("|#.......................|")
else:
print("|O.......................|")
print("|", end = '')
for i in range(1, 12):
if i <= b4:
print('O.', end = '')
else:
print('#.', end = '')
print('|.|)')
print("+------------------------+")
main()
|
{
"input": [
"9\n",
"20\n",
"10\n",
"18\n",
"0\n",
"23\n",
"21\n",
"1\n",
"11\n",
"13\n",
"6\n",
"3\n",
"22\n",
"5\n",
"19\n",
"30\n",
"16\n",
"2\n",
"15\n",
"28\n",
"31\n",
"33\n",
"14\n",
"12\n",
"32\n",
"8\n",
"26\n",
"4\n",
"29\n",
"24\n",
"17\n",
"25\n",
"27\n",
"7\n",
"34\n",
"001\n",
"011\n",
"000\n",
"010\n"
],
"output": [
"+------------------------+\n|O.O.O.#.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.#.#.#.#.|D|)\n|O.O.O.O.O.O.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.#.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.#.#.#.#.#.|D|)\n|O.O.O.O.O.O.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|#.#.#.#.#.#.#.#.#.#.#.|D|)\n|#.#.#.#.#.#.#.#.#.#.#.|.|\n|#.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.#.#.#.|D|)\n|O.O.O.O.O.O.O.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.#.#.#.#.|D|)\n|O.O.O.O.O.O.O.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.#.#.#.#.#.#.#.#.#.#.|D|)\n|#.#.#.#.#.#.#.#.#.#.#.|.|\n|#.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.#.#.#.#.#.#.#.|D|)\n|O.O.O.O.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.#.#.#.#.#.#.#.#.#.|D|)\n|O.O.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.#.#.#.#.#.#.#.#.#.#.|D|)\n|O.#.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.#.#.#.#.|D|)\n|O.O.O.O.O.O.O.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.#.#.#.#.#.#.#.#.#.|D|)\n|O.#.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.#.#.#.#.#.|D|)\n|O.O.O.O.O.O.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.#.|D|)\n|O.O.O.O.O.O.O.O.O.O.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.#.#.#.#.#.#.|D|)\n|O.O.O.O.O.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.#.#.#.#.#.#.#.#.#.#.|D|)\n|O.#.#.#.#.#.#.#.#.#.#.|.|\n|#.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.#.#.#.#.#.#.|D|)\n|O.O.O.O.O.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.#.#.|D|)\n|O.O.O.O.O.O.O.O.O.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.#.|D|)\n|O.O.O.O.O.O.O.O.O.O.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.O.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.O.|D|)\n|O.O.O.O.O.O.O.O.O.O.O.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.O.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.#.#.#.#.#.#.|D|)\n|O.O.O.O.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.#.#.#.#.#.#.#.|D|)\n|O.O.O.O.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.O.|D|)\n|O.O.O.O.O.O.O.O.O.O.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.O.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.#.#.#.#.#.#.#.#.|D|)\n|O.O.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.#.#.|D|)\n|O.O.O.O.O.O.O.O.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.#.#.#.#.#.#.#.#.#.#.|D|)\n|O.#.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.#.|D|)\n|O.O.O.O.O.O.O.O.O.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.#.#.#.|D|)\n|O.O.O.O.O.O.O.O.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.#.#.#.#.#.|D|)\n|O.O.O.O.O.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.#.#.#.|D|)\n|O.O.O.O.O.O.O.O.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.#.#.|D|)\n|O.O.O.O.O.O.O.O.O.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.#.#.#.#.#.#.#.#.#.|D|)\n|O.O.#.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.O.O.O.O.O.O.O.|D|)\n|O.O.O.O.O.O.O.O.O.O.O.|.|\n|O.......................|\n|O.O.O.O.O.O.O.O.O.O.O.|.|)\n+------------------------+\n",
"+------------------------+\n|O.#.#.#.#.#.#.#.#.#.#.|D|)\n|#.#.#.#.#.#.#.#.#.#.#.|.|\n|#.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.O.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|#.#.#.#.#.#.#.#.#.#.#.|D|)\n|#.#.#.#.#.#.#.#.#.#.#.|.|\n|#.......................|\n|#.#.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n",
"+------------------------+\n|O.O.O.#.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.#.#.#.#.#.#.#.#.|.|)\n+------------------------+\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The final round of Bayan Programming Contest will be held in Tehran, and the participants will be carried around with a yellow bus. The bus has 34 passenger seats: 4 seats in the last row and 3 seats in remaining rows.
<image>
The event coordinator has a list of k participants who should be picked up at the airport. When a participant gets on the bus, he will sit in the last row with an empty seat. If there is more than one empty seat in that row, he will take the leftmost one.
In order to keep track of the people who are on the bus, the event coordinator needs a figure showing which seats are going to be taken by k participants. Your task is to draw the figure representing occupied seats.
Input
The only line of input contains integer k, (0 ≤ k ≤ 34), denoting the number of participants.
Output
Print the figure of a bus with k passengers as described in sample tests. Character '#' denotes an empty seat, while 'O' denotes a taken seat. 'D' is the bus driver and other characters in the output are for the purpose of beautifying the figure. Strictly follow the sample test cases output format. Print exactly six lines. Do not output extra space or other characters.
Examples
Input
9
Output
+------------------------+
|O.O.O.#.#.#.#.#.#.#.#.|D|)
|O.O.O.#.#.#.#.#.#.#.#.|.|
|O.......................|
|O.O.#.#.#.#.#.#.#.#.#.|.|)
+------------------------+
Input
20
Output
+------------------------+
|O.O.O.O.O.O.O.#.#.#.#.|D|)
|O.O.O.O.O.O.#.#.#.#.#.|.|
|O.......................|
|O.O.O.O.O.O.#.#.#.#.#.|.|)
+------------------------+
### Input:
9
### Output:
+------------------------+
|O.O.O.#.#.#.#.#.#.#.#.|D|)
|O.O.O.#.#.#.#.#.#.#.#.|.|
|O.......................|
|O.O.#.#.#.#.#.#.#.#.#.|.|)
+------------------------+
### Input:
20
### Output:
+------------------------+
|O.O.O.O.O.O.O.#.#.#.#.|D|)
|O.O.O.O.O.O.#.#.#.#.#.|.|
|O.......................|
|O.O.O.O.O.O.#.#.#.#.#.|.|)
+------------------------+
### Code:
def main():
n = int(input())
print("+------------------------+")
b1 = 0
if n == 0:
b1 = 0
elif 1 <= n <= 4:
b1 = 1
else:
b1 = (n + 1) // 3
if 0 <= n <= 1:
b2 = 0
elif 2 <= n <= 5:
b2 = 1
else:
b2 = n // 3
b3 = 0
if n < 3:
b3 = 0
else:
b3 = 1
b4 = 0
if n <= 3:
b4 = 0
else:
b4 = (n - 1) // 3
print("|", end = '')
for i in range(1, 12):
if i <= b1:
print('O.', end = '')
else:
print('#.', end = '')
print('|D|)')
print("|", end = '')
for i in range(1, 12):
if i <= b2:
print('O.', end = '')
else:
print('#.', end = '')
print('|.|')
if b3 == 0:
print("|#.......................|")
else:
print("|O.......................|")
print("|", end = '')
for i in range(1, 12):
if i <= b4:
print('O.', end = '')
else:
print('#.', end = '')
print('|.|)')
print("+------------------------+")
main()
|
499_A. Watching a movie_28344
|
You have decided to watch the best moments of some movie. There are two buttons on your player:
1. Watch the current minute of the movie. By pressing this button, you watch the current minute of the movie and the player automatically proceeds to the next minute of the movie.
2. Skip exactly x minutes of the movie (x is some fixed positive integer). If the player is now at the t-th minute of the movie, then as a result of pressing this button, it proceeds to the minute (t + x).
Initially the movie is turned on in the player on the first minute, and you want to watch exactly n best moments of the movie, the i-th best moment starts at the li-th minute and ends at the ri-th minute (more formally, the i-th best moment consists of minutes: li, li + 1, ..., ri).
Determine, what is the minimum number of minutes of the movie you have to watch if you want to watch all the best moments?
Input
The first line contains two space-separated integers n, x (1 ≤ n ≤ 50, 1 ≤ x ≤ 105) — the number of the best moments of the movie and the value of x for the second button.
The following n lines contain the descriptions of the best moments of the movie, the i-th line of the description contains two integers separated by a space li, ri (1 ≤ li ≤ ri ≤ 105).
It is guaranteed that for all integers i from 2 to n the following condition holds: ri - 1 < li.
Output
Output a single number — the answer to the problem.
Examples
Input
2 3
5 6
10 12
Output
6
Input
1 1
1 100000
Output
100000
Note
In the first sample, the player was initially standing on the first minute. As the minutes from the 1-st to the 4-th one don't contain interesting moments, we press the second button. Now we can not press the second button and skip 3 more minutes, because some of them contain interesting moments. Therefore, we watch the movie from the 4-th to the 6-th minute, after that the current time is 7. Similarly, we again skip 3 minutes and then watch from the 10-th to the 12-th minute of the movie. In total, we watch 6 minutes of the movie.
In the second sample, the movie is very interesting, so you'll have to watch all 100000 minutes of the movie.
|
class CodeforcesTask499ASolution:
def __init__(self):
self.result = ''
self.n_x = []
self.best_moments = []
def read_input(self):
self.n_x = [int(x) for x in input().split(" ")]
for x in range(self.n_x[0]):
self.best_moments.append([int(j) for j in input().split(" ")])
def process_task(self):
watch_time = 0
watch_time += (self.best_moments[0][0] - 1) % self.n_x[1]
for moment in self.best_moments:
watch_time += moment[1] - moment[0] + 1
for x in range(len(self.best_moments) - 1):
watch_time += (self.best_moments[x + 1][0] - 1 - self.best_moments[x][1]) % self.n_x[1]
self.result = str(watch_time)
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask499ASolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
|
{
"input": [
"2 3\n5 6\n10 12\n",
"1 1\n1 100000\n",
"1 100\n5 6\n",
"1 3\n4 100000\n",
"1 2\n2 100000\n",
"2 100\n5 6\n7 7\n",
"12 14\n2156 3497\n4784 7775\n14575 23857\n29211 30739\n31932 33447\n35902 36426\n47202 48772\n60522 63982\n68417 78537\n79445 86918\n90081 90629\n94325 95728\n",
"3 1\n1 2\n3 4\n6 7\n",
"1 5\n7 10\n",
"2 10\n14575 36426\n60522 79445\n",
"1 100000\n1 100000\n",
"1 1\n1 1\n",
"1 3\n5 6\n",
"10 1000\n2156 3497\n4784 7775\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 10000\n500 600\n",
"10 3\n2156 3497\n4784 7775\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 2\n1 1\n",
"18 111\n1449 2156\n3497 4784\n7775 14575\n23857 24593\n29211 30739\n31932 33447\n35902 36426\n36991 38506\n39679 47202\n48772 60016\n60522 61868\n63340 63982\n68417 78537\n79445 86568\n86918 87940\n90081 90310\n90629 94325\n95728 96263\n",
"12 17\n2156 3497\n4784 7775\n14575 23857\n29211 30739\n31932 33447\n35902 36426\n47202 48772\n60522 63982\n68417 78537\n79445 86918\n90081 90629\n94325 95728\n",
"1 1\n14575 60522\n",
"10 10\n2156 3497\n4784 7775\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 100000\n100000 100000\n",
"3 1\n14575 36426\n48772 60522\n79445 90081\n",
"10 1\n2156 3497\n4784 7775\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 10\n14575 60522\n",
"2 3\n1 3\n4 8\n",
"2 3\n1 1\n5 6\n",
"1 100\n5 10\n",
"1 5\n10 10\n",
"2 10\n14575 57309\n60522 79445\n",
"1 10010\n500 600\n",
"1 1\n14575 63405\n",
"1 100100\n100000 100000\n",
"2 6\n1 3\n4 8\n",
"2 3\n1 1\n5 7\n",
"1 1\n1 100001\n",
"1 5\n10 17\n",
"2 10\n14575 35453\n60522 79445\n",
"2 3\n1 1\n5 14\n",
"2 9\n14575 35453\n60522 79445\n",
"1 4\n14575 63405\n",
"2 3\n1 1\n5 27\n",
"2 9\n19461 35453\n60522 79445\n",
"1 4\n19636 63405\n",
"2 9\n19461 35453\n60522 86488\n",
"2 9\n11746 35453\n60522 86488\n",
"2 9\n19376 35453\n60522 86488\n",
"2 9\n24949 35453\n60522 86488\n",
"2 9\n24949 53265\n60522 86488\n",
"2 9\n2523 53265\n60522 86488\n",
"1 3\n8 100000\n",
"2 10\n14575 22619\n60522 79445\n",
"1 3\n3 6\n",
"10 1000\n2156 3497\n4784 10620\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 10000\n500 1103\n",
"18 111\n1449 2156\n3497 4784\n7775 14575\n23857 24593\n29211 30739\n31932 33447\n35902 36426\n36991 38506\n39679 47202\n48772 60016\n60522 61868\n63340 63982\n68417 78537\n79445 83654\n86918 87940\n90081 90310\n90629 94325\n95728 96263\n",
"1 1\n8398 60522\n",
"10 1\n2156 3497\n4178 7775\n14575 31932\n33447 35902\n36426 47202\n48772 60522\n63982 68417\n78537 79445\n90081 90629\n94325 95728\n",
"1 2\n14575 60522\n",
"1 3\n1 1\n5 6\n",
"1 3\n5 6\n10 12\n",
"1 2\n10 17\n",
"1 2\n14575 86824\n",
"2 3\n1 1\n5 26\n",
"2 18\n14575 35453\n60522 79445\n",
"1 4\n21431 63405\n",
"2 9\n19461 35453\n61572 79445\n",
"1 4\n6220 63405\n",
"2 9\n33232 35453\n60522 86488\n",
"2 9\n3305 53265\n60522 86488\n",
"1 1\n433 60522\n",
"1 00010\n369 600\n",
"1 1\n4 100001\n",
"2 4\n1 1\n5 26\n",
"2 18\n14575 40391\n60522 79445\n",
"2 9\n15226 35453\n61572 79445\n",
"1 4\n11181 63405\n",
"2 11\n33232 35453\n60522 86488\n",
"2 9\n6534 53265\n60522 86488\n",
"1 1\n433 49957\n",
"1 00010\n543 600\n",
"1 2\n4 100001\n",
"2 4\n1 1\n5 29\n",
"2 9\n6233 35453\n61572 79445\n",
"1 4\n3647 63405\n",
"1 1\n433 96953\n",
"1 3\n1 2\n6 8\n",
"1 4\n1645 63405\n",
"1 100\n10 10\n",
"1 10011\n500 600\n",
"1 2\n14575 63405\n",
"1 101\n10 10\n",
"2 3\n1 1\n4 8\n",
"1 10010\n369 600\n",
"2 6\n1 3\n4 5\n",
"2 3\n1 1\n6 7\n",
"1 1\n2 100001\n",
"1 001\n10 10\n",
"1 4\n3 6\n",
"1 3\n1 1\n4 8\n",
"1 3\n1 1\n5 8\n",
"2 6\n2 3\n4 5\n",
"1 3\n10 17\n",
"1 1\n14575 86824\n",
"1 3\n1 1\n6 8\n",
"2 1\n2 3\n4 5\n",
"1 1\n2 3\n4 5\n",
"2 4\n1 2\n5 29\n",
"1 2\n433 96953\n",
"1 3\n1 3\n6 8\n"
],
"output": [
"6\n",
"100000\n",
"6\n",
"99997\n",
"100000\n",
"7\n",
"41870\n",
"6\n",
"5\n",
"40785\n",
"100000\n",
"1\n",
"3\n",
"58728\n",
"600\n",
"53983\n",
"1\n",
"58967\n",
"41872\n",
"45948\n",
"54038\n",
"100000\n",
"44240\n",
"53974\n",
"45952\n",
"8\n",
"3\n",
"10\n",
"5\n",
"61665\n",
"600\n",
"48831\n",
"100000\n",
"8\n",
"4\n",
"100001\n",
"12\n",
"39815\n",
"11\n",
"39809\n",
"48833\n",
"24\n",
"34922\n",
"43773\n",
"41965\n",
"49678\n",
"42055\n",
"36475\n",
"54286\n",
"76714\n",
"99994\n",
"26975\n",
"6\n",
"61728\n",
"1103\n",
"56081\n",
"52125\n",
"54580\n",
"45948\n",
"1\n",
"3\n",
"9\n",
"72250\n",
"23\n",
"39827\n",
"41977\n",
"33869\n",
"57189\n",
"28195\n",
"75931\n",
"60090\n",
"240\n",
"99998\n",
"26\n",
"44759\n",
"38108\n",
"52225\n",
"28199\n",
"72709\n",
"49525\n",
"60\n",
"99999\n",
"29\n",
"47099\n",
"59761\n",
"96521\n",
"2\n",
"61761\n",
"10\n",
"600\n",
"48831\n",
"10\n",
"8\n",
"600\n",
"5\n",
"4\n",
"100000\n",
"1\n",
"6\n",
"1\n",
"1\n",
"5\n",
"8\n",
"72250\n",
"1\n",
"4\n",
"2\n",
"29\n",
"96521\n",
"3\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have decided to watch the best moments of some movie. There are two buttons on your player:
1. Watch the current minute of the movie. By pressing this button, you watch the current minute of the movie and the player automatically proceeds to the next minute of the movie.
2. Skip exactly x minutes of the movie (x is some fixed positive integer). If the player is now at the t-th minute of the movie, then as a result of pressing this button, it proceeds to the minute (t + x).
Initially the movie is turned on in the player on the first minute, and you want to watch exactly n best moments of the movie, the i-th best moment starts at the li-th minute and ends at the ri-th minute (more formally, the i-th best moment consists of minutes: li, li + 1, ..., ri).
Determine, what is the minimum number of minutes of the movie you have to watch if you want to watch all the best moments?
Input
The first line contains two space-separated integers n, x (1 ≤ n ≤ 50, 1 ≤ x ≤ 105) — the number of the best moments of the movie and the value of x for the second button.
The following n lines contain the descriptions of the best moments of the movie, the i-th line of the description contains two integers separated by a space li, ri (1 ≤ li ≤ ri ≤ 105).
It is guaranteed that for all integers i from 2 to n the following condition holds: ri - 1 < li.
Output
Output a single number — the answer to the problem.
Examples
Input
2 3
5 6
10 12
Output
6
Input
1 1
1 100000
Output
100000
Note
In the first sample, the player was initially standing on the first minute. As the minutes from the 1-st to the 4-th one don't contain interesting moments, we press the second button. Now we can not press the second button and skip 3 more minutes, because some of them contain interesting moments. Therefore, we watch the movie from the 4-th to the 6-th minute, after that the current time is 7. Similarly, we again skip 3 minutes and then watch from the 10-th to the 12-th minute of the movie. In total, we watch 6 minutes of the movie.
In the second sample, the movie is very interesting, so you'll have to watch all 100000 minutes of the movie.
### Input:
2 3
5 6
10 12
### Output:
6
### Input:
1 1
1 100000
### Output:
100000
### Code:
class CodeforcesTask499ASolution:
def __init__(self):
self.result = ''
self.n_x = []
self.best_moments = []
def read_input(self):
self.n_x = [int(x) for x in input().split(" ")]
for x in range(self.n_x[0]):
self.best_moments.append([int(j) for j in input().split(" ")])
def process_task(self):
watch_time = 0
watch_time += (self.best_moments[0][0] - 1) % self.n_x[1]
for moment in self.best_moments:
watch_time += moment[1] - moment[0] + 1
for x in range(len(self.best_moments) - 1):
watch_time += (self.best_moments[x + 1][0] - 1 - self.best_moments[x][1]) % self.n_x[1]
self.result = str(watch_time)
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask499ASolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
|
522_B. Photo to Remember_28348
|
One day n friends met at a party, they hadn't seen each other for a long time and so they decided to make a group photo together.
Simply speaking, the process of taking photos can be described as follows. On the photo, each photographed friend occupies a rectangle of pixels: the i-th of them occupies the rectangle of width wi pixels and height hi pixels. On the group photo everybody stands in a line, thus the minimum pixel size of the photo including all the photographed friends, is W × H, where W is the total sum of all widths and H is the maximum height of all the photographed friends.
As is usually the case, the friends made n photos — the j-th (1 ≤ j ≤ n) photo had everybody except for the j-th friend as he was the photographer.
Print the minimum size of each made photo in pixels.
Input
The first line contains integer n (2 ≤ n ≤ 200 000) — the number of friends.
Then n lines follow: the i-th line contains information about the i-th friend. The line contains a pair of integers wi, hi (1 ≤ wi ≤ 10, 1 ≤ hi ≤ 1000) — the width and height in pixels of the corresponding rectangle.
Output
Print n space-separated numbers b1, b2, ..., bn, where bi — the total number of pixels on the minimum photo containing all friends expect for the i-th one.
Examples
Input
3
1 10
5 5
10 1
Output
75 110 60
Input
3
2 1
1 2
2 1
Output
6 4 6
|
h,w=[],[]
n=int(input())
for i in range(n):
a,b=map(int,input().split())
w.append(a)
h.append(b)
maxh=max(h)
maxh2=-1
if h.count(maxh)>1: maxh2=maxh
else:
for i in h:
if i<maxh:
maxh2=max(maxh2,i)
sumw=sum(w)
for i in range(n):
W=sumw-w[i]
if h[i]==maxh: H=maxh2
else: H=maxh
print(W*H)
|
{
"input": [
"3\n1 10\n5 5\n10 1\n",
"3\n2 1\n1 2\n2 1\n",
"10\n6 386\n9 816\n9 268\n9 481\n8 284\n10 715\n9 351\n7 580\n4 327\n7 392\n",
"10\n9 292\n4 6\n6 638\n8 461\n10 970\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n1 12\n1 13\n",
"10\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n",
"3\n1 11\n1 12\n2 10\n",
"3\n1 1\n3 2\n2 3\n",
"2\n1 1\n1 2\n",
"3\n2 22\n1 11\n2 22\n",
"3\n1 10\n2 10\n3 10\n",
"2\n2 3\n1 1\n",
"10\n6 20\n1 175\n1 758\n1 169\n2 490\n2 600\n4 463\n7 377\n9 40\n4 961\n",
"10\n7 549\n9 115\n8 141\n3 650\n5 730\n3 841\n7 18\n9 170\n2 217\n1 155\n",
"3\n2 10\n1 9\n3 7\n",
"2\n1 5\n2 3\n",
"3\n3 123\n1 456\n2 789\n",
"3\n2 987\n3 654\n1 321\n",
"3\n3 143\n2 543\n1 893\n",
"10\n8 158\n1 709\n6 766\n4 335\n5 356\n2 972\n1 108\n4 235\n3 631\n1 414\n",
"10\n6 386\n9 816\n9 268\n9 481\n16 284\n10 715\n9 351\n7 580\n4 327\n7 392\n",
"10\n9 503\n4 6\n6 638\n8 461\n10 970\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n1 12\n2 13\n",
"10\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n8 1000\n10 1000\n10 1000\n10 1000\n",
"3\n1 1\n3 0\n2 3\n",
"3\n2 22\n1 11\n2 20\n",
"2\n2 6\n1 1\n",
"10\n6 20\n1 175\n1 758\n0 169\n2 490\n2 600\n4 463\n7 377\n9 40\n4 961\n",
"10\n12 549\n9 115\n8 141\n3 650\n5 730\n3 841\n7 18\n9 170\n2 217\n1 155\n",
"3\n2 10\n1 9\n3 13\n",
"2\n2 5\n2 3\n",
"3\n3 123\n1 456\n4 789\n",
"3\n2 987\n4 654\n1 321\n",
"3\n3 143\n2 718\n1 893\n",
"10\n12 158\n1 709\n6 766\n4 335\n5 356\n2 972\n1 108\n4 235\n3 631\n1 414\n",
"3\n1 10\n5 5\n2 1\n",
"3\n2 1\n1 2\n2 0\n",
"10\n9 503\n4 6\n6 923\n8 461\n10 970\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n1 9\n2 13\n",
"3\n1 2\n1 12\n2 26\n",
"3\n0 1\n3 0\n2 3\n",
"3\n2 17\n1 11\n2 20\n",
"2\n2 6\n0 1\n",
"3\n2 10\n1 13\n3 13\n",
"2\n2 10\n2 3\n",
"3\n6 123\n1 456\n4 789\n",
"3\n3 143\n2 718\n0 893\n",
"10\n12 158\n1 709\n6 766\n4 335\n5 356\n2 300\n1 108\n4 235\n3 631\n1 414\n",
"3\n1 10\n5 7\n2 1\n",
"10\n6 386\n9 816\n3 268\n9 481\n16 284\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"10\n9 503\n4 6\n6 923\n8 461\n10 121\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n1 9\n2 17\n",
"10\n10 0000\n10 1000\n10 1000\n10 1000\n11 1000\n10 1000\n8 1000\n10 1000\n10 1000\n10 1000\n",
"3\n1 2\n1 7\n2 26\n",
"2\n2 1\n0 1\n",
"10\n6 20\n1 175\n1 758\n0 169\n3 396\n2 600\n4 463\n7 377\n9 40\n4 961\n",
"10\n12 549\n2 115\n8 114\n3 650\n5 730\n3 841\n7 18\n9 170\n2 217\n1 155\n",
"3\n2 10\n1 13\n3 24\n",
"2\n2 10\n0 3\n",
"3\n11 123\n1 456\n4 789\n",
"3\n3 143\n2 718\n0 684\n",
"10\n12 158\n1 709\n11 766\n4 335\n5 356\n2 300\n1 108\n4 235\n3 631\n1 414\n",
"3\n1 10\n5 4\n2 1\n",
"10\n9 503\n4 6\n6 923\n8 461\n7 121\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n1 9\n2 12\n",
"10\n10 0000\n16 1000\n10 1000\n10 1000\n11 1000\n10 1000\n8 1000\n10 1000\n10 1000\n10 1000\n",
"3\n1 2\n1 7\n3 26\n",
"2\n1 1\n0 1\n",
"10\n6 20\n1 175\n1 758\n0 169\n3 396\n2 600\n4 463\n7 377\n9 40\n6 961\n",
"3\n4 10\n1 13\n3 24\n",
"2\n2 13\n0 3\n",
"3\n11 123\n1 456\n4 308\n",
"10\n12 158\n1 709\n11 766\n4 335\n8 356\n2 300\n1 108\n4 235\n3 631\n1 414\n",
"3\n0 10\n5 4\n2 1\n",
"10\n9 503\n4 6\n6 923\n12 461\n7 121\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n2 9\n2 12\n",
"3\n0 2\n1 7\n3 26\n",
"3\n2 17\n1 16\n2 39\n",
"10\n2 20\n1 175\n1 758\n0 169\n3 396\n2 600\n4 463\n7 377\n9 40\n6 961\n",
"2\n2 9\n0 3\n",
"3\n11 123\n2 456\n4 308\n",
"3\n6 64\n2 718\n0 684\n",
"10\n12 158\n1 709\n11 766\n4 335\n8 356\n2 300\n2 108\n4 235\n3 631\n1 414\n",
"3\n0 7\n5 4\n2 1\n",
"10\n6 386\n9 816\n3 57\n9 481\n26 359\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"10\n9 503\n4 6\n9 923\n12 461\n7 121\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 11\n2 9\n2 2\n",
"3\n0 2\n1 1\n3 26\n",
"3\n2 17\n1 30\n2 39\n",
"10\n12 549\n2 115\n8 114\n3 195\n5 730\n0 841\n7 18\n9 13\n2 217\n1 155\n",
"3\n11 123\n2 738\n4 308\n",
"3\n6 64\n2 718\n0 369\n",
"3\n0 7\n5 1\n2 1\n",
"10\n6 386\n9 816\n3 57\n17 481\n26 359\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"10\n9 503\n4 6\n9 923\n19 461\n7 121\n10 488\n9 769\n10 644\n8 280\n5 334\n",
"3\n1 2\n1 12\n2 13\n",
"10\n6 386\n9 816\n9 268\n9 481\n16 284\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"10\n10 0000\n10 1000\n10 1000\n10 1000\n10 1000\n10 1000\n8 1000\n10 1000\n10 1000\n10 1000\n",
"10\n6 20\n1 175\n1 758\n0 169\n2 396\n2 600\n4 463\n7 377\n9 40\n4 961\n",
"10\n12 549\n9 115\n8 114\n3 650\n5 730\n3 841\n7 18\n9 170\n2 217\n1 155\n",
"3\n2 17\n1 15\n2 20\n",
"10\n6 386\n9 816\n3 57\n9 481\n16 284\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"3\n2 17\n1 16\n2 20\n",
"10\n12 549\n2 115\n8 114\n3 650\n5 730\n3 841\n7 18\n9 13\n2 217\n1 155\n",
"3\n3 64\n2 718\n0 684\n",
"10\n6 386\n9 816\n3 57\n9 481\n16 359\n10 715\n9 351\n7 580\n4 327\n7 229\n",
"2\n1 2\n0 1\n",
"10\n12 549\n2 115\n8 114\n3 195\n5 730\n3 841\n7 18\n9 13\n2 217\n1 155\n",
"10\n2 20\n1 175\n1 758\n0 169\n3 396\n2 600\n4 336\n7 377\n9 40\n6 961\n",
"2\n2 9\n0 4\n"
],
"output": [
"75 110 60 ",
"6 4 6 ",
"58752 49335 56304 56304 57120 55488 56304 57936 60384 57936 ",
"67900 72750 70810 68870 53061 66930 67900 66930 68870 71780 ",
"26 26 24 ",
"90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 ",
"36 33 24 ",
"15 9 8 ",
"2 1 ",
"66 88 66 ",
"50 40 30 ",
"1 6 ",
"29791 34596 34596 34596 33635 33635 31713 28830 26908 25014 ",
"39527 37845 38686 42891 41209 37230 39527 37845 43732 44573 ",
"36 50 30 ",
"6 5 ",
"2367 3945 1824 ",
"2616 2961 4935 ",
"2679 3572 2715 ",
"26244 33048 28188 30132 29160 25278 33048 30132 31104 33048 ",
"65280 55055 62832 62832 57120 62016 62832 64464 66912 64464\n",
"67900 72750 70810 68870 53061 66930 67900 66930 68870 71780\n",
"39 39 24\n",
"88000 88000 88000 88000 88000 88000 90000 88000 88000 88000\n",
"15 9 4\n",
"60 88 66\n",
"1 12\n",
"28830 33635 33635 34596 32674 32674 30752 27869 25947 24256\n",
"39527 42050 42891 47096 45414 40880 43732 42050 47937 48778\n",
"52 65 30\n",
"6 10\n",
"3945 5523 1824\n",
"3270 2961 5922\n",
"2679 3572 3590\n",
"26244 36936 32076 34020 33048 28342 36936 34020 34992 36936\n",
"35 30 60\n",
"6 4 6\n",
"67900 72750 70810 68870 63687 66930 67900 66930 68870 71780\n",
"39 39 22\n",
"78 78 24\n",
"15 6 3\n",
"60 80 51\n",
"0 12\n",
"52 65 39\n",
"6 20\n",
"3945 7890 3192\n",
"1786 2679 3590\n",
"20682 29108 23397 26810 26044 28342 29108 26810 27576 29108\n",
"49 30 60\n",
"60384 50765 62832 57936 52224 57120 57936 59568 62016 59568\n",
"64610 69225 56137 65533 63687 63687 64610 63687 65533 68302\n",
"51 51 22\n",
"89000 89000 89000 89000 88000 89000 91000 89000 89000 89000\n",
"78 78 14\n",
"0 2\n",
"29791 34596 34596 35557 32674 33635 31713 28830 26908 25014\n",
"33640 42050 37004 41209 39527 35770 37845 36163 42050 42891\n",
"96 120 39\n",
"0 20\n",
"3945 11835 5472\n",
"1436 2052 3590\n",
"24512 32938 23397 30640 29874 32172 32938 30640 31406 32938\n",
"28 30 60\n",
"61841 66456 53830 62764 63687 60918 61841 60918 62764 65533\n",
"36 36 22\n",
"95000 89000 95000 95000 94000 95000 97000 95000 95000 95000\n",
"104 104 14\n",
"0 1\n",
"31713 36518 36518 37479 34596 35557 33635 30752 28830 25014\n",
"96 168 65\n",
"0 26\n",
"2280 4620 5472\n",
"26810 35236 25524 32938 29874 34470 35236 32938 33704 35236\n",
"28 20 50\n",
"65533 70148 56906 62764 67379 64610 65533 64610 66456 69225\n",
"48 36 33\n",
"104 78 7\n",
"117 156 51\n",
"31713 32674 32674 33635 30752 31713 29791 26908 24986 21982\n",
"0 18\n",
"2736 4620 5928\n",
"1436 4104 5744\n",
"27576 36002 26233 33704 30640 35236 35236 33704 34470 36002\n",
"28 14 35\n",
"68544 57915 70992 66096 52224 65280 66096 67728 70176 67728\n",
"68302 72917 56906 65533 70148 67379 68302 67379 69225 71994\n",
"36 33 33\n",
"104 78 2\n",
"117 156 90\n",
"31117 39527 34481 38686 37004 35770 35322 33640 39527 40368\n",
"4428 4620 9594\n",
"1436 2214 5744\n",
"7 14 35\n",
"75072 63635 77520 66096 58752 71808 72624 74256 76704 74256\n",
"74763 79378 62289 65533 76609 73840 74763 73840 75686 78455\n",
"39 39 24\n",
"65280 55055 62832 62832 57120 62016 62832 64464 66912 64464\n",
"88000 88000 88000 88000 88000 88000 90000 88000 88000 88000\n",
"28830 33635 33635 34596 32674 32674 30752 27869 25947 24256\n",
"39527 42050 42891 47096 45414 40880 43732 42050 47937 48778\n",
"60 80 51\n",
"60384 50765 62832 57936 52224 57120 57936 59568 62016 59568\n",
"60 80 51\n",
"33640 42050 37004 41209 39527 35770 37845 36163 42050 42891\n",
"1436 2052 3590\n",
"60384 50765 62832 57936 52224 57120 57936 59568 62016 59568\n",
"0 2\n",
"33640 42050 37004 41209 39527 35770 37845 36163 42050 42891\n",
"31713 32674 32674 33635 30752 31713 29791 26908 24986 21982\n",
"0 18\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One day n friends met at a party, they hadn't seen each other for a long time and so they decided to make a group photo together.
Simply speaking, the process of taking photos can be described as follows. On the photo, each photographed friend occupies a rectangle of pixels: the i-th of them occupies the rectangle of width wi pixels and height hi pixels. On the group photo everybody stands in a line, thus the minimum pixel size of the photo including all the photographed friends, is W × H, where W is the total sum of all widths and H is the maximum height of all the photographed friends.
As is usually the case, the friends made n photos — the j-th (1 ≤ j ≤ n) photo had everybody except for the j-th friend as he was the photographer.
Print the minimum size of each made photo in pixels.
Input
The first line contains integer n (2 ≤ n ≤ 200 000) — the number of friends.
Then n lines follow: the i-th line contains information about the i-th friend. The line contains a pair of integers wi, hi (1 ≤ wi ≤ 10, 1 ≤ hi ≤ 1000) — the width and height in pixels of the corresponding rectangle.
Output
Print n space-separated numbers b1, b2, ..., bn, where bi — the total number of pixels on the minimum photo containing all friends expect for the i-th one.
Examples
Input
3
1 10
5 5
10 1
Output
75 110 60
Input
3
2 1
1 2
2 1
Output
6 4 6
### Input:
3
1 10
5 5
10 1
### Output:
75 110 60
### Input:
3
2 1
1 2
2 1
### Output:
6 4 6
### Code:
h,w=[],[]
n=int(input())
for i in range(n):
a,b=map(int,input().split())
w.append(a)
h.append(b)
maxh=max(h)
maxh2=-1
if h.count(maxh)>1: maxh2=maxh
else:
for i in h:
if i<maxh:
maxh2=max(maxh2,i)
sumw=sum(w)
for i in range(n):
W=sumw-w[i]
if h[i]==maxh: H=maxh2
else: H=maxh
print(W*H)
|
549_D. Haar Features_28352
|
The first algorithm for detecting a face on the image working in realtime was developed by Paul Viola and Michael Jones in 2001. A part of the algorithm is a procedure that computes Haar features. As part of this task, we consider a simplified model of this concept.
Let's consider a rectangular image that is represented with a table of size n × m. The table elements are integers that specify the brightness of each pixel in the image.
A feature also is a rectangular table of size n × m. Each cell of a feature is painted black or white.
To calculate the value of the given feature at the given image, you must perform the following steps. First the table of the feature is put over the table of the image (without rotations or reflections), thus each pixel is entirely covered with either black or white cell. The value of a feature in the image is the value of W - B, where W is the total brightness of the pixels in the image, covered with white feature cells, and B is the total brightness of the pixels covered with black feature cells.
Some examples of the most popular Haar features are given below.
<image>
Your task is to determine the number of operations that are required to calculate the feature by using the so-called prefix rectangles.
A prefix rectangle is any rectangle on the image, the upper left corner of which coincides with the upper left corner of the image.
You have a variable value, whose value is initially zero. In one operation you can count the sum of pixel values at any prefix rectangle, multiply it by any integer and add to variable value.
You are given a feature. It is necessary to calculate the minimum number of operations required to calculate the values of this attribute at an arbitrary image. For a better understanding of the statement, read the explanation of the first sample.
Input
The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 100) — the number of rows and columns in the feature.
Next n lines contain the description of the feature. Each line consists of m characters, the j-th character of the i-th line equals to "W", if this element of the feature is white and "B" if it is black.
Output
Print a single number — the minimum number of operations that you need to make to calculate the value of the feature.
Examples
Input
6 8
BBBBBBBB
BBBBBBBB
BBBBBBBB
WWWWWWWW
WWWWWWWW
WWWWWWWW
Output
2
Input
3 3
WBW
BWW
WWW
Output
4
Input
3 6
WWBBWW
WWBBWW
WWBBWW
Output
3
Input
4 4
BBBB
BBBB
BBBB
BBBW
Output
4
Note
The first sample corresponds to feature B, the one shown in the picture. The value of this feature in an image of size 6 × 8 equals to the difference of the total brightness of the pixels in the lower and upper half of the image. To calculate its value, perform the following two operations:
1. add the sum of pixels in the prefix rectangle with the lower right corner in the 6-th row and 8-th column with coefficient 1 to the variable value (the rectangle is indicated by a red frame); <image>
2. add the number of pixels in the prefix rectangle with the lower right corner in the 3-rd row and 8-th column with coefficient - 2 and variable value. <image>
Thus, all the pixels in the lower three rows of the image will be included with factor 1, and all pixels in the upper three rows of the image will be included with factor 1 - 2 = - 1, as required.
|
n,m=map(int,input().strip().split())
s=[]
for i in range(n):
s.append(input())
f=[[0 for i in range(m+1)] for j in range(n+1)]
ans=0
for k in range(n+m,1,-1):
for i in range(n,0,-1):
j=k-i
if (j>m or j<1):
continue
#print(str(i)+" "+str(j)+s[i-1][j-1])
tmp=0
if (s[i-1][j-1]=='W'):
tmp=1-f[i][j]
else:
tmp=-1-f[i][j]
if (tmp!=0):
ans=ans+1
for x in range(1,i+1):
for y in range(1,j+1):
f[x][y]=f[x][y]+tmp
print(ans)
|
{
"input": [
"3 3\nWBW\nBWW\nWWW\n",
"3 6\nWWBBWW\nWWBBWW\nWWBBWW\n",
"6 8\nBBBBBBBB\nBBBBBBBB\nBBBBBBBB\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\n",
"4 4\nBBBB\nBBBB\nBBBB\nBBBW\n",
"1 52\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"2 10\nBBWBWWBWBB\nBBBBBBBBBW\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nWBWWB\n",
"2 8\nBBBBBBBB\nBBBBBBBB\n",
"1 100\nWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"2 9\nWBBBWBBBW\nBWWBBBBBB\n",
"1 1\nB\n",
"1 8\nWWBWWWWW\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWBWWWBWWW\nWBBWBWBWW\nBBWWBWWBB\nBBWWBWWBW\n",
"100 1\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\n",
"11 8\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWBWWWW\nWWWWWWWW\nWBWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\n",
"1 1\nW\n",
"6 6\nBBWWWB\nWBBBWB\nBBBBBW\nWWWWWW\nBBBBBW\nBWWBBB\n",
"4 1\nW\nW\nB\nB\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nBWWBW\n",
"6 6\nBWWWBB\nWBBBWB\nBBBBBW\nWWWWWW\nBBBBBW\nBWWBBB\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWBWWWBWWW\nWWBWBWBBW\nBBWWBWWBB\nBBWWBWWBW\n",
"3 3\nWWB\nBWW\nWWW\n",
"4 5\nBBWWB\nBWBBW\nWBWWW\nWBWWB\n",
"1 100\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW\n",
"1 100\nBBBBBBBBBBBBBBBBBBBBBBBBBWBBBBBBBBBBBBBBBBBBBBBBBBWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBWW\n",
"4 5\nBBWWB\nBWBBW\nWWWBW\nBWWBW\n",
"1 8\nWWWWWBWW\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nBBWWBWWBW\n",
"4 5\nBBWWB\nWBBBW\nWBWWW\nBWWBW\n",
"10 9\nBWWWBWWBB\nBBBWBWBWW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWBWWWBWWW\nWBBWBWBWW\nBBWWBWWBB\nBBWWBWWBW\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWWWBBBW\nBWWBWWBBW\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nBBWWBWWBW\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWWWBBBW\nBWWBWWBBW\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nWBWWBWWBB\n",
"4 5\nBWWBB\nBWWBB\nWBWWW\nWBWWB\n",
"4 5\nBWWBB\nBWBWB\nWBWWW\nWWBWB\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBBBWBBBBW\nBBWWWBBBW\nBWWBWWBBW\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nWBWWBWWBB\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBBBWBBBBW\nBBWWWBBBW\nBBWWWWBBW\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nWBWWBWWBB\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWBWWWBWWW\nWBBWBWBWW\nBBWWBWWBB\nWBWWBBWBW\n",
"4 5\nBBWWB\nBWBBW\nWBWWW\nBWWBW\n",
"4 5\nBBWWB\nBWBBW\nWWWBW\nWBWWB\n",
"4 2\nBWWBB\nBWBBW\nWBWWW\nBWWBW\n",
"4 5\nBBWWB\nBWBBW\nWBWWW\nWBWBW\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWWWBWBWWW\nWBBWBWBWW\nBBWWBWWBB\nBBWWBWWBW\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nWWBWB\n",
"4 4\nBBBB\nBBBB\nBBBB\nWBBB\n",
"4 5\nBBWWB\nWBBWB\nWBWWW\nWBWWB\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nWBWBW\n",
"4 5\nBWWBB\nWBBWB\nWBWWW\nWWBWB\n",
"6 6\nBBWWWB\nBWBBBW\nBBBBBW\nWWWWWW\nBBBBBW\nBWWBBB\n",
"3 3\nWBW\nWWB\nWWW\n",
"4 5\nBBWWB\nWBWBB\nWBWWW\nBWWBW\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nBWBWW\n",
"6 6\nBBWWWB\nBWBBBW\nBBBBBW\nWWWWWW\nWBBBBB\nBWWBBB\n",
"4 5\nBBWWB\nWWBBB\nWBWWW\nBWWBW\n",
"6 6\nBWWWBB\nBWBBBW\nBBBBBW\nWWWWWW\nWBBBBB\nBWWBBB\n",
"3 3\nBWW\nBWW\nWWW\n",
"1 100\nWWBWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBBBBBBBBBBBBBBBBBBBBBBBBWBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"4 5\nBWWBB\nWBBWB\nWBWWW\nWBWWB\n",
"10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWWWBBBW\nWBBWWBWWB\nWWWBWBWWW\nWWBWBWBBW\nBBWWBWWBB\nBBWWBWWBW\n",
"4 5\nBWWBB\nBBBWW\nWBWWW\nWBWBW\n",
"4 5\nBBWWB\nBWWBB\nWBWWW\nBWWBW\n",
"1 100\nWWBWWWWWWWWWWWWBWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBBBBBBWBBBBBBBBBBBBBBBBBWBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"4 5\nBWWBB\nBBBWW\nWWWBW\nWBWBW\n",
"4 5\nBWWBB\nBWBBW\nWWWBW\nWBWWB\n",
"4 5\nBWWBB\nBWBBW\nWBWWW\nWWBBW\n",
"4 5\nBWWBB\nWWBBB\nWBWWW\nBWWBW\n"
],
"output": [
"4\n",
"3\n",
"2\n",
"4\n",
"1\n",
"10\n",
"13\n",
"1\n",
"2\n",
"9\n",
"1\n",
"3\n",
"61\n",
"2\n",
"9\n",
"1\n",
"16\n",
"2\n",
"15\n",
"16\n",
"62\n",
"5\n",
"13\n",
"2\n",
"6\n",
"12\n",
"3\n",
"58\n",
"14\n",
"60\n",
"57\n",
"56\n",
"10\n",
"17\n",
"54\n",
"52\n",
"65\n",
"15\n",
"16\n",
"6\n",
"14\n",
"58\n",
"16\n",
"3\n",
"13\n",
"14\n",
"16\n",
"15\n",
"6\n",
"13\n",
"14\n",
"14\n",
"13\n",
"14\n",
"2\n",
"6\n",
"13\n",
"58\n",
"13\n",
"16\n",
"10\n",
"12\n",
"16\n",
"13\n",
"14\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The first algorithm for detecting a face on the image working in realtime was developed by Paul Viola and Michael Jones in 2001. A part of the algorithm is a procedure that computes Haar features. As part of this task, we consider a simplified model of this concept.
Let's consider a rectangular image that is represented with a table of size n × m. The table elements are integers that specify the brightness of each pixel in the image.
A feature also is a rectangular table of size n × m. Each cell of a feature is painted black or white.
To calculate the value of the given feature at the given image, you must perform the following steps. First the table of the feature is put over the table of the image (without rotations or reflections), thus each pixel is entirely covered with either black or white cell. The value of a feature in the image is the value of W - B, where W is the total brightness of the pixels in the image, covered with white feature cells, and B is the total brightness of the pixels covered with black feature cells.
Some examples of the most popular Haar features are given below.
<image>
Your task is to determine the number of operations that are required to calculate the feature by using the so-called prefix rectangles.
A prefix rectangle is any rectangle on the image, the upper left corner of which coincides with the upper left corner of the image.
You have a variable value, whose value is initially zero. In one operation you can count the sum of pixel values at any prefix rectangle, multiply it by any integer and add to variable value.
You are given a feature. It is necessary to calculate the minimum number of operations required to calculate the values of this attribute at an arbitrary image. For a better understanding of the statement, read the explanation of the first sample.
Input
The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 100) — the number of rows and columns in the feature.
Next n lines contain the description of the feature. Each line consists of m characters, the j-th character of the i-th line equals to "W", if this element of the feature is white and "B" if it is black.
Output
Print a single number — the minimum number of operations that you need to make to calculate the value of the feature.
Examples
Input
6 8
BBBBBBBB
BBBBBBBB
BBBBBBBB
WWWWWWWW
WWWWWWWW
WWWWWWWW
Output
2
Input
3 3
WBW
BWW
WWW
Output
4
Input
3 6
WWBBWW
WWBBWW
WWBBWW
Output
3
Input
4 4
BBBB
BBBB
BBBB
BBBW
Output
4
Note
The first sample corresponds to feature B, the one shown in the picture. The value of this feature in an image of size 6 × 8 equals to the difference of the total brightness of the pixels in the lower and upper half of the image. To calculate its value, perform the following two operations:
1. add the sum of pixels in the prefix rectangle with the lower right corner in the 6-th row and 8-th column with coefficient 1 to the variable value (the rectangle is indicated by a red frame); <image>
2. add the number of pixels in the prefix rectangle with the lower right corner in the 3-rd row and 8-th column with coefficient - 2 and variable value. <image>
Thus, all the pixels in the lower three rows of the image will be included with factor 1, and all pixels in the upper three rows of the image will be included with factor 1 - 2 = - 1, as required.
### Input:
3 3
WBW
BWW
WWW
### Output:
4
### Input:
3 6
WWBBWW
WWBBWW
WWBBWW
### Output:
3
### Code:
n,m=map(int,input().strip().split())
s=[]
for i in range(n):
s.append(input())
f=[[0 for i in range(m+1)] for j in range(n+1)]
ans=0
for k in range(n+m,1,-1):
for i in range(n,0,-1):
j=k-i
if (j>m or j<1):
continue
#print(str(i)+" "+str(j)+s[i-1][j-1])
tmp=0
if (s[i-1][j-1]=='W'):
tmp=1-f[i][j]
else:
tmp=-1-f[i][j]
if (tmp!=0):
ans=ans+1
for x in range(1,i+1):
for y in range(1,j+1):
f[x][y]=f[x][y]+tmp
print(ans)
|
598_A. Tricky Sum_28359
|
In this problem you are to calculate the sum of all integers from 1 to n, but you should take all powers of two with minus in the sum.
For example, for n = 4 the sum is equal to - 1 - 2 + 3 - 4 = - 4, because 1, 2 and 4 are 20, 21 and 22 respectively.
Calculate the answer for t values of n.
Input
The first line of the input contains a single integer t (1 ≤ t ≤ 100) — the number of values of n to be processed.
Each of next t lines contains a single integer n (1 ≤ n ≤ 109).
Output
Print the requested sum for each of t integers n given in the input.
Examples
Input
2
4
1000000000
Output
-4
499999998352516354
Note
The answer for the first sample is explained in the statement.
|
t = int(input())
while(t):
n = int(input())
s = n*(n+1) // 2
k = len(format(n, "b"))
s_pair = 2**k - 1
print(s - 2*s_pair)
t-=1
|
{
"input": [
"2\n4\n1000000000\n",
"1\n414232\n",
"10\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n32\n32\n91\n42\n73\n",
"1\n121\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n540\n986\n950\n729\n104\n244\n500\n461\n251\n685\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n410\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n400\n788\n985\n792\n103\n248\n570\n839\n253\n417\n",
"60\n536870912\n536870911\n536870913\n1000000000\n999999999\n1\n2\n3\n4\n268435456\n268435455\n268435457\n536870912\n536870911\n536870913\n1000000000\n999999999\n1\n2\n3\n4\n268435456\n268435455\n268435457\n536870912\n536870911\n536870913\n1000000000\n999999999\n1\n2\n3\n4\n268435456\n268435455\n268435457\n536870912\n536870911\n536870913\n1000000000\n999999999\n1\n2\n3\n4\n268435456\n268435455\n268435457\n536870912\n536870911\n536870913\n1000000000\n999999999\n1\n2\n3\n4\n268435456\n268435455\n268435457\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n",
"1\n414234\n",
"1\n16\n",
"1\n16383\n",
"3\n414231\n414231\n414231\n",
"10\n10\n9\n47\n33\n99\n83\n62\n1\n100\n53\n",
"1\n118556\n",
"10\n1\n2\n5\n4\n5\n6\n7\n8\n9\n10\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n32\n32\n91\n42\n125\n",
"1\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n540\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n410\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n400\n788\n985\n792\n103\n248\n570\n839\n253\n417\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100000\n100100\n100100\n100100\n100100\n",
"1\n530142\n",
"1\n4\n",
"1\n3397\n",
"3\n414231\n147046\n414231\n",
"10\n10\n9\n47\n33\n99\n24\n62\n1\n100\n53\n",
"2\n4\n1000001000\n",
"1\n130345\n",
"10\n1\n2\n5\n4\n5\n6\n7\n11\n9\n10\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n32\n32\n91\n42\n90\n",
"1\n14\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n127\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n410\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n400\n788\n985\n792\n103\n248\n570\n839\n253\n417\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n100110\n100100\n100100\n100100\n100000\n100100\n100100\n100100\n100100\n",
"1\n91814\n",
"1\n8\n",
"1\n3682\n",
"3\n145175\n147046\n414231\n",
"10\n10\n9\n47\n33\n99\n24\n62\n1\n101\n53\n",
"2\n7\n1000001000\n",
"1\n186113\n",
"10\n1\n2\n5\n4\n5\n6\n7\n11\n10\n10\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n13\n32\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n127\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n410\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n417\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n110110\n100100\n100100\n100100\n100000\n100100\n100100\n100100\n100100\n",
"1\n17722\n",
"1\n2\n",
"1\n502\n",
"3\n145175\n147046\n253907\n",
"10\n10\n7\n47\n33\n99\n24\n62\n1\n101\n53\n",
"2\n7\n1000001010\n",
"1\n280102\n",
"10\n1\n2\n8\n4\n5\n6\n7\n11\n10\n10\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n13\n55\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n127\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n417\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n110110\n000100\n100100\n100100\n100000\n100100\n100100\n100100\n100100\n",
"1\n11164\n",
"1\n3\n",
"1\n203\n",
"3\n145175\n276029\n253907\n",
"10\n10\n7\n47\n33\n99\n24\n62\n1\n001\n53\n",
"2\n7\n1010001010\n",
"1\n74154\n",
"13\n1\n19\n31\n19\n19\n92\n74\n69\n13\n85\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n591\n984\n1\n61\n127\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n698\n",
"16\n100100\n100100\n100100\n100100\n100100\n100100\n100100\n110110\n000100\n100100\n100100\n100001\n100100\n100100\n100100\n100100\n",
"1\n5948\n",
"1\n6\n",
"1\n84\n",
"3\n31825\n276029\n253907\n",
"10\n10\n7\n47\n33\n99\n17\n62\n1\n001\n53\n",
"2\n7\n1011001010\n",
"1\n29756\n",
"13\n1\n19\n31\n19\n7\n92\n74\n69\n13\n85\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n714\n984\n1\n61\n127\n986\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n698\n",
"16\n100100\n100100\n100100\n100100\n100100\n100000\n100100\n110110\n000100\n100100\n100100\n100001\n100100\n100100\n100100\n100100\n",
"1\n8067\n",
"1\n104\n",
"3\n31825\n212935\n253907\n",
"10\n10\n7\n47\n33\n99\n17\n62\n1\n001\n13\n",
"2\n4\n1011001010\n",
"1\n9111\n",
"13\n1\n19\n51\n19\n7\n92\n74\n69\n13\n85\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n714\n984\n1\n61\n127\n74\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n96\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n698\n",
"16\n100100\n100100\n100100\n100100\n100100\n100000\n100100\n110110\n001100\n100100\n100100\n100001\n100100\n100100\n100100\n100100\n",
"1\n4158\n",
"1\n5\n",
"3\n31825\n212935\n465506\n",
"10\n10\n7\n47\n33\n102\n17\n62\n1\n001\n13\n",
"1\n15862\n",
"13\n1\n19\n51\n18\n7\n92\n74\n69\n13\n85\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n714\n984\n1\n61\n127\n74\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n166\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n65\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n698\n",
"16\n100100\n100100\n100100\n100100\n100100\n100000\n100100\n110110\n000100\n100100\n100100\n100101\n100100\n100100\n100100\n100100\n",
"1\n3704\n",
"1\n7\n",
"3\n31825\n212935\n662702\n",
"10\n10\n10\n47\n33\n102\n17\n62\n1\n001\n13\n",
"1\n28756\n",
"13\n1\n19\n1\n18\n7\n92\n74\n69\n13\n85\n91\n42\n90\n",
"100\n901\n712\n3\n677\n652\n757\n963\n134\n205\n888\n847\n283\n714\n984\n1\n61\n127\n74\n950\n729\n104\n244\n500\n461\n251\n228\n631\n803\n526\n600\n1000\n899\n411\n219\n597\n342\n771\n348\n507\n775\n454\n102\n486\n333\n580\n431\n537\n355\n624\n23\n429\n276\n84\n704\n166\n536\n855\n653\n72\n718\n776\n658\n802\n777\n995\n285\n328\n405\n184\n555\n956\n165\n846\n853\n525\n983\n40\n549\n839\n929\n620\n725\n635\n303\n201\n878\n580\n139\n182\n69\n771\n788\n985\n792\n103\n248\n570\n839\n253\n698\n",
"16\n100100\n100100\n100100\n100100\n100100\n100000\n100100\n010110\n000100\n100100\n100100\n100101\n100100\n100100\n100100\n100100\n",
"1\n4215\n",
"3\n31825\n212935\n667658\n",
"10\n10\n10\n47\n33\n102\n17\n62\n1\n101\n13\n"
],
"output": [
"-4\n499999998352516354\n",
"85793233454\n",
"-1\n-3\n0\n-4\n1\n7\n14\n6\n15\n25\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n402\n402\n3932\n777\n2447\n",
"7127\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n144024\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n232909\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n83233\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n79178\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n86131\n",
"144115186196807682\n144115186733678594\n144115186733678595\n499999998352516354\n499999997352516354\n-1\n-3\n0\n-4\n36028796079439874\n36028796347875330\n36028796347875331\n144115186196807682\n144115186733678594\n144115186733678595\n499999998352516354\n499999997352516354\n-1\n-3\n0\n-4\n36028796079439874\n36028796347875330\n36028796347875331\n144115186196807682\n144115186733678594\n144115186733678595\n499999998352516354\n499999997352516354\n-1\n-3\n0\n-4\n36028796079439874\n36028796347875330\n36028796347875331\n144115186196807682\n144115186733678594\n144115186733678595\n499999998352516354\n499999997352516354\n-1\n-3\n0\n-4\n36028796079439874\n36028796347875330\n36028796347875331\n144115186196807682\n144115186733678594\n144115186733678595\n499999998352516354\n499999997352516354\n-1\n-3\n0\n-4\n36028796079439874\n36028796347875330\n36028796347875331\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n",
"85794061921\n",
"74\n",
"134176770\n",
"85792819222\n85792819222\n85792819222\n",
"25\n15\n1002\n435\n4696\n3232\n1827\n-1\n4796\n1305\n",
"7027559704\n",
"-1\n-3\n1\n-4\n1\n7\n14\n6\n15\n25\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n402\n402\n3932\n777\n7621\n",
"3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n144024\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n83233\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n79178\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n86131\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n5009792908\n5009792908\n5009792908\n",
"140523438003\n",
"-4\n",
"5763313\n",
"85792819222\n10810812295\n85792819222\n",
"25\n15\n1002\n435\n4696\n238\n1827\n-1\n4796\n1305\n",
"-4\n500000998353016854\n",
"8494712543\n",
"-1\n-3\n1\n-4\n1\n7\n14\n36\n15\n25\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n402\n402\n3932\n777\n3841\n",
"75\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n7874\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n83233\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n79178\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n86131\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5010793963\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n5009792908\n5009792908\n5009792908\n",
"4214689063\n",
"6\n",
"6772213\n",
"10537438614\n10810812295\n85792819222\n",
"25\n15\n1002\n435\n4696\n238\n1827\n-1\n4897\n1305\n",
"14\n500000998353016854\n",
"17318593155\n",
"-1\n-3\n1\n-4\n1\n7\n14\n36\n25\n25\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n61\n402\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n7874\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n83233\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n86131\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n6061898963\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n5009792908\n5009792908\n5009792908\n",
"156977969\n",
"-3\n",
"125231\n",
"10537438614\n10810812295\n32233984992\n",
"25\n14\n1002\n435\n4696\n238\n1827\n-1\n4897\n1305\n",
"14\n500001008353026909\n",
"39227656679\n",
"-1\n-3\n6\n-4\n1\n7\n14\n36\n25\n25\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n61\n1414\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n7874\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n86131\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n6061898963\n4796\n5009792908\n5009792908\n4999787858\n5009792908\n5009792908\n5009792908\n5009792908\n",
"62290264\n",
"0\n",
"20196\n",
"10537438614\n38095093861\n32233984992\n",
"25\n14\n1002\n435\n4696\n238\n1827\n-1\n-1\n1305\n",
"14\n510051018458026909\n",
"2749182793\n",
"-1\n128\n434\n128\n128\n4024\n2521\n2161\n61\n3401\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n172890\n482574\n-1\n1765\n7874\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n241905\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n6061898963\n4796\n5009792908\n5009792908\n4999887859\n5009792908\n5009792908\n5009792908\n5009792908\n",
"17675944\n",
"7\n",
"3316\n",
"506365691\n38095093861\n32233984992\n",
"25\n14\n1002\n435\n4696\n91\n1827\n-1\n-1\n1305\n",
"14\n511061519468526909\n",
"442659112\n",
"-1\n128\n434\n128\n14\n4024\n2521\n2161\n61\n3401\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n253209\n482574\n-1\n1765\n7874\n484545\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n241905\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n6061898963\n4796\n5009792908\n5009792908\n4999887859\n5009792908\n5009792908\n5009792908\n5009792908\n",
"32525896\n",
"5206\n",
"506365691\n22670239294\n32233984992\n",
"25\n14\n1002\n435\n4696\n91\n1827\n-1\n-1\n61\n",
"-4\n511061519468526909\n",
"41476950\n",
"-1\n128\n1200\n128\n14\n4024\n2521\n2161\n61\n3401\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n253209\n482574\n-1\n1765\n7874\n2521\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n4402\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n241905\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n6061898963\n601456\n5009792908\n5009792908\n4999887859\n5009792908\n5009792908\n5009792908\n5009792908\n",
"8630179\n",
"1\n",
"506365691\n22670239294\n108347102197\n",
"25\n14\n1002\n435\n4999\n91\n1827\n-1\n-1\n61\n",
"125776687\n",
"-1\n128\n1200\n109\n14\n4024\n2521\n2161\n61\n3401\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n253209\n482574\n-1\n1765\n7874\n2521\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n13351\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n1891\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n241905\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n6061898963\n4796\n5009792908\n5009792908\n5009893009\n5009792908\n5009792908\n5009792908\n5009792908\n",
"6853470\n",
"14\n",
"506365691\n22670239294\n219585204603\n",
"25\n25\n1002\n435\n4999\n91\n1827\n-1\n-1\n61\n",
"413402612\n",
"-1\n128\n-1\n109\n14\n4024\n2521\n2161\n61\n3401\n3932\n777\n3841\n",
"404305\n251782\n0\n227457\n210832\n284857\n462120\n8535\n20605\n392670\n357082\n39164\n253209\n482574\n-1\n1765\n7874\n2521\n449679\n264039\n5206\n29380\n124228\n105469\n31116\n25596\n197350\n320760\n136555\n178254\n498454\n402504\n83644\n23580\n176457\n57631\n295560\n59704\n127756\n298654\n102263\n4999\n117319\n54589\n166444\n92074\n142407\n62168\n192954\n214\n91213\n37204\n3316\n246114\n13351\n141870\n363894\n211485\n2374\n256075\n299430\n214765\n319957\n300207\n493464\n39733\n52934\n81193\n16510\n152244\n455400\n13185\n356235\n362185\n136029\n481590\n694\n148929\n350334\n429939\n190464\n261129\n199884\n45034\n19791\n383835\n166444\n9220\n16143\n2161\n295560\n308820\n483559\n311982\n5102\n30366\n160689\n350334\n31621\n241905\n",
"5009792908\n5009792908\n5009792908\n5009792908\n5009792908\n4999787858\n5009792908\n51078339\n4796\n5009792908\n5009792908\n5009893009\n5009792908\n5009792908\n5009792908\n5009792908\n",
"8868838\n",
"506365691\n22670239294\n222881839161\n",
"25\n25\n1002\n435\n4999\n91\n1827\n-1\n4897\n61\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In this problem you are to calculate the sum of all integers from 1 to n, but you should take all powers of two with minus in the sum.
For example, for n = 4 the sum is equal to - 1 - 2 + 3 - 4 = - 4, because 1, 2 and 4 are 20, 21 and 22 respectively.
Calculate the answer for t values of n.
Input
The first line of the input contains a single integer t (1 ≤ t ≤ 100) — the number of values of n to be processed.
Each of next t lines contains a single integer n (1 ≤ n ≤ 109).
Output
Print the requested sum for each of t integers n given in the input.
Examples
Input
2
4
1000000000
Output
-4
499999998352516354
Note
The answer for the first sample is explained in the statement.
### Input:
2
4
1000000000
### Output:
-4
499999998352516354
### Input:
1
414232
### Output:
85793233454
### Code:
t = int(input())
while(t):
n = int(input())
s = n*(n+1) // 2
k = len(format(n, "b"))
s_pair = 2**k - 1
print(s - 2*s_pair)
t-=1
|
667_A. Pouring Rain_28367
|
A lot of people in Berland hates rain, but you do not. Rain pacifies, puts your thoughts in order. By these years you have developed a good tradition — when it rains, you go on the street and stay silent for a moment, contemplate all around you, enjoy freshness, think about big deeds you have to do.
Today everything had changed quietly. You went on the street with a cup contained water, your favorite drink. In a moment when you were drinking a water you noticed that the process became quite long: the cup still contained water because of rain. You decided to make a formal model of what was happening and to find if it was possible to drink all water in that situation.
Thus, your cup is a cylinder with diameter equals d centimeters. Initial level of water in cup equals h centimeters from the bottom.
<image>
You drink a water with a speed equals v milliliters per second. But rain goes with such speed that if you do not drink a water from the cup, the level of water increases on e centimeters per second. The process of drinking water from the cup and the addition of rain to the cup goes evenly and continuously.
Find the time needed to make the cup empty or find that it will never happen. It is guaranteed that if it is possible to drink all water, it will happen not later than after 104 seconds.
Note one milliliter equals to one cubic centimeter.
Input
The only line of the input contains four integer numbers d, h, v, e (1 ≤ d, h, v, e ≤ 104), where:
* d — the diameter of your cylindrical cup,
* h — the initial level of water in the cup,
* v — the speed of drinking process from the cup in milliliters per second,
* e — the growth of water because of rain if you do not drink from the cup.
Output
If it is impossible to make the cup empty, print "NO" (without quotes).
Otherwise print "YES" (without quotes) in the first line. In the second line print a real number — time in seconds needed the cup will be empty. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4. It is guaranteed that if the answer exists, it doesn't exceed 104.
Examples
Input
1 2 3 100
Output
NO
Input
1 1 1 1
Output
YES
3.659792366325
Note
In the first example the water fills the cup faster than you can drink from it.
In the second example area of the cup's bottom equals to <image>, thus we can conclude that you decrease the level of water by <image> centimeters per second. At the same time water level increases by 1 centimeter per second due to rain. Thus, cup will be empty in <image> seconds.
|
from math import pi
d,h,v,e=map(int,input().split())
v=v/(pi*((d/2)**2))
d=h/(v-e)
if v-e>0 and d<=10000:
print('YES')
print(d)
else:
print('NO')
|
{
"input": [
"1 1 1 1\n",
"1 2 3 100\n",
"5 2797 5925 9\n",
"6 1976 8455 3\n",
"72 8534 7042 65\n",
"4 495 8813 1\n",
"100 5635 9099 23\n",
"72 6791 8546 46\n",
"72 5272 4552 64\n",
"1 47 80 68\n",
"10000 10000 10000 10000\n",
"48 7946 7992 72\n",
"48 6428 9807 83\n",
"2 5000 12 3\n",
"10 1000 100 1\n",
"20 287 3845 5\n",
"20 2961 9852 15\n",
"3 4183 5491 98\n",
"1 8324 4362 23\n",
"48 1805 3109 93\n",
"100 4117 5106 34\n",
"7 2644 8080 5\n",
"2 8591 320 101\n",
"5 2797 2212 9\n",
"6 1976 8455 4\n",
"59 8534 7042 65\n",
"4 350 8813 1\n",
"20 287 5341 5\n",
"20 5750 9852 15\n",
"3 4191 5491 98\n",
"1 7940 4362 23\n",
"12 2644 8080 5\n",
"2 8591 320 100\n",
"1 1 2 1\n",
"5 4296 2212 9\n",
"6 1976 10963 3\n",
"4 350 6293 1\n",
"20 341 5341 5\n",
"20 5750 12756 15\n",
"3 4191 4126 98\n",
"2 7940 4362 23\n",
"7 2644 8080 7\n",
"2 8591 442 100\n",
"1 1 4 1\n",
"7 4296 2212 9\n",
"1 1976 10963 3\n",
"20 341 8555 5\n",
"20 2910 12756 15\n",
"2 7940 4362 15\n",
"7 3497 8080 7\n",
"7 5765 2212 9\n",
"1 1976 10963 2\n",
"20 341 14187 5\n",
"20 2726 12756 15\n",
"2 15461 4362 15\n",
"7 5413 8080 7\n",
"7 5765 1298 9\n",
"1 1976 13656 2\n",
"100 6283 8504 0\n",
"35 341 14187 5\n",
"20 2726 6670 15\n",
"1 15461 4362 15\n",
"7 5413 8080 14\n",
"7 5765 1298 6\n",
"1 1976 2333 2\n",
"101 6283 8504 0\n",
"2 1010 100 2\n",
"20 1992 6670 15\n",
"100 5635 9099 8\n",
"72 6791 8546 25\n",
"72 5272 5260 64\n",
"10000 10001 10000 10000\n",
"48 7946 4042 72\n",
"48 7692 9807 83\n",
"2 5000 4 3\n",
"10 1000 100 2\n",
"48 3564 3109 93\n",
"101 4117 5106 34\n",
"1 2 4 100\n",
"59 8534 7042 22\n",
"100 5635 8504 8\n",
"72 6791 2515 25\n",
"72 687 5260 64\n",
"48 7946 523 72\n",
"48 13350 9807 83\n",
"13 1000 100 2\n",
"17 3564 3109 93\n",
"111 4117 5106 34\n",
"1 2 1 100\n",
"59 7437 7042 22\n",
"100 6283 8504 8\n",
"97 6791 2515 25\n",
"72 687 5260 118\n",
"48 14589 523 72\n",
"48 13350 9807 93\n",
"13 1000 110 2\n",
"17 3564 307 93\n",
"111 4117 5106 42\n",
"3 8591 442 100\n",
"1 1 0 1\n",
"1 2 2 100\n",
"59 7437 7180 22\n",
"100 6283 8504 4\n",
"146 6791 2515 25\n",
"60 687 5260 118\n",
"48 14589 220 72\n",
"48 13350 9807 97\n",
"13 1010 110 2\n",
"17 3564 307 33\n",
"111 977 5106 42\n",
"3 8591 442 110\n",
"1 2 2 110\n",
"59 7437 7180 11\n",
"146 6791 1239 25\n",
"60 687 5260 149\n",
"48 14589 220 20\n",
"48 13350 9807 10\n",
"13 1010 100 2\n",
"17 5019 307 33\n",
"111 977 1487 42\n",
"5 8591 442 110\n",
"2 2 2 110\n",
"31 7437 7180 11\n"
],
"output": [
"YES\n3.6597923663254868\n",
"NO\n",
"YES\n9.553973511669104\n",
"YES\n6.674898722265244\n",
"NO\n",
"YES\n0.7068235175750123\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1.3881028068103165\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n6099.653943875813\n",
"YES\n3659.7923663254865\n",
"YES\n39.646277165209504\n",
"YES\n180.99143712972335\n",
"YES\n6.162185601824184\n",
"YES\n1.5050071063541184\n",
"NO\n",
"NO\n",
"YES\n12.900417790197096\n",
"YES\n9999.259991757186\n",
"YES\n26.983422677932776\n",
"YES\n6.69752285523526\n",
"NO\n",
"YES\n0.4997742043459682\n",
"YES\n23.914811233892205\n",
"YES\n351.46935612830436\n",
"YES\n6.173970800202045\n",
"YES\n1.4355786189874697\n",
"YES\n39.79357575290362\n",
"YES\n4620.895169151784\n",
"YES\n0.6466301463814189\n",
"YES\n41.444684956882085\n",
"YES\n5.135978552279435\n",
"YES\n0.7003066945006391\n",
"YES\n28.414462128074017\n",
"YES\n224.57771408997397\n",
"YES\n8.628612728340546\n",
"YES\n5.814857329217617\n",
"YES\n13.027543932030179\n",
"YES\n211.11754843068405\n",
"YES\n0.24432206640792561\n",
"YES\n88.61811886412748\n",
"YES\n0.14159266539555\n",
"YES\n15.338657705302854\n",
"YES\n113.65585182640422\n",
"YES\n5.780987688281275\n",
"YES\n17.230454285291053\n",
"YES\n118.92072980719153\n",
"YES\n0.14158252012915395\n",
"YES\n8.491326889001973\n",
"YES\n106.46936497552505\n",
"YES\n11.256908142130579\n",
"YES\n26.67098914677737\n",
"YES\n233.1378859151222\n",
"YES\n0.1136588536748109\n",
"YES\n5802.747719456924\n",
"YES\n34.98988731817154\n",
"YES\n437.4710546617521\n",
"YES\n2.7913631307730893\n",
"YES\n27.623745150799586\n",
"YES\n207.9136613868006\n",
"YES\n0.6656632628725077\n",
"YES\n5919.3829486180075\n",
"YES\n33.857409585739724\n",
"YES\n319.67804141093546\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A lot of people in Berland hates rain, but you do not. Rain pacifies, puts your thoughts in order. By these years you have developed a good tradition — when it rains, you go on the street and stay silent for a moment, contemplate all around you, enjoy freshness, think about big deeds you have to do.
Today everything had changed quietly. You went on the street with a cup contained water, your favorite drink. In a moment when you were drinking a water you noticed that the process became quite long: the cup still contained water because of rain. You decided to make a formal model of what was happening and to find if it was possible to drink all water in that situation.
Thus, your cup is a cylinder with diameter equals d centimeters. Initial level of water in cup equals h centimeters from the bottom.
<image>
You drink a water with a speed equals v milliliters per second. But rain goes with such speed that if you do not drink a water from the cup, the level of water increases on e centimeters per second. The process of drinking water from the cup and the addition of rain to the cup goes evenly and continuously.
Find the time needed to make the cup empty or find that it will never happen. It is guaranteed that if it is possible to drink all water, it will happen not later than after 104 seconds.
Note one milliliter equals to one cubic centimeter.
Input
The only line of the input contains four integer numbers d, h, v, e (1 ≤ d, h, v, e ≤ 104), where:
* d — the diameter of your cylindrical cup,
* h — the initial level of water in the cup,
* v — the speed of drinking process from the cup in milliliters per second,
* e — the growth of water because of rain if you do not drink from the cup.
Output
If it is impossible to make the cup empty, print "NO" (without quotes).
Otherwise print "YES" (without quotes) in the first line. In the second line print a real number — time in seconds needed the cup will be empty. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4. It is guaranteed that if the answer exists, it doesn't exceed 104.
Examples
Input
1 2 3 100
Output
NO
Input
1 1 1 1
Output
YES
3.659792366325
Note
In the first example the water fills the cup faster than you can drink from it.
In the second example area of the cup's bottom equals to <image>, thus we can conclude that you decrease the level of water by <image> centimeters per second. At the same time water level increases by 1 centimeter per second due to rain. Thus, cup will be empty in <image> seconds.
### Input:
1 1 1 1
### Output:
YES
3.6597923663254868
### Input:
1 2 3 100
### Output:
NO
### Code:
from math import pi
d,h,v,e=map(int,input().split())
v=v/(pi*((d/2)**2))
d=h/(v-e)
if v-e>0 and d<=10000:
print('YES')
print(d)
else:
print('NO')
|
690_B2. Recover Polygon (medium)_28370
|
Now that Heidi has made sure her Zombie Contamination level checker works, it's time to strike! This time, the zombie lair is a strictly convex polygon on the lattice. Each vertex of the polygon occupies a point on the lattice. For each cell of the lattice, Heidi knows the level of Zombie Contamination – the number of corners of the cell that are inside or on the border of the lair.
Given this information, Heidi wants to know the exact shape of the lair to rain destruction on the zombies. Help her!
<image>
Input
The input contains multiple test cases.
The first line of each test case contains one integer N, the size of the lattice grid (5 ≤ N ≤ 500). The next N lines each contain N characters, describing the level of Zombie Contamination of each cell in the lattice. Every character of every line is a digit between 0 and 4.
Cells are given in the same order as they are shown in the picture above: rows go in the decreasing value of y coordinate, and in one row cells go in the order of increasing x coordinate. This means that the first row corresponds to cells with coordinates (1, N), ..., (N, N) and the last row corresponds to cells with coordinates (1, 1), ..., (N, 1).
The last line of the file contains a zero. This line should not be treated as a test case. The sum of the N values for all tests in one file will not exceed 5000.
Output
For each test case, give the following output:
The first line of the output should contain one integer V, the number of vertices of the polygon that is the secret lair. The next V lines each should contain two integers, denoting the vertices of the polygon in the clockwise order, starting from the lexicographically smallest vertex.
Examples
Input
8
00000000
00000110
00012210
01234200
02444200
01223200
00001100
00000000
5
00000
01210
02420
01210
00000
7
0000000
0122100
0134200
0013200
0002200
0001100
0000000
0
Output
4
2 3
2 4
6 6
5 2
4
2 2
2 3
3 3
3 2
3
2 5
4 5
4 2
Note
It is guaranteed that the solution always exists and is unique. It is guaranteed that in the correct solution the coordinates of the polygon vertices are between 2 and N - 2. A vertex (x1, y1) is lexicographically smaller than vertex (x2, y2) if x1 < x2 or <image>.
|
import math
def lexComp(a, b):
if a[0] != b[0]:
return -1 if a[0] < b[0] else 1
if a[1] != b[1]:
return -1 if a[1] < b[1] else 1
return 0
def turn(a, b, c):
return (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
def dist2(a, b):
return (a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2
def solve(n):
a = [list(map(int, input())) for _ in range(n)]
points = []
for i in range(n):
for j in range(n):
if a[i][j] == 1:
curPoints = []
for dx in range(0, 2):
for dy in range(0, 2):
ok = True
for ddx in range(0, 2):
for ddy in range(0, 2):
x, y = i - 1 + dx + ddx, j - 1 + dy + ddy
if 0 <= x < n and 0 <= y < n and a[x][y] == 0:
ok = False
if ok:
curPoints.append((i + dx, j + dy))
points.append(curPoints[0])
points = list(set(points))
for i in range(1, len(points)):
if lexComp(points[0], points[i]) > 0:
points[0], points[i] = points[i], points[0]
points[1:] = sorted(points[1:], key=lambda p: (math.atan2(p[1] - points[0][1], p[0] - points[0][0]), dist2(p, points[0])))
hull = []
for p in points:
while len(hull) >= 2 and turn(hull[-2], hull[-1], p) <= 0:
hull.pop()
hull.append(p)
hull = [(p[1], n - p[0]) for p in hull]
hull = hull[::-1]
start = 0
for i in range(1, len(hull)):
if lexComp(hull[i], hull[start]) < 0:
start = i
newHull = hull[start:]
newHull.extend(hull[:start])
hull = newHull
print(len(hull))
for p in hull:
print(p[0], p[1])
while True:
n = int(input())
if n == 0:
break
solve(n)
|
{
"input": [
"8\n00000000\n00000110\n00012210\n01234200\n02444200\n01223200\n00001100\n00000000\n5\n00000\n01210\n02420\n01210\n00000\n7\n0000000\n0122100\n0134200\n0013200\n0002200\n0001100\n0000000\n0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 5 2 5 3 5 6 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7\n5 8\n2 2 2 3 2 4 3 2 3 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 5 2 5 3 5 6 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 3 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 3 5 2 6 2 6 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 3 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 3 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 4 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 22 8 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 4 4 2 2 6 0 1 0 0 0 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 4 4 2 2 6 1 1 0 0 -1 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 5 2 5 3 5 2 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 3 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 5 2 5 3 5 2 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 3 5 2 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 3 5 2 6 2 6 3 12 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 2 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 3 5 2 6 2 6 3 12 4 6 5 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 3 5 1 6 2 6 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 5 1 6 2 6 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 6 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 7 7 6 7 7\n5 8\n1 2 2 3 2 4 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 7 6 7 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 7 6 7 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 7 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 7 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 3 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 7 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 6 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 6 4 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 2 7 3 2 0 4 4 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 2 8 3 2 0 4 4 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 6 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 4 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 4 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 4 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 3 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 4 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 3 4 4 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 4 3 3 4 2 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 2 3 3 4 2 6 6 2 5 4 0 1 6 2 9 3 12 4 6 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 2 3 3 4 2 6 6 2 5 4 0 1 6 2 9 3 12 4 1 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 2 3 3 4 2 6 6 2 5 4 0 1 6 1 9 3 12 4 1 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 3 3 4 2 6 6 2 5 4 0 1 6 1 9 3 12 4 1 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 3 3 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n1 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 3 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n0 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 3 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n1 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 1 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n1 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 1 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 9 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 1 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 2 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 1 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 4 0 1 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 1 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 8\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 19\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 12\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 18\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 12\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 3 15 4 1 7 6 16 6 4 3 6 2 7\n5 12\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 6 16 6 4 3 6 2 7\n5 12\n0 2 2 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 6 16 6 4 3 6 2 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 5 16 6 4 3 6 2 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 2 2 4 2 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 27\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 1 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 3 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 12\n0 2 0 1 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 8 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 6 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 2 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 3 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 5 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 6 2 4\n2 0\n",
"8 2\n1 3 2 4 2 5 5 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n1 3 2 4 2 1 5 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 6 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 1 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 7 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 3 6 6 0 5 7 0 2 11 1 9 2 15 4 1 14 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 3 6 6 0 5 7 0 4 11 1 9 2 15 4 1 14 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 1 9 2 15 4 1 14 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 15 4 1 14 5 16 2 4 3 6 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 15 4 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 22 4 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 4 2 2 4\n2 0\n",
"8 2\n0 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 22 4 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 22 4 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 3 3 5 3 0 2 4 2 6 6 0 5 7 0 4 11 2 9 2 22 8 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 4 3 5 3 0 2 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 1 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 1 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 5 16 2 4 3 6 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 5 16 2 4 3 1 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-1 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 1 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 3 0 4 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 7 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 3 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 0 0 4 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 3 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 0 0 3 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 3 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 6 6 0 1 0 0 3 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 0 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 11 2 9 2 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 11 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 0 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 3 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 11 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 11 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n0 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 3 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 3 4 2 2 6 0 1 0 0 0 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 0 4 4 2 2 6 0 1 0 0 -1 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 3 5 3 -1 4 4 2 2 6 1 1 0 0 -1 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n-2 2 2 4 2 0 5 4 6 5 3 -1 4 4 2 2 6 1 1 0 0 -1 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n",
"8 2\n0 2 2 4 2 0 5 4 6 5 3 -1 4 4 2 2 6 1 1 0 0 -1 21 2 9 3 22 8 2 14 3 16 2 4 3 1 1 7\n5 14\n1 2 -1 -1 0 1 3 5 0 3 0 3 5 2 2 4\n2 0\n"
],
"output": [
"4\n2 3\n2 4\n6 6\n5 2\n4\n2 2\n2 3\n3 3\n3 2\n3\n2 5\n4 5\n4 2\n",
"4\n2 3\n2 4\n6 6\n5 2\n4\n2 2\n2 3\n3 3\n3 2\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Now that Heidi has made sure her Zombie Contamination level checker works, it's time to strike! This time, the zombie lair is a strictly convex polygon on the lattice. Each vertex of the polygon occupies a point on the lattice. For each cell of the lattice, Heidi knows the level of Zombie Contamination – the number of corners of the cell that are inside or on the border of the lair.
Given this information, Heidi wants to know the exact shape of the lair to rain destruction on the zombies. Help her!
<image>
Input
The input contains multiple test cases.
The first line of each test case contains one integer N, the size of the lattice grid (5 ≤ N ≤ 500). The next N lines each contain N characters, describing the level of Zombie Contamination of each cell in the lattice. Every character of every line is a digit between 0 and 4.
Cells are given in the same order as they are shown in the picture above: rows go in the decreasing value of y coordinate, and in one row cells go in the order of increasing x coordinate. This means that the first row corresponds to cells with coordinates (1, N), ..., (N, N) and the last row corresponds to cells with coordinates (1, 1), ..., (N, 1).
The last line of the file contains a zero. This line should not be treated as a test case. The sum of the N values for all tests in one file will not exceed 5000.
Output
For each test case, give the following output:
The first line of the output should contain one integer V, the number of vertices of the polygon that is the secret lair. The next V lines each should contain two integers, denoting the vertices of the polygon in the clockwise order, starting from the lexicographically smallest vertex.
Examples
Input
8
00000000
00000110
00012210
01234200
02444200
01223200
00001100
00000000
5
00000
01210
02420
01210
00000
7
0000000
0122100
0134200
0013200
0002200
0001100
0000000
0
Output
4
2 3
2 4
6 6
5 2
4
2 2
2 3
3 3
3 2
3
2 5
4 5
4 2
Note
It is guaranteed that the solution always exists and is unique. It is guaranteed that in the correct solution the coordinates of the polygon vertices are between 2 and N - 2. A vertex (x1, y1) is lexicographically smaller than vertex (x2, y2) if x1 < x2 or <image>.
### Input:
8
00000000
00000110
00012210
01234200
02444200
01223200
00001100
00000000
5
00000
01210
02420
01210
00000
7
0000000
0122100
0134200
0013200
0002200
0001100
0000000
0
### Output:
4
2 3
2 4
6 6
5 2
4
2 2
2 3
3 3
3 2
3
2 5
4 5
4 2
### Input:
8 19
2 3 2 4 2 5 3 3 3 5 4 3 4 5 4 6 5 2 5 3 5 6 6 2 6 3 6 4 6 5 6 6 6 7 7 6 7 7
5 8
2 2 2 3 2 4 3 2 3 4 4 2 4 3 4 4
0 0
### Output:
4
2 3
2 4
6 6
5 2
4
2 2
2 3
3 3
3 2
### Code:
import math
def lexComp(a, b):
if a[0] != b[0]:
return -1 if a[0] < b[0] else 1
if a[1] != b[1]:
return -1 if a[1] < b[1] else 1
return 0
def turn(a, b, c):
return (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
def dist2(a, b):
return (a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2
def solve(n):
a = [list(map(int, input())) for _ in range(n)]
points = []
for i in range(n):
for j in range(n):
if a[i][j] == 1:
curPoints = []
for dx in range(0, 2):
for dy in range(0, 2):
ok = True
for ddx in range(0, 2):
for ddy in range(0, 2):
x, y = i - 1 + dx + ddx, j - 1 + dy + ddy
if 0 <= x < n and 0 <= y < n and a[x][y] == 0:
ok = False
if ok:
curPoints.append((i + dx, j + dy))
points.append(curPoints[0])
points = list(set(points))
for i in range(1, len(points)):
if lexComp(points[0], points[i]) > 0:
points[0], points[i] = points[i], points[0]
points[1:] = sorted(points[1:], key=lambda p: (math.atan2(p[1] - points[0][1], p[0] - points[0][0]), dist2(p, points[0])))
hull = []
for p in points:
while len(hull) >= 2 and turn(hull[-2], hull[-1], p) <= 0:
hull.pop()
hull.append(p)
hull = [(p[1], n - p[0]) for p in hull]
hull = hull[::-1]
start = 0
for i in range(1, len(hull)):
if lexComp(hull[i], hull[start]) < 0:
start = i
newHull = hull[start:]
newHull.extend(hull[:start])
hull = newHull
print(len(hull))
for p in hull:
print(p[0], p[1])
while True:
n = int(input())
if n == 0:
break
solve(n)
|
713_C. Sonya and Problem Wihtout a Legend_28374
|
Sonya was unable to think of a story for this problem, so here comes the formal description.
You are given the array containing n positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 3000) — the length of the array.
Next line contains n integer ai (1 ≤ ai ≤ 109).
Output
Print the minimum number of operation required to make the array strictly increasing.
Examples
Input
7
2 1 5 11 5 9 11
Output
9
Input
5
5 4 3 2 1
Output
12
Note
In the first sample, the array is going to look as follows:
2 3 5 6 7 9 11
|2 - 2| + |1 - 3| + |5 - 5| + |11 - 6| + |5 - 7| + |9 - 9| + |11 - 11| = 9
And for the second sample:
1 2 3 4 5
|5 - 1| + |4 - 2| + |3 - 3| + |2 - 4| + |1 - 5| = 12
|
# Idea:
# convert the problem to making array a non decreasing by decreasing each ai by i
# Now we can argue that the optimal final array must have
# each element equal to some element of the array a.
# Proof is to assume optimal solution does not satisfy this then you can
# always increase or decrease one element while maintaining the
# non decreasing property and decreasing or not changing the number of
# operations used. The point at which we cannot keep increasing or decreasing
# is when the element i we are changing reaches some a[j] since then we may
# go from removing to increasing operations (kind of like slope/events trick)
n = int(input())
a = list(map(int,input().split()))
for i in range(n):
a[i] -= i
sorted_a = sorted(a)
dp = [0.0]*n # dp[j] = min operations such a[i] = sorted_a[j]
dp2 = [0.0]*n
for i in range(n):
# we are changing a[i]
mn_prev_state = 1e13
for j in range(n):
mn_prev_state = min(mn_prev_state, dp[j])
# we change a[i] to sorted_a[j]
# ofc this means the changed value of a[i-1] <= sorted_a[j]
# so the changed value of a[i-1] = sorted_a[0...j]
# hence mn_prev_state is all min(dp[0...j])
dp2[j] = mn_prev_state + abs(a[i] - sorted_a[j])
for j in range(n):
dp[j] = dp2[j]
print(int(min(dp)))
|
{
"input": [
"5\n5 4 3 2 1\n",
"7\n2 1 5 11 5 9 11\n",
"5\n850 840 521 42 169\n",
"1\n1000\n",
"2\n1000 1\n",
"75\n392 593 98 533 515 448 220 310 386 79 539 294 208 828 75 534 875 493 94 205 656 105 546 493 60 188 222 108 788 504 809 621 934 455 307 212 630 298 938 62 850 421 839 134 950 256 934 817 209 559 866 67 990 835 534 672 468 768 757 516 959 893 275 315 692 927 321 554 801 805 885 12 67 245 495\n",
"20\n245 891 363 6 193 704 420 447 237 947 664 894 512 194 513 616 671 623 686 378\n",
"1\n1\n",
"5\n1 1 1 2 3\n",
"50\n499 780 837 984 481 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 313 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"5\n100 80 60 70 90\n",
"20\n103 103 110 105 107 119 113 121 116 132 128 124 128 125 138 137 140 136 154 158\n",
"10\n10 16 17 11 1213 1216 1216 1209 3061 3062\n",
"2\n1 1000\n",
"10\n26 723 970 13 422 968 875 329 234 983\n",
"5\n1282 840 521 42 169\n",
"1\n1100\n",
"2\n1001 1\n",
"75\n392 593 98 533 515 448 220 310 386 28 539 294 208 828 75 534 875 493 94 205 656 105 546 493 60 188 222 108 788 504 809 621 934 455 307 212 630 298 938 62 850 421 839 134 950 256 934 817 209 559 866 67 990 835 534 672 468 768 757 516 959 893 275 315 692 927 321 554 801 805 885 12 67 245 495\n",
"20\n245 891 363 6 193 704 433 447 237 947 664 894 512 194 513 616 671 623 686 378\n",
"5\n1 1 2 2 3\n",
"50\n499 780 837 984 481 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 93 224 17 873 648 120 694 996 244 313 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"5\n100 105 60 70 90\n",
"20\n103 103 110 105 107 119 113 121 15 132 128 124 128 125 138 137 140 136 154 158\n",
"10\n10 16 17 16 1213 1216 1216 1209 3061 3062\n",
"10\n26 723 970 13 422 968 875 329 235 983\n",
"7\n2 0 5 11 5 9 11\n",
"5\n2537 840 521 42 169\n",
"2\n1001 0\n",
"75\n392 593 98 533 515 448 220 310 386 28 539 294 208 828 75 534 875 493 94 205 656 105 546 493 60 188 222 108 788 504 809 621 934 455 307 178 630 298 938 62 850 421 839 134 950 256 934 817 209 559 866 67 990 835 534 672 468 768 757 516 959 893 275 315 692 927 321 554 801 805 885 12 67 245 495\n",
"20\n245 891 363 6 193 704 566 447 237 947 664 894 512 194 513 616 671 623 686 378\n",
"5\n1 2 2 2 3\n",
"50\n499 780 837 984 481 347 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 93 224 17 873 648 120 694 996 244 313 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"5\n100 150 60 70 90\n",
"20\n103 103 110 105 188 119 113 121 15 132 128 124 128 125 138 137 140 136 154 158\n",
"10\n10 16 17 16 1796 1216 1216 1209 3061 3062\n",
"10\n26 723 970 13 422 968 1658 329 235 983\n",
"5\n5 5 3 2 2\n",
"7\n2 0 5 11 5 14 11\n",
"2\n1101 0\n",
"75\n392 593 98 533 515 448 220 310 386 28 539 294 208 828 75 534 875 493 94 205 656 105 546 493 60 188 222 108 788 504 809 621 934 455 307 178 630 298 938 62 850 421 839 134 950 256 934 817 209 559 866 67 990 835 534 672 468 768 757 516 959 893 275 136 692 927 321 554 801 805 885 12 67 245 495\n",
"20\n245 891 363 6 193 704 566 447 237 947 407 894 512 194 513 616 671 623 686 378\n",
"5\n1 2 2 1 3\n",
"50\n499 780 837 984 481 347 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 93 224 17 873 648 120 694 996 244 313 404 129 899 583 541 314 525 496 443 1003 297 78 575 2 430 137 387 319\n",
"5\n100 150 60 42 90\n",
"20\n103 103 110 105 188 119 113 121 15 132 128 124 128 125 222 137 140 136 154 158\n",
"10\n10 16 34 16 1796 1216 1216 1209 3061 3062\n",
"10\n26 723 970 11 422 968 1658 329 235 983\n",
"5\n5 5 0 2 2\n",
"7\n4 0 5 11 5 14 11\n",
"2\n1111 0\n",
"75\n392 1038 98 533 515 448 220 310 386 28 539 294 208 828 75 534 875 493 94 205 656 105 546 493 60 188 222 108 788 504 809 621 934 455 307 178 630 298 938 62 850 421 839 134 950 256 934 817 209 559 866 67 990 835 534 672 468 768 757 516 959 893 275 136 692 927 321 554 801 805 885 12 67 245 495\n",
"20\n245 891 363 6 193 704 566 447 282 947 407 894 512 194 513 616 671 623 686 378\n",
"5\n1 2 0 1 3\n",
"50\n499 780 837 984 481 347 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 93 224 17 873 648 120 694 996 244 313 404 129 899 865 541 314 525 496 443 1003 297 78 575 2 430 137 387 319\n",
"20\n103 18 110 105 188 119 113 121 15 132 128 124 128 125 222 137 140 136 154 158\n",
"10\n10 16 34 16 1796 1216 1555 1209 3061 3062\n",
"10\n26 723 970 11 422 1595 1658 329 235 983\n",
"7\n8 0 5 11 5 14 11\n",
"5\n2537 1643 399 42 169\n",
"1\n2\n",
"5\n5 4 3 2 2\n",
"1\n0100\n",
"1\n4\n",
"5\n2537 840 294 42 169\n",
"1\n1110\n",
"1\n5\n",
"5\n2537 840 399 42 169\n",
"1\n1010\n",
"1\n10\n",
"1\n0010\n"
],
"output": [
"12\n",
"9\n",
"1485\n",
"0\n",
"1000\n",
"17691\n",
"3208\n",
"0\n",
"3\n",
"12423\n",
"54\n",
"43\n",
"16\n",
"0\n",
"2546\n",
"1917\n",
"0\n",
"1001\n",
"17742\n",
"3195\n",
"3\n",
"12432\n",
"79\n",
"144\n",
"11\n",
"2545\n",
"10\n",
"3172\n",
"1002\n",
"17776\n",
"3302\n",
"4\n",
"12523\n",
"124\n",
"214\n",
"593\n",
"3328\n",
"12\n",
"14\n",
"1102\n",
"17955\n",
"3251\n",
"5\n",
"12669\n",
"152\n",
"298\n",
"610\n",
"3330\n",
"13\n",
"16\n",
"1112\n",
"18400\n",
"3206\n",
"6\n",
"12951\n",
"383\n",
"947\n",
"3957\n",
"20\n",
"3975\n",
"0\n",
"11\n",
"0\n",
"0\n",
"3172\n",
"0\n",
"0\n",
"3172\n",
"0\n",
"0\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Sonya was unable to think of a story for this problem, so here comes the formal description.
You are given the array containing n positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 3000) — the length of the array.
Next line contains n integer ai (1 ≤ ai ≤ 109).
Output
Print the minimum number of operation required to make the array strictly increasing.
Examples
Input
7
2 1 5 11 5 9 11
Output
9
Input
5
5 4 3 2 1
Output
12
Note
In the first sample, the array is going to look as follows:
2 3 5 6 7 9 11
|2 - 2| + |1 - 3| + |5 - 5| + |11 - 6| + |5 - 7| + |9 - 9| + |11 - 11| = 9
And for the second sample:
1 2 3 4 5
|5 - 1| + |4 - 2| + |3 - 3| + |2 - 4| + |1 - 5| = 12
### Input:
5
5 4 3 2 1
### Output:
12
### Input:
7
2 1 5 11 5 9 11
### Output:
9
### Code:
# Idea:
# convert the problem to making array a non decreasing by decreasing each ai by i
# Now we can argue that the optimal final array must have
# each element equal to some element of the array a.
# Proof is to assume optimal solution does not satisfy this then you can
# always increase or decrease one element while maintaining the
# non decreasing property and decreasing or not changing the number of
# operations used. The point at which we cannot keep increasing or decreasing
# is when the element i we are changing reaches some a[j] since then we may
# go from removing to increasing operations (kind of like slope/events trick)
n = int(input())
a = list(map(int,input().split()))
for i in range(n):
a[i] -= i
sorted_a = sorted(a)
dp = [0.0]*n # dp[j] = min operations such a[i] = sorted_a[j]
dp2 = [0.0]*n
for i in range(n):
# we are changing a[i]
mn_prev_state = 1e13
for j in range(n):
mn_prev_state = min(mn_prev_state, dp[j])
# we change a[i] to sorted_a[j]
# ofc this means the changed value of a[i-1] <= sorted_a[j]
# so the changed value of a[i-1] = sorted_a[0...j]
# hence mn_prev_state is all min(dp[0...j])
dp2[j] = mn_prev_state + abs(a[i] - sorted_a[j])
for j in range(n):
dp[j] = dp2[j]
print(int(min(dp)))
|
734_A. Anton and Danik_28378
|
Anton likes to play chess, and so does his friend Danik.
Once they have played n games in a row. For each game it's known who was the winner — Anton or Danik. None of the games ended with a tie.
Now Anton wonders, who won more games, he or Danik? Help him determine this.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of games played.
The second line contains a string s, consisting of n uppercase English letters 'A' and 'D' — the outcome of each of the games. The i-th character of the string is equal to 'A' if the Anton won the i-th game and 'D' if Danik won the i-th game.
Output
If Anton won more games than Danik, print "Anton" (without quotes) in the only line of the output.
If Danik won more games than Anton, print "Danik" (without quotes) in the only line of the output.
If Anton and Danik won the same number of games, print "Friendship" (without quotes).
Examples
Input
6
ADAAAA
Output
Anton
Input
7
DDDAADA
Output
Danik
Input
6
DADADA
Output
Friendship
Note
In the first sample, Anton won 6 games, while Danik — only 1. Hence, the answer is "Anton".
In the second sample, Anton won 3 games and Danik won 4 games, so the answer is "Danik".
In the third sample, both Anton and Danik won 3 games and the answer is "Friendship".
|
n=int(input())
s=input()
c=0
c1=0
for i in s:
if i=="D":
c=c+1
else:
c1=c1+1
if c>c1:
print("Danik")
elif c<c1:
print("Anton")
else:
print("Friendship")
|
{
"input": [
"7\nDDDAADA\n",
"6\nDADADA\n",
"6\nADAAAA\n",
"40\nAAAAAAAAADDAAAAAAAAAAADADDAAAAAAAAAAADAA\n",
"3\nDAD\n",
"200\nDDDDDDDADDDDDDAADADAADAAADAADADAAADDDADDDDDDADDDAADDDAADADDDDDADDDAAAADAAADDDDDAAADAADDDAAAADDADADDDAADDAADAAADAADAAAADDAADDADAAAADADDDAAAAAADDAADAADAADADDDAAADAAAADADDADAAAAAADADADDDADDDAADDADDDAAAAD\n",
"1\nA\n",
"1\nD\n",
"10\nDDDDADDADD\n",
"4\nDAAD\n",
"379\nAADAAAAAADDAAAAAADAADADADDAAAAADADDAADAAAADDDADAAAAAAADAADAAAAAAADAAAAAAAAADAAAAAAADAAAAAAAAAAADDDADAAAAAAAADAADADAAAADAAAAAAAAAAAAAAAAADAAAADDDAADAAAAAAADAAADAAADAADDDADDAAADAAAAAADDDADDDAAADAAAADAAAAAAAAADAAADAAAAAAAAADAAAAAAAAAAAAAAAAAADADAAAAAAAAAAADAAAAADAAAADAAAAAAAAAAAAADADAADAAAAAAAADAADAAAAAAAADAAAAAAAADDDAAAAAADAAADAAAAAADAADAAAAAADAAAADADAADAAAAAADAAAADAADDAADAADAAA\n",
"3\nADD\n",
"4\nDADA\n",
"2\nDA\n",
"3\nDDA\n",
"4\nADDA\n",
"40\nAADAAAAAAAAAAADDADAAAAAAAAAAADDAAAAAAAAA\n",
"2\nAD\n",
"6\nDDDAAA\n",
"4\nADAD\n",
"6\nAADDDA\n",
"6\nAAAADA\n",
"4\nDDAA\n",
"6\nADDDAA\n",
"6\nADDADA\n",
"4\nAADD\n",
"6\nADADDA\n",
"6\nADAADD\n",
"6\nDDAADA\n",
"6\nAADADD\n",
"6\nADADAD\n",
"40\nAAAAAAAAADDAAAAAAAAAAADADDAAAAAAAAADAAAA\n",
"6\nDADDAA\n",
"40\nAAADAAAAADDAAAAAAAAAAADADAAAAAAAAAADAAAA\n",
"200\nDAAAADDDADDAADDDADDDADADAAAAAADADDADAAAADAAADDDADAADAADAADDAAAAAADDDADAAAADADDAADDAAAADAADAAADAADDAADDDADADDAAAADDDAADAAADDDDDAAADAAAADDDADDDDDADAADDDAADDDADDDDDDADDDAAADADAADAAADAADADAADDDDDDADDDDDDD\n",
"379\nAAADAADAADDAADAAAADAAAAAADAADADAAAADAAAAAADAADAAAAAADAAADAAAAAADDDAAAAAAAADAAAAAAAADAADAAAAAAAADAADADAAAAAAAAAAAAADAAAADAAAAADAAAAAAAAAAADADAAAAAAAAAAAAAAAAAADAAAAAAAAADAAADAAAAAAAAADAAAADAAADDDADDDAAAAAADAAADDADDDAADAAADAAADAAAAAAADAADDDAAAADAAAAAAAAAAAAAAAAADAAAADADAADAAAAAAAADADDDAAAAAAAAAAADAAAAAAADAAAAAAAAADAAAAAAADAADAAAAAAADADDDAAAADAADDADAAAAADDADADAADAAAAAADDAAAAAADAA\n",
"6\nDDAAAD\n",
"40\nAAAADAAAAAAAAADDADAAAAAAAAAAADDAAAAAAAAA\n",
"6\nAADDAD\n",
"40\nAAAADAAAAAAAAAADADAAAAAAAAAAADDAAAAADAAA\n",
"379\nAAADAADAADDAADAAAADAAAAAADAADADAAAADAAAAAADAADAAAAAADAAADAAAAAADDDAAAAAAAADAAAAAAAADAADAAAAAAAADAADADAAAAAAAAAAAAADAAAADADAAADAAAAAAAAAAADADAAAAAAAAAAAAAAAAAADAAAAAAAAADAAADAAAAAAAAADAAAADAAADDDADADAAAAAADAAADDADDDAADAAADAAADAAAAAAADAADDDAAAADAAAAAAAAAAAAAAAAADAAAADADAADAAAAAAAADADDDAAAAAAAAAAADAAAAAAADAAAAAAAAADAAAAAAADAADAAAAAAADADDDAAAADAADDADAAAAADDADADAADAAAAAADDAAAAAADAA\n",
"379\nAADAAAAAADDAAAAAADAADADADDAAAAADADDAADAAAADDDADAAAAAAADAADAAAAAAADAAAAAAAAADAAAAAAADAAAAAAAAAAADDDADAAAAAAAADAADADAAAADAAAAAAAAAAAAAAAAADAAAADDDAADAAAAAAADAAADAAADAADDDADDAAADAAAAAADADADDDAAADAAAADAAAAAAAAADAAADAAAAAAAAADAAAAAAAAAAAAAAAAAADADAAAAAAAAAAADAAADADAAAADAAAAAAAAAAAAADADAADAAAAAAAADAADAAAAAAAADAAAAAAAADDDAAAAAADAAADAAAAAADAADAAAAAADAAAADADAADAAAAAADAAAADAADDAADAADAAA\n",
"6\nDDADAA\n",
"6\nDADAAD\n",
"6\nDAAADD\n",
"6\nAAADDD\n",
"6\nDAADAD\n",
"379\nAADAAAAAADDAAAAAAAAADADADDAAAAADADDAADAAAADDDADAAAAAAADAADAAAAAAADAAAAAAAAADAAAAAAADAAAAAAAAAAADDDADAAAAAAAADAADADAAAADAAAAAAAAAAAAAAAAADAAAADDDAADAAAAAAADAAADAAADAADDDADDAAADAAAAAADDDADDDAAADAAADDAAAAAAAAADAAADAAAAAAAAADAAAAAAAAAAAAAAAAAADADAAAAAAAAAAADAAAAADAAAADAAAAAAAAAAAAADADAADAAAAAAAADAADAAAAAAAADAAAAAAAADDDAAAAAADAAADAAAAAADAADAAAAAADAAAADADAADAAAAAADAAAADAADDAADAADAAA\n"
],
"output": [
"Danik\n",
"Friendship\n",
"Anton\n",
"Anton\n",
"Danik\n",
"Friendship\n",
"Anton\n",
"Danik\n",
"Danik\n",
"Friendship\n",
"Anton\n",
"Danik\n",
"Friendship\n",
"Friendship\n",
"Danik\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Anton\n",
"Friendship\n",
"Anton\n",
"Anton\n",
"Anton\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Anton\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Anton likes to play chess, and so does his friend Danik.
Once they have played n games in a row. For each game it's known who was the winner — Anton or Danik. None of the games ended with a tie.
Now Anton wonders, who won more games, he or Danik? Help him determine this.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of games played.
The second line contains a string s, consisting of n uppercase English letters 'A' and 'D' — the outcome of each of the games. The i-th character of the string is equal to 'A' if the Anton won the i-th game and 'D' if Danik won the i-th game.
Output
If Anton won more games than Danik, print "Anton" (without quotes) in the only line of the output.
If Danik won more games than Anton, print "Danik" (without quotes) in the only line of the output.
If Anton and Danik won the same number of games, print "Friendship" (without quotes).
Examples
Input
6
ADAAAA
Output
Anton
Input
7
DDDAADA
Output
Danik
Input
6
DADADA
Output
Friendship
Note
In the first sample, Anton won 6 games, while Danik — only 1. Hence, the answer is "Anton".
In the second sample, Anton won 3 games and Danik won 4 games, so the answer is "Danik".
In the third sample, both Anton and Danik won 3 games and the answer is "Friendship".
### Input:
7
DDDAADA
### Output:
Danik
### Input:
6
DADADA
### Output:
Friendship
### Code:
n=int(input())
s=input()
c=0
c1=0
for i in s:
if i=="D":
c=c+1
else:
c1=c1+1
if c>c1:
print("Danik")
elif c<c1:
print("Anton")
else:
print("Friendship")
|
758_A. Holiday Of Equality_28382
|
In Berland it is the holiday of equality. In honor of the holiday the king decided to equalize the welfare of all citizens in Berland by the expense of the state treasury.
Totally in Berland there are n citizens, the welfare of each of them is estimated as the integer in ai burles (burle is the currency in Berland).
You are the royal treasurer, which needs to count the minimum charges of the kingdom on the king's present. The king can only give money, he hasn't a power to take away them.
Input
The first line contains the integer n (1 ≤ n ≤ 100) — the number of citizens in the kingdom.
The second line contains n integers a1, a2, ..., an, where ai (0 ≤ ai ≤ 106) — the welfare of the i-th citizen.
Output
In the only line print the integer S — the minimum number of burles which are had to spend.
Examples
Input
5
0 1 2 3 4
Output
10
Input
5
1 1 0 1 1
Output
1
Input
3
1 3 1
Output
4
Input
1
12
Output
0
Note
In the first example if we add to the first citizen 4 burles, to the second 3, to the third 2 and to the fourth 1, then the welfare of all citizens will equal 4.
In the second example it is enough to give one burle to the third citizen.
In the third example it is necessary to give two burles to the first and the third citizens to make the welfare of citizens equal 3.
In the fourth example it is possible to give nothing to everyone because all citizens have 12 burles.
|
n = int(input())
s = 0
mx = 0
a = list((map(int,input().split())))
for i in range(n):
s+=a[i]
mx = max(mx,a[i])
print(mx*n-s)
|
{
"input": [
"1\n12\n",
"5\n0 1 2 3 4\n",
"3\n1 3 1\n",
"5\n1 1 0 1 1\n",
"45\n908719 394261 815134 419990 926993 383792 772842 277695 527137 655356 684956 695716 273062 550324 106247 399133 442382 33076 462920 294674 846052 817752 421365 474141 290471 358990 109812 74492 543281 169434 919692 786809 24028 197184 310029 801476 699355 429672 51343 374128 776726 850380 293868 981569 550763\n",
"3\n1 2 3\n",
"3\n3 2 1\n",
"3\n0 0 0\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000\n",
"1\n0\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"9\n31078 645168 695751 126111 375934 150495 838412 434477 993107\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"3\n5 0 0\n",
"21\n842556 216391 427181 626688 775504 168309 851038 448402 880826 73697 593338 519033 135115 20128 424606 939484 846242 756907 377058 241543 29353\n",
"1\n228503\n",
"100\n1000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"3\n2 3 1\n",
"1\n1000000\n",
"56\n100728 972537 13846 385421 756708 184642 259487 319707 376662 221694 675284 972837 499419 13846 38267 289898 901299 831197 954715 197515 514102 910423 127555 883934 362472 870788 538802 741008 973434 448124 391526 363321 947321 544618 68006 782313 955075 741981 815027 723297 585059 718114 700739 413489 454091 736144 308999 98065 3716 347323 9635 289003 986510 607065 60236 273351\n",
"30\n315421 772664 560686 654312 151528 356749 351486 707462 820089 226682 546700 136028 824236 842130 578079 337807 665903 764100 617900 822937 992759 591749 651310 742085 767695 695442 17967 515106 81059 186025\n",
"6\n433864 631347 597596 794426 713555 231193\n",
"3\n2 1 3\n",
"14\n52518 718438 358883 462189 853171 592966 225788 46977 814826 295697 676256 561479 56545 764281\n",
"3\n1 3 2\n",
"2\n32576 550340\n",
"50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"3\n910648 542843 537125\n",
"4\n751720 572344 569387 893618\n",
"3\n3 1 2\n",
"70\n644488 5444 150441 714420 602059 335330 510670 196555 546346 740011 509449 850947 692874 524857 750434 952985 223744 374727 896124 753037 367352 679050 560202 172728 569291 778616 332116 286927 843598 372698 244906 498046 900681 709791 420904 724593 864493 813094 791377 39998 296710 625656 403891 579231 706693 984045 16901 574259 562265 761104 930361 256045 124461 538980 573508 372148 988722 108592 784354 55302 232524 277205 782251 299943 436488 743389 324618 742543 266915 99642\n",
"5\n2 10 0 0 0\n",
"45\n908719 394261 815134 419990 926993 383792 772842 277695 527137 655356 1124196 695716 273062 550324 106247 399133 442382 33076 462920 294674 846052 817752 421365 474141 290471 358990 109812 74492 543281 169434 919692 786809 24028 197184 310029 801476 699355 429672 51343 374128 776726 850380 293868 981569 550763\n",
"3\n1 2 2\n",
"3\n3 4 1\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000\n",
"9\n31078 645168 695751 40160 375934 150495 838412 434477 993107\n",
"3\n5 1 0\n",
"21\n842556 216391 427181 626688 775504 168309 851038 448402 880826 73697 593338 519033 135115 20128 424606 939484 846242 756907 113554 241543 29353\n",
"1\n253365\n",
"3\n2 3 2\n",
"56\n100728 972537 13846 385421 756708 184642 259487 319707 376662 221694 675284 972837 499419 13846 38267 289898 901299 831197 954715 197515 514102 910423 127555 883934 362472 870788 538802 741008 973434 448124 391526 329155 947321 544618 68006 782313 955075 741981 815027 723297 585059 718114 700739 413489 454091 736144 308999 98065 3716 347323 9635 289003 986510 607065 60236 273351\n",
"30\n315421 772664 560686 654312 151528 356749 351486 707462 593826 226682 546700 136028 824236 842130 578079 337807 665903 764100 617900 822937 992759 591749 651310 742085 767695 695442 17967 515106 81059 186025\n",
"6\n433864 631347 597596 794426 867252 231193\n",
"3\n2 1 5\n",
"14\n52518 718438 358883 462189 853171 592966 225788 46977 814826 170098 676256 561479 56545 764281\n",
"3\n1 0 2\n",
"2\n32576 25385\n",
"3\n910648 542843 88624\n",
"4\n751720 123996 569387 893618\n",
"70\n644488 5444 150441 714420 602059 335330 510670 196555 546346 740011 509449 850947 692874 524857 750434 952985 223744 374727 896124 609694 367352 679050 560202 172728 569291 778616 332116 286927 843598 372698 244906 498046 900681 709791 420904 724593 864493 813094 791377 39998 296710 625656 403891 579231 706693 984045 16901 574259 562265 761104 930361 256045 124461 538980 573508 372148 988722 108592 784354 55302 232524 277205 782251 299943 436488 743389 324618 742543 266915 99642\n",
"5\n2 10 1 0 0\n",
"45\n908719 394261 815134 419990 926993 383792 772842 277695 527137 655356 1124196 522615 273062 550324 106247 399133 442382 33076 462920 294674 846052 817752 421365 474141 290471 358990 109812 74492 543281 169434 919692 786809 24028 197184 310029 801476 699355 429672 51343 374128 776726 850380 293868 981569 550763\n",
"3\n3 5 1\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1000000\n",
"9\n31078 645168 695751 40160 375934 150495 838412 434477 725925\n",
"3\n5 1 1\n",
"21\n842556 216391 427181 626688 775504 168309 851038 448402 880826 73697 593338 519033 135115 20128 424606 939484 846242 756907 113554 319003 29353\n",
"56\n100728 972537 13846 385421 756708 184642 259487 319707 376662 221694 675284 972837 499419 13846 38267 289898 901299 831197 954715 197515 514102 910423 127555 883934 362472 870788 538802 741008 1830261 448124 391526 329155 947321 544618 68006 782313 955075 741981 815027 723297 585059 718114 700739 413489 454091 736144 308999 98065 3716 347323 9635 289003 986510 607065 60236 273351\n",
"30\n315421 772664 560686 654312 151528 356749 464813 707462 593826 226682 546700 136028 824236 842130 578079 337807 665903 764100 617900 822937 992759 591749 651310 742085 767695 695442 17967 515106 81059 186025\n",
"6\n846935 631347 597596 794426 867252 231193\n",
"14\n52518 718438 358883 462189 853171 592966 225788 46977 814826 170098 1206414 561479 56545 764281\n",
"2\n32576 17961\n",
"50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"3\n910648 542843 26177\n",
"4\n751720 109543 569387 893618\n",
"70\n644488 5444 150441 714420 602059 335330 510670 196555 546346 740011 509449 850947 692874 524857 750434 952985 223744 533151 896124 609694 367352 679050 560202 172728 569291 778616 332116 286927 843598 372698 244906 498046 900681 709791 420904 724593 864493 813094 791377 39998 296710 625656 403891 579231 706693 984045 16901 574259 562265 761104 930361 256045 124461 538980 573508 372148 988722 108592 784354 55302 232524 277205 782251 299943 436488 743389 324618 742543 266915 99642\n",
"5\n0 0 2 3 4\n",
"45\n908719 394261 815134 419990 926993 383792 772842 277695 527137 655356 1124196 522615 273062 550324 106247 399133 442382 33076 462920 294674 846052 817752 421365 474141 290471 358990 109812 74492 543281 169434 919692 786809 24028 197184 310029 801476 699355 429672 51343 696005 776726 850380 293868 981569 550763\n",
"3\n3 7 1\n",
"100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1000000\n",
"9\n31078 645168 695751 40160 375934 150495 838412 434477 435669\n",
"3\n9 1 1\n",
"21\n842556 216391 427181 626688 775504 168309 851038 448402 880826 73697 644395 519033 135115 20128 424606 939484 846242 756907 113554 319003 29353\n",
"56\n100728 972537 13846 385421 756708 184642 259487 112337 376662 221694 675284 972837 499419 13846 38267 289898 901299 831197 954715 197515 514102 910423 127555 883934 362472 870788 538802 741008 1830261 448124 391526 329155 947321 544618 68006 782313 955075 741981 815027 723297 585059 718114 700739 413489 454091 736144 308999 98065 3716 347323 9635 289003 986510 607065 60236 273351\n",
"30\n315421 772664 560686 654312 151528 356749 464813 707462 593826 311352 546700 136028 824236 842130 578079 337807 665903 764100 617900 822937 992759 591749 651310 742085 767695 695442 17967 515106 81059 186025\n",
"6\n846935 106960 597596 794426 867252 231193\n",
"14\n52518 718438 358883 462189 1427515 592966 225788 46977 814826 170098 1206414 561479 56545 764281\n",
"2\n23567 17961\n",
"50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"3\n910648 357142 26177\n",
"4\n1389344 109543 569387 893618\n",
"70\n644488 5444 150441 714420 602059 335330 510670 196555 546346 740011 509449 850947 692874 524857 750434 952985 223744 533151 896124 609694 367352 679050 560202 172728 569291 778616 332116 286927 843598 372698 244906 498046 900681 709791 420904 724593 864493 813094 791377 39998 296710 1033347 403891 579231 706693 984045 16901 574259 562265 761104 930361 256045 124461 538980 573508 372148 988722 108592 784354 55302 232524 277205 782251 299943 436488 743389 324618 742543 266915 99642\n",
"5\n2 0 1 1 1\n",
"45\n908719 394261 815134 641700 926993 383792 772842 277695 527137 655356 1124196 522615 273062 550324 106247 399133 442382 33076 462920 294674 846052 817752 421365 474141 290471 358990 109812 74492 543281 169434 919692 786809 24028 197184 310029 801476 699355 429672 51343 696005 776726 850380 293868 981569 550763\n",
"3\n1 7 1\n",
"9\n31078 645168 695751 40160 375934 150495 838412 434477 11408\n",
"3\n10 1 1\n",
"21\n842556 216391 427181 626688 775504 168309 851038 696879 880826 73697 644395 519033 135115 20128 424606 939484 846242 756907 113554 319003 29353\n",
"56\n100728 972537 13846 385421 756708 184642 259487 112337 376662 221694 675284 972837 499419 13846 38267 289898 901299 831197 954715 197515 514102 910423 127555 883934 362472 1339807 538802 741008 1830261 448124 391526 329155 947321 544618 68006 782313 955075 741981 815027 723297 585059 718114 700739 413489 454091 736144 308999 98065 3716 347323 9635 289003 986510 607065 60236 273351\n",
"30\n315421 772664 560686 654312 151528 317007 464813 707462 593826 311352 546700 136028 824236 842130 578079 337807 665903 764100 617900 822937 992759 591749 651310 742085 767695 695442 17967 515106 81059 186025\n",
"6\n1094565 106960 597596 794426 867252 231193\n",
"14\n52518 622357 358883 462189 1427515 592966 225788 46977 814826 170098 1206414 561479 56545 764281\n",
"2\n23567 35170\n",
"50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"3\n595712 357142 26177\n",
"4\n1389344 94963 569387 893618\n",
"70\n644488 5444 150441 714420 602059 335330 510670 196555 546346 740011 509449 850947 692874 524857 750434 952985 223744 533151 896124 609694 367352 679050 560202 172728 569291 778616 332116 286927 843598 372698 244906 498046 900681 709791 420904 724593 864493 813094 791377 39998 296710 1033347 403891 579231 706693 474403 16901 574259 562265 761104 930361 256045 124461 538980 573508 372148 988722 108592 784354 55302 232524 277205 782251 299943 436488 743389 324618 742543 266915 99642\n",
"5\n1 0 2 3 5\n",
"1\n0000000\n",
"50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"3\n3 2 2\n",
"1\n17\n",
"5\n0 1 3 3 4\n",
"3\n1 1 1\n",
"5\n1 1 1 1 1\n",
"3\n1 2 1\n",
"1\n118367\n",
"3\n1 3 3\n",
"1\n0000100\n",
"3\n2 2 5\n",
"3\n3 3 2\n",
"1\n14\n",
"3\n1 1 2\n",
"5\n2 1 1 1 1\n",
"3\n2 2 2\n",
"1\n85212\n",
"3\n1 2 0\n",
"1\n0100100\n",
"3\n3 1 5\n",
"3\n3 0 2\n",
"1\n9\n",
"5\n1 0 2 3 4\n",
"3\n1 1 4\n",
"3\n1 4 0\n",
"1\n106759\n",
"3\n1 0 0\n",
"1\n0101100\n",
"3\n0 1 5\n",
"3\n0 0 2\n",
"1\n10\n"
],
"output": [
"0\n",
"10\n",
"4\n",
"1\n",
"21993384\n",
"3\n",
"3\n",
"0\n",
"99000000\n",
"0\n",
"99000000\n",
"4647430\n",
"0\n",
"10\n",
"9535765\n",
"0\n",
"99000000\n",
"3\n",
"0\n",
"26984185\n",
"13488674\n",
"1364575\n",
"3\n",
"5464380\n",
"3\n",
"517764\n",
"0\n",
"741328\n",
"787403\n",
"3\n",
"32816391\n",
"38\n",
"27972359\n",
"1\n",
"4\n",
"98999999\n",
"4733381\n",
"9\n",
"9799269\n",
"0\n",
"2\n",
"27018351\n",
"13714937\n",
"1647834\n",
"7\n",
"5589979\n",
"3\n",
"7191\n",
"1189829\n",
"1235751\n",
"32959734\n",
"37\n",
"28145460\n",
"6\n",
"98999998\n",
"3608308\n",
"8\n",
"9721809\n",
"73411580\n",
"13601610\n",
"1234763\n",
"10005223\n",
"14615\n",
"50\n",
"1252276\n",
"1250204\n",
"32801310\n",
"11\n",
"27823583\n",
"10\n",
"98999997\n",
"3898564\n",
"16\n",
"9670752\n",
"73618950\n",
"13516940\n",
"1759150\n",
"12526293\n",
"5606\n",
"51\n",
"1437977\n",
"2595484\n",
"35517369\n",
"5\n",
"27601873\n",
"12\n",
"4322825\n",
"18\n",
"9422275\n",
"73149931\n",
"13556682\n",
"2875398\n",
"12622374\n",
"11603\n",
"52\n",
"808105\n",
"2610064\n",
"36027011\n",
"14\n",
"0\n",
"1\n",
"2\n",
"0\n",
"9\n",
"0\n",
"0\n",
"2\n",
"0\n",
"2\n",
"0\n",
"6\n",
"1\n",
"0\n",
"2\n",
"4\n",
"0\n",
"0\n",
"3\n",
"0\n",
"6\n",
"4\n",
"0\n",
"10\n",
"6\n",
"7\n",
"0\n",
"2\n",
"0\n",
"9\n",
"4\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In Berland it is the holiday of equality. In honor of the holiday the king decided to equalize the welfare of all citizens in Berland by the expense of the state treasury.
Totally in Berland there are n citizens, the welfare of each of them is estimated as the integer in ai burles (burle is the currency in Berland).
You are the royal treasurer, which needs to count the minimum charges of the kingdom on the king's present. The king can only give money, he hasn't a power to take away them.
Input
The first line contains the integer n (1 ≤ n ≤ 100) — the number of citizens in the kingdom.
The second line contains n integers a1, a2, ..., an, where ai (0 ≤ ai ≤ 106) — the welfare of the i-th citizen.
Output
In the only line print the integer S — the minimum number of burles which are had to spend.
Examples
Input
5
0 1 2 3 4
Output
10
Input
5
1 1 0 1 1
Output
1
Input
3
1 3 1
Output
4
Input
1
12
Output
0
Note
In the first example if we add to the first citizen 4 burles, to the second 3, to the third 2 and to the fourth 1, then the welfare of all citizens will equal 4.
In the second example it is enough to give one burle to the third citizen.
In the third example it is necessary to give two burles to the first and the third citizens to make the welfare of citizens equal 3.
In the fourth example it is possible to give nothing to everyone because all citizens have 12 burles.
### Input:
1
12
### Output:
0
### Input:
5
0 1 2 3 4
### Output:
10
### Code:
n = int(input())
s = 0
mx = 0
a = list((map(int,input().split())))
for i in range(n):
s+=a[i]
mx = max(mx,a[i])
print(mx*n-s)
|
779_E. Bitwise Formula_28386
|
Bob recently read about bitwise operations used in computers: AND, OR and XOR. He have studied their properties and invented a new game.
Initially, Bob chooses integer m, bit depth of the game, which means that all numbers in the game will consist of m bits. Then he asks Peter to choose some m-bit number. After that, Bob computes the values of n variables. Each variable is assigned either a constant m-bit number or result of bitwise operation. Operands of the operation may be either variables defined before, or the number, chosen by Peter. After that, Peter's score equals to the sum of all variable values.
Bob wants to know, what number Peter needs to choose to get the minimum possible score, and what number he needs to choose to get the maximum possible score. In both cases, if there are several ways to get the same score, find the minimum number, which he can choose.
Input
The first line contains two integers n and m, the number of variables and bit depth, respectively (1 ≤ n ≤ 5000; 1 ≤ m ≤ 1000).
The following n lines contain descriptions of the variables. Each line describes exactly one variable. Description has the following format: name of a new variable, space, sign ":=", space, followed by one of:
1. Binary number of exactly m bits.
2. The first operand, space, bitwise operation ("AND", "OR" or "XOR"), space, the second operand. Each operand is either the name of variable defined before or symbol '?', indicating the number chosen by Peter.
Variable names are strings consisting of lowercase Latin letters with length at most 10. All variable names are different.
Output
In the first line output the minimum number that should be chosen by Peter, to make the sum of all variable values minimum possible, in the second line output the minimum number that should be chosen by Peter, to make the sum of all variable values maximum possible. Both numbers should be printed as m-bit binary numbers.
Examples
Input
3 3
a := 101
b := 011
c := ? XOR b
Output
011
100
Input
5 1
a := 1
bb := 0
cx := ? OR a
d := ? XOR ?
e := d AND bb
Output
0
0
Note
In the first sample if Peter chooses a number 0112, then a = 1012, b = 0112, c = 0002, the sum of their values is 8. If he chooses the number 1002, then a = 1012, b = 0112, c = 1112, the sum of their values is 15.
For the second test, the minimum and maximum sum of variables a, bb, cx, d and e is 2, and this sum doesn't depend on the number chosen by Peter, so the minimum Peter can choose is 0.
|
n, m = map(int, input().split())
v = [('?', '')]
temp = [(0, 1)]
d = {}
d['?'] = 0
mn, mx = '', ''
for i in range(n):
name, val = input().split(' := ')
v.append((name, val.split()))
temp.append((-1, -1))
d[name] = i + 1
def eval(expr, bit1, bit2):
if expr == 'OR':
return bit1 | bit2
elif expr == 'AND':
return bit1 and bit2
elif expr == 'XOR':
return bit1 ^ bit2
else:
raise AttributeError()
for i in range(m):
for name, expr in v[1:]:
j = d[name]
if len(expr) == 1:
temp[j] = (int(expr[0][i]), int(expr[0][i]))
else:
bit1, bit2 = temp[d[expr[0]]], temp[d[expr[2]]]
temp[j] = (eval(expr[1], bit1[0], bit2[0]), eval(expr[1], bit1[1], bit2[1]))
z, o = sum(temp[_][0] for _ in range(1, n + 1)), sum(temp[_][1] for _ in range(1, n + 1))
mn += '1' if o < z else '0'
mx += '1' if o > z else '0'
print(mn)
print(mx)
|
{
"input": [
"3 3\na := 101\nb := 011\nc := ? XOR b\n",
"5 1\na := 1\nbb := 0\ncx := ? OR a\nd := ? XOR ?\ne := d AND bb\n",
"1 6\na := ? OR ?\n",
"29 2\naa := 10\nba := 11\nca := 01\nda := aa AND ?\nea := ba OR ?\nfa := da XOR ?\nga := 11\nha := fa XOR ea\nia := 01\nja := ca OR ha\nka := ha XOR ia\nla := ha OR ?\nma := ba AND ba\nna := ma OR ?\noa := 11\npa := oa OR ba\nqa := 00\nra := qa AND ia\nsa := fa OR ?\nta := ha OR ga\nua := 00\nva := 00\nwa := 11\nxa := 10\nya := ja XOR ?\nza := 00\nab := 00\nbb := pa OR qa\ncb := bb AND ?\n",
"12 14\na := 01100010000111\nb := ? XOR a\nc := 01101111001010\nd := ? XOR c\ne := 10000011101111\nf := ? XOR e\ng := 10100011001010\nh := ? XOR g\ni := 10010110111111\nj := ? XOR i\nk := 10000111110001\nl := ? XOR k\n",
"1 10\na := 0110110011\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\nd := 010110101110110\ne := 111111000010110\nf := 011001110111110\ng := 110011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110110\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 111001110011001\nq := 000100110001000\n",
"2 10\nb := 0100101101\na := ? XOR b\n",
"14 14\na := 10000100110000\nb := 01111011001111\nc := 11110001111101\nd := 00001110000010\ne := 00111100000010\nf := 11000011111101\ng := ? XOR a\nh := b XOR ?\ni := ? XOR c\nj := d XOR ?\nk := ? XOR e\nl := f XOR ?\nm := 11110011011001\nn := ? XOR m\n",
"22 9\na := 100101111\nb := 010001100\nc := b AND b\nd := 111000010\ne := c AND a\nf := a OR e\ng := e AND ?\nh := 000010001\ni := b OR ?\nj := d AND ?\nk := g AND h\nl := 010100000\nm := a AND a\nn := j AND ?\no := m OR n\np := o AND ?\nq := f OR ?\nr := 000011011\ns := 001110011\nt := 100111100\nu := l AND p\nv := g OR h\n",
"14 8\na := 01010000\nb := 10101111\nc := 01100100\nd := 10011011\ne := 01001100\nf := 10110011\ng := ? XOR a\nh := b XOR ?\ni := ? XOR c\nj := d XOR ?\nk := ? XOR e\nl := f XOR ?\nm := 00101111\nn := ? XOR m\n",
"12 3\na := 101\nb := a XOR ?\nc := b XOR b\nd := b XOR a\ne := c XOR ?\nf := e XOR ?\ng := c XOR f\nh := 100\ni := c XOR h\nj := c XOR i\nk := b XOR ?\nl := 111\n",
"10 3\na := 011\nb := ? OR a\nc := 000\nd := ? AND c\ne := 101\nf := ? AND e\ng := 001\nh := ? XOR g\ni := 001\nj := ? XOR i\n",
"13 6\na := 111010\nb := 100100\nc := 001110\nd := b AND b\ne := c AND ?\nf := e OR c\ng := 011110\nh := d XOR ?\ni := 010111\nj := 000011\nk := d OR ?\nl := 011101\nm := b OR j\n",
"2 109\na := 1010101010100000000000011111111111111111111111111111111111111111111000000000000000000000000000111111111111111\nb := ? XOR a\n",
"16 3\na := 011\nb := 110\nc := a XOR b\nd := 110\ne := a XOR b\nf := b XOR a\ng := b XOR e\nh := 111\ni := a XOR h\nj := f XOR ?\nk := 100\nl := 000\nm := 100\nn := 110\no := 110\np := 110\n",
"1 2\na := ? OR ?\n",
"1 10\na := 0110111011\n",
"2 109\na := 1010101010100000000000011111111111111111111111111111111111111101111000000000000000000000000000111111111111111\nb := ? XOR a\n",
"12 14\na := 01100010000111\nb := ? XOR a\nc := 01101111001010\nd := ? XOR c\ne := 10000011101111\nf := ? XOR e\ng := 10100011001110\nh := ? XOR g\ni := 10010110111111\nj := ? XOR i\nk := 10000111110001\nl := ? XOR k\n",
"22 9\na := 100101111\nb := 010001000\nc := b AND b\nd := 111000010\ne := c AND a\nf := a OR e\ng := e AND ?\nh := 000010001\ni := b OR ?\nj := d AND ?\nk := g AND h\nl := 010100000\nm := a AND a\nn := j AND ?\no := m OR n\np := o AND ?\nq := f OR ?\nr := 000011011\ns := 001110011\nt := 100111100\nu := l AND p\nv := g OR h\n",
"16 3\na := 011\nb := 110\nc := a XOR b\nd := 110\ne := a XOR b\nf := b XOR a\ng := b XOR e\nh := 111\ni := a XOR h\nj := f XOR ?\nk := 100\nl := 000\nm := 100\nn := 111\no := 110\np := 110\n",
"2 109\na := 1010101010100000000000011111111111111111111111111111111111111101111000000000000000000000000000111111111101111\nb := ? XOR a\n",
"12 14\na := 01100010000111\nb := ? XOR a\nc := 01001111001010\nd := ? XOR c\ne := 10000011101111\nf := ? XOR e\ng := 10100011001110\nh := ? XOR g\ni := 10010110111111\nj := ? XOR i\nk := 10000111110001\nl := ? XOR k\n",
"12 14\na := 01100010000111\nb := ? XOR a\nc := 01101111001010\nd := ? XOR c\ne := 10000011101111\nf := ? XOR e\ng := 11100011001010\nh := ? XOR g\ni := 10010110111111\nj := ? XOR i\nk := 10000111110001\nl := ? XOR k\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\nd := 010110101110110\ne := 111111000010110\nf := 011001110111110\ng := 110011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110010\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 111001110011001\nq := 000100110001000\n",
"1 6\na := 1110111001\n",
"1 4\n_ := ? OR ?\n",
"3 3\na := 100\nb := 011\nc := ? XOR b\n",
"1 7\na := 1110111001\n",
"1 10\na := 0110111001\n",
"1 10\n` := 0110111011\n",
"1 10\na := 1110111001\n",
"1 10\n` := 0110101011\n",
"1 10\na := 1010111001\n",
"1 10\na := 0110101011\n",
"1 10\na := 1010110001\n",
"1 10\nb := 0110101011\n",
"1 10\na := 1000110001\n",
"16 3\na := 011\nb := 110\nc := a XOR b\nd := 110\ne := a XOR b\nf := b XOR a\ng := b XOR e\nh := 111\ni := a XOR h\nj := e XOR ?\nk := 100\nl := 000\nm := 100\nn := 110\no := 110\np := 110\n",
"1 2\n` := ? OR ?\n",
"1 10\na := 0110111111\n",
"1 10\na := 0110101010\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\nd := 010110101110110\ne := 111111000010110\nf := 011001110111110\ng := 010011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110010\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 111001110011001\nq := 000100110001000\n",
"1 2\n_ := ? OR ?\n",
"1 6\na := 1110011001\n",
"1 10\na := 0110111010\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\nd := 010110101110110\ne := 111111000010110\nf := 011001110111110\ng := 010011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110010\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 110001110011001\nq := 000100110001000\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\nd := 010110101110110\ne := 110111000010110\nf := 011001110111110\ng := 110011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110110\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 111001110011001\nq := 000100110001000\n",
"1 10\n` := 0110111001\n",
"1 10\n` := 0110011011\n",
"1 10\nb := 1110111001\n",
"1 10\na := 1010110101\n",
"1 10\nc := 0110101011\n",
"17 15\na := 010000111111110\nb := 101100110000100\nc := 100101100100111\ne := 010110101110110\ne := 111111000010110\nf := 011001110111110\ng := 110011010100101\nh := 000001010010001\ni := 110000111001011\nj := 000010000010111\nk := 110110111110010\nl := 010000110000100\nm := 000111101101000\nn := 011111011000111\no := 010110110010100\np := 111001110011001\nq := 000100110001000\n",
"16 3\na := 011\nb := 110\nc := a XOR b\nd := 110\ne := a XOR b\nf := b XOR a\ng := b XOR e\nh := 101\ni := a XOR h\nj := e XOR ?\nk := 100\nl := 000\nm := 100\nn := 110\no := 110\np := 110\n"
],
"output": [
"011\n100\n",
"0\n0\n",
"000000\n111111\n",
"00\n11\n",
"10000011001011\n01011000010000\n",
"0000000000\n0000000000\n",
"000000000000000\n000000000000000\n",
"0100101101\n1011010010\n",
"11110011011001\n00001100100110\n",
"000000000\n111111111\n",
"00101111\n11010000\n",
"000\n111\n",
"001\n110\n",
"100000\n011011\n",
"1010101010100000000000011111111111111111111111111111111111111111111000000000000000000000000000111111111111111\n0101010101011111111111100000000000000000000000000000000000000000000111111111111111111111111111000000000000000\n",
"101\n010\n",
"00\n11\n",
"0000000000\n0000000000\n",
"1010101010100000000000011111111111111111111111111111111111111101111000000000000000000000000000111111111111111\n0101010101011111111111100000000000000000000000000000000000000010000111111111111111111111111111000000000000000\n",
"10000011001111\n01011000010000\n",
"000000000\n111111111\n",
"101\n010\n",
"1010101010100000000000011111111111111111111111111111111111111101111000000000000000000000000000111111111101111\n0101010101011111111111100000000000000000000000000000000000000010000111111111111111111111111111000000000010000\n",
"10000011001111\n01111000010000\n",
"10000011001011\n00011000010000\n",
"000000000000000\n000000000000000\n",
"000000\n000000\n",
"0000\n1111\n",
"011\n100\n",
"0000000\n0000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"101\n010\n",
"00\n11\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"000000000000000\n000000000000000\n",
"00\n11\n",
"000000\n000000\n",
"0000000000\n0000000000\n",
"000000000000000\n000000000000000\n",
"000000000000000\n000000000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"0000000000\n0000000000\n",
"000000000000000\n000000000000000\n",
"101\n010\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bob recently read about bitwise operations used in computers: AND, OR and XOR. He have studied their properties and invented a new game.
Initially, Bob chooses integer m, bit depth of the game, which means that all numbers in the game will consist of m bits. Then he asks Peter to choose some m-bit number. After that, Bob computes the values of n variables. Each variable is assigned either a constant m-bit number or result of bitwise operation. Operands of the operation may be either variables defined before, or the number, chosen by Peter. After that, Peter's score equals to the sum of all variable values.
Bob wants to know, what number Peter needs to choose to get the minimum possible score, and what number he needs to choose to get the maximum possible score. In both cases, if there are several ways to get the same score, find the minimum number, which he can choose.
Input
The first line contains two integers n and m, the number of variables and bit depth, respectively (1 ≤ n ≤ 5000; 1 ≤ m ≤ 1000).
The following n lines contain descriptions of the variables. Each line describes exactly one variable. Description has the following format: name of a new variable, space, sign ":=", space, followed by one of:
1. Binary number of exactly m bits.
2. The first operand, space, bitwise operation ("AND", "OR" or "XOR"), space, the second operand. Each operand is either the name of variable defined before or symbol '?', indicating the number chosen by Peter.
Variable names are strings consisting of lowercase Latin letters with length at most 10. All variable names are different.
Output
In the first line output the minimum number that should be chosen by Peter, to make the sum of all variable values minimum possible, in the second line output the minimum number that should be chosen by Peter, to make the sum of all variable values maximum possible. Both numbers should be printed as m-bit binary numbers.
Examples
Input
3 3
a := 101
b := 011
c := ? XOR b
Output
011
100
Input
5 1
a := 1
bb := 0
cx := ? OR a
d := ? XOR ?
e := d AND bb
Output
0
0
Note
In the first sample if Peter chooses a number 0112, then a = 1012, b = 0112, c = 0002, the sum of their values is 8. If he chooses the number 1002, then a = 1012, b = 0112, c = 1112, the sum of their values is 15.
For the second test, the minimum and maximum sum of variables a, bb, cx, d and e is 2, and this sum doesn't depend on the number chosen by Peter, so the minimum Peter can choose is 0.
### Input:
3 3
a := 101
b := 011
c := ? XOR b
### Output:
011
100
### Input:
5 1
a := 1
bb := 0
cx := ? OR a
d := ? XOR ?
e := d AND bb
### Output:
0
0
### Code:
n, m = map(int, input().split())
v = [('?', '')]
temp = [(0, 1)]
d = {}
d['?'] = 0
mn, mx = '', ''
for i in range(n):
name, val = input().split(' := ')
v.append((name, val.split()))
temp.append((-1, -1))
d[name] = i + 1
def eval(expr, bit1, bit2):
if expr == 'OR':
return bit1 | bit2
elif expr == 'AND':
return bit1 and bit2
elif expr == 'XOR':
return bit1 ^ bit2
else:
raise AttributeError()
for i in range(m):
for name, expr in v[1:]:
j = d[name]
if len(expr) == 1:
temp[j] = (int(expr[0][i]), int(expr[0][i]))
else:
bit1, bit2 = temp[d[expr[0]]], temp[d[expr[2]]]
temp[j] = (eval(expr[1], bit1[0], bit2[0]), eval(expr[1], bit1[1], bit2[1]))
z, o = sum(temp[_][0] for _ in range(1, n + 1)), sum(temp[_][1] for _ in range(1, n + 1))
mn += '1' if o < z else '0'
mx += '1' if o > z else '0'
print(mn)
print(mx)
|
802_M. April Fools' Problem (easy)_28390
|
The marmots have prepared a very easy problem for this year's HC2 – this one. It involves numbers n, k and a sequence of n positive integers a1, a2, ..., an. They also came up with a beautiful and riveting story for the problem statement. It explains what the input means, what the program should output, and it also reads like a good criminal.
However I, Heidi, will have none of that. As my joke for today, I am removing the story from the statement and replacing it with these two unhelpful paragraphs. Now solve the problem, fools!
Input
The first line of the input contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 2200). The second line contains n space-separated integers a1, ..., an (1 ≤ ai ≤ 104).
Output
Output one number.
Examples
Input
8 5
1 1 1 1 1 1 1 1
Output
5
Input
10 3
16 8 2 4 512 256 32 128 64 1
Output
7
Input
5 1
20 10 50 30 46
Output
10
Input
6 6
6 6 6 6 6 6
Output
36
Input
1 1
100
Output
100
|
n,k=map(int,input().split());print(sum(sorted(list(map(int,input().split())))[:k]))
|
{
"input": [
"8 5\n1 1 1 1 1 1 1 1\n",
"10 3\n16 8 2 4 512 256 32 128 64 1\n",
"6 6\n6 6 6 6 6 6\n",
"1 1\n100\n",
"5 1\n20 10 50 30 46\n",
"10 5\n147 1917 5539 7159 5763 416 711 1412 6733 4402\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 9332 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 6510 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 1877 2897 6115 3191 2878 9258 2849 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"1 1\n1\n",
"10 5\n88 1917 5539 7159 5763 416 711 1412 6733 4402\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 9332 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 9244 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 1877 2897 6115 3191 2878 9258 2849 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"1 1\n2\n",
"8 5\n2 1 1 1 1 1 1 1\n",
"10 3\n16 8 2 4 250 256 32 128 64 1\n",
"6 6\n6 11 6 6 6 6\n",
"1 0\n100\n",
"4 1\n20 10 50 30 46\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 9332 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 9244 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2849 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"8 5\n2 1 1 1 1 1 0 1\n",
"6 6\n6 11 1 6 6 6\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 9332 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 9244 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"6 6\n6 11 0 6 6 6\n",
"10 5\n88 1980 5539 7159 6530 416 711 1412 6733 3335\n",
"6 6\n6 21 0 6 6 6\n",
"10 5\n5 1980 5539 7159 6530 416 711 1412 6733 3335\n",
"10 3\n29 8 2 4 000 186 32 128 64 1\n",
"6 6\n4 21 0 6 6 6\n",
"10 5\n5 2814 5539 7159 6530 416 711 1412 6733 3335\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"100 60\n313 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 5\n5 2814 129 7159 6530 416 711 1412 6733 4940\n",
"10 5\n5 2814 129 7159 6530 416 711 1716 6733 4940\n",
"100 60\n313 3849 6174 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 44 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 44 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 44 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 44 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"5 2\n15 5 69 17 46\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 5\n5 7032 129 7159 6530 271 711 1716 6733 4475\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 5\n5 7032 158 7159 6530 271 711 1716 6733 4475\n",
"100 60\n313 3849 9072 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"5 2\n15 4 69 5 46\n",
"10 5\n5 7032 158 7159 6530 319 711 1716 6733 4475\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 7\n5 7032 158 7159 6530 319 711 1716 6733 4475\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"5 4\n7 4 69 5 46\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 985 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 7\n5 1674 158 7159 6530 319 711 1716 6646 4475\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 985 1203 12615 7088 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 2751 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 985 1203 12615 3301 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 2751 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 7\n5 1674 158 9567 6530 319 711 634 6646 4475\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 985 1203 12615 3301 5429 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 6481 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 2751 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 7\n5 1674 158 9567 6530 319 711 683 6646 4475\n",
"10 7\n5 1674 158 9567 6530 319 711 369 6646 4475\n",
"100 60\n313 3849 9072 13256 696 4508 3461 9159 4468 2496 3044 2301 810 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 985 1203 12615 3301 5429 3860 2794 8014 6951 1160 8616 970 10154 2421 17193 4885 5246 6146 8849 6481 8602 9486 7257 3300 5373 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 4106 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 1648 9258 2303 8103 6678 8714 8024 44 9894 504 6759 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 5\n88 1917 5539 7159 5763 416 711 1412 6733 3335\n",
"1 0\n1\n",
"10 3\n16 8 2 4 100 256 32 128 64 1\n",
"1 1\n000\n",
"4 1\n20 10 75 30 46\n",
"10 5\n88 1917 5539 7159 6530 416 711 1412 6733 3335\n",
"1 0\n0\n",
"8 5\n3 1 1 1 1 1 0 1\n",
"10 3\n16 8 2 4 100 186 32 128 64 1\n",
"4 1\n18 10 75 30 46\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 9332 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"8 5\n3 1 1 1 1 1 1 1\n",
"10 3\n29 8 2 4 100 186 32 128 64 1\n",
"4 1\n18 10 75 43 46\n",
"100 60\n1443 3849 6174 8249 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3823 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"8 5\n3 1 1 1 2 1 1 1\n",
"5 1\n18 10 75 43 46\n",
"8 5\n3 1 1 1 2 1 2 1\n",
"10 3\n29 8 2 4 000 186 32 128 48 1\n",
"5 1\n18 3 75 43 46\n",
"10 5\n5 2814 5539 7159 6530 416 711 1412 6733 4940\n",
"8 5\n3 1 1 1 2 1 3 1\n",
"10 4\n29 8 2 4 000 186 32 128 48 1\n",
"5 1\n18 3 69 43 46\n",
"100 60\n313 3849 6174 13256 696 8715 3461 9159 4468 2496 3044 2301 2437 7559 7235 7956 8959 2036 4399 9595 8664 9743 7688 3730 3705 1203 12615 7088 8563 3860 2794 8014 6951 1160 8616 970 9885 2421 17193 4885 5246 6146 8849 5141 8602 9486 7257 3300 8323 4797 4082 7135 80 9622 4543 6567 2747 5013 4626 9091 9028 9851 1654 7021 6843 3209 5350 3809 4697 4617 4450 81 5208 2228 2897 6115 3191 2878 9258 2303 8103 6678 8714 8024 80 9894 321 8074 6797 457 1348 8652 811 7215 4381 5000 7406 7899 9974 844\n",
"10 4\n29 8 2 7 000 186 32 128 48 1\n",
"5 1\n15 3 69 43 46\n",
"10 3\n29 8 2 7 000 186 32 128 48 1\n",
"5 1\n15 5 69 43 46\n",
"10 5\n5 3662 129 7159 6530 416 711 1716 6733 4940\n",
"10 3\n5 8 2 7 000 186 32 128 48 1\n",
"5 1\n15 5 69 67 46\n",
"10 5\n5 3662 129 7159 6530 416 711 1716 6733 4552\n",
"10 3\n5 14 2 7 000 186 32 128 48 1\n",
"5 1\n15 5 69 17 46\n",
"10 5\n5 3662 129 7159 6530 416 711 1716 6733 4475\n",
"10 3\n5 14 2 7 000 186 32 128 90 1\n",
"10 5\n5 7032 129 7159 6530 416 711 1716 6733 4475\n",
"10 3\n5 14 2 12 000 186 32 128 90 1\n",
"5 2\n15 5 69 21 46\n",
"10 3\n5 14 2 12 000 186 32 128 113 1\n",
"5 2\n15 5 69 5 46\n",
"10 3\n5 14 2 12 000 100 32 128 113 1\n",
"10 3\n5 14 2 12 000 100 32 128 113 0\n",
"5 2\n7 4 69 5 46\n",
"10 3\n5 14 2 12 000 100 33 128 113 0\n",
"10 7\n5 7032 158 7159 6530 319 711 1716 6646 4475\n",
"10 3\n5 14 2 12 000 100 33 128 145 0\n",
"10 2\n5 14 2 12 000 100 33 128 145 0\n",
"10 7\n5 1674 158 9567 6530 319 711 1716 6646 4475\n",
"10 2\n5 14 0 12 000 100 33 128 145 0\n",
"10 2\n5 21 0 12 000 100 33 128 145 0\n"
],
"output": [
"5",
"7",
"36",
"100",
"10",
"4603",
"206735",
"1",
"4544\n",
"207176\n",
"2\n",
"5\n",
"7\n",
"41\n",
"0\n",
"10\n",
"207527\n",
"4\n",
"36\n",
"206981\n",
"35\n",
"4607\n",
"45\n",
"4524\n",
"3\n",
"43\n",
"5358\n",
"207018\n",
"205888\n",
"2673\n",
"2977\n",
"205852\n",
"206699\n",
"205107\n",
"203529\n",
"20\n",
"202299\n",
"2832\n",
"202482\n",
"2861\n",
"202398\n",
"9\n",
"2909\n",
"200109\n",
"13914\n",
"198482\n",
"62\n",
"195762\n",
"9058\n",
"191754\n",
"188377\n",
"7976\n",
"189717\n",
"8025\n",
"7711\n",
"191072\n",
"4544\n",
"0\n",
"7\n",
"0\n",
"10\n",
"4544\n",
"0\n",
"4\n",
"7\n",
"10\n",
"206981\n",
"5\n",
"7\n",
"10\n",
"206981\n",
"5\n",
"10\n",
"5\n",
"3\n",
"3\n",
"5358\n",
"5\n",
"7\n",
"3\n",
"205888\n",
"10\n",
"3\n",
"3\n",
"5\n",
"2977\n",
"3\n",
"5\n",
"2977\n",
"3\n",
"5\n",
"2977\n",
"3\n",
"2977\n",
"3\n",
"20\n",
"3\n",
"10\n",
"3\n",
"2\n",
"9\n",
"2\n",
"13914\n",
"2\n",
"0\n",
"9058\n",
"0\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The marmots have prepared a very easy problem for this year's HC2 – this one. It involves numbers n, k and a sequence of n positive integers a1, a2, ..., an. They also came up with a beautiful and riveting story for the problem statement. It explains what the input means, what the program should output, and it also reads like a good criminal.
However I, Heidi, will have none of that. As my joke for today, I am removing the story from the statement and replacing it with these two unhelpful paragraphs. Now solve the problem, fools!
Input
The first line of the input contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 2200). The second line contains n space-separated integers a1, ..., an (1 ≤ ai ≤ 104).
Output
Output one number.
Examples
Input
8 5
1 1 1 1 1 1 1 1
Output
5
Input
10 3
16 8 2 4 512 256 32 128 64 1
Output
7
Input
5 1
20 10 50 30 46
Output
10
Input
6 6
6 6 6 6 6 6
Output
36
Input
1 1
100
Output
100
### Input:
8 5
1 1 1 1 1 1 1 1
### Output:
5
### Input:
10 3
16 8 2 4 512 256 32 128 64 1
### Output:
7
### Code:
n,k=map(int,input().split());print(sum(sorted(list(map(int,input().split())))[:k]))
|
827_B. High Load_28394
|
Arkady needs your help again! This time he decided to build his own high-speed Internet exchange point. It should consist of n nodes connected with minimum possible number of wires into one network (a wire directly connects two nodes). Exactly k of the nodes should be exit-nodes, that means that each of them should be connected to exactly one other node of the network, while all other nodes should be connected to at least two nodes in order to increase the system stability.
Arkady wants to make the system as fast as possible, so he wants to minimize the maximum distance between two exit-nodes. The distance between two nodes is the number of wires a package needs to go through between those two nodes.
Help Arkady to find such a way to build the network that the distance between the two most distant exit-nodes is as small as possible.
Input
The first line contains two integers n and k (3 ≤ n ≤ 2·105, 2 ≤ k ≤ n - 1) — the total number of nodes and the number of exit-nodes.
Note that it is always possible to build at least one network with n nodes and k exit-nodes within the given constraints.
Output
In the first line print the minimum possible distance between the two most distant exit-nodes. In each of the next n - 1 lines print two integers: the ids of the nodes connected by a wire. The description of each wire should be printed exactly once. You can print wires and wires' ends in arbitrary order. The nodes should be numbered from 1 to n. Exit-nodes can have any ids.
If there are multiple answers, print any of them.
Examples
Input
3 2
Output
2
1 2
2 3
Input
5 3
Output
3
1 2
2 3
3 4
3 5
Note
In the first example the only network is shown on the left picture.
In the second example one of optimal networks is shown on the right picture.
Exit-nodes are highlighted.
<image>
|
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**9+7
Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
n,k = Ri()
lis = [i for i in range(k)]
ans = []
cur = k
totans = 0
while True:
tlis = []
while len(lis):
if cur == n-1: break
# temp =
ans.append((lis[-1], cur))
tlis.append(cur)
cur+=1
lis.pop()
if len(lis) != 0:
for i in tlis:
ans.append((i, cur))
for i in lis:
ans.append((i, cur))
if len(tlis) == 1:
totans+=2
totans = totans+(totans-1)
elif len(tlis) >= 2:
totans+=2
totans = totans*2
else:
# print(totans)
totans+=1
totans = 2*totans
break
lis = tlis
totans+=1
print(totans)
for i in ans:
print(i[0]+1, i[1]+1)
|
{
"input": [
"5 3\n",
"3 2\n",
"5 2\n",
"1013 2\n",
"1000 999\n",
"4 2\n",
"1000 5\n",
"7 6\n",
"1024 511\n",
"7 5\n",
"1024 512\n",
"6 4\n",
"7 4\n",
"1013 16\n",
"1024 513\n",
"7 3\n",
"1000 670\n",
"100 99\n",
"10 6\n",
"1013 23\n",
"7 2\n",
"1024 1023\n",
"1024 16\n",
"1024 23\n",
"1000 998\n",
"1013 508\n",
"6 5\n",
"1013 507\n",
"100 59\n",
"100 98\n",
"4 3\n",
"1013 1012\n",
"100 5\n",
"5 4\n",
"6 2\n",
"1000 245\n",
"1024 2\n",
"1000 2\n",
"100 2\n",
"6 3\n",
"8 2\n",
"555 2\n",
"1010 999\n",
"1000 10\n",
"1024 725\n",
"1024 557\n",
"10 4\n",
"1912 16\n",
"996 513\n",
"1010 670\n",
"110 99\n",
"1013 14\n",
"140 16\n",
"1892 23\n",
"1000 285\n",
"587 508\n",
"575 507\n",
"100 66\n",
"10 3\n",
"1234 1012\n",
"110 5\n",
"1100 245\n",
"1131 2\n",
"101 2\n",
"8 3\n",
"598 2\n",
"1000 11\n",
"1024 446\n",
"1024 579\n",
"10 5\n",
"1912 20\n",
"996 177\n",
"1261 14\n",
"140 32\n",
"1457 23\n",
"1000 269\n",
"575 488\n",
"101 66\n",
"1100 368\n",
"12 3\n",
"1000 8\n",
"1024 271\n",
"756 579\n",
"10 7\n",
"1071 20\n",
"996 324\n",
"1261 21\n",
"140 36\n",
"1457 5\n",
"010 5\n"
],
"output": [
"3\n1 2\n1 3\n1 4\n2 5\n",
"2\n1 2\n1 3\n",
"4\n1 2\n1 3\n2 4\n3 5\n",
"1012\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n554 556\n555 557\n556 558\n557 559\n558 560\n559 561\n560 562\n561 563\n562 564\n563 565\n564 566\n565 567\n566 568\n567 569\n568 570\n569 571\n570 572\n571 573\n572 574\n573 575\n574 576\n575 577\n576 578\n577 579\n578 580\n579 581\n580 582\n581 583\n582 584\n583 585\n584 586\n585 587\n586 588\n587 589\n588 590\n589 591\n590 592\n591 593\n592 594\n593 595\n594 596\n595 597\n596 598\n597 599\n598 600\n599 601\n600 602\n601 603\n602 604\n603 605\n604 606\n605 607\n606 608\n607 609\n608 610\n609 611\n610 612\n611 613\n612 614\n613 615\n614 616\n615 617\n616 618\n617 619\n618 620\n619 621\n620 622\n621 623\n622 624\n623 625\n624 626\n625 627\n626 628\n627 629\n628 630\n629 631\n630 632\n631 633\n632 634\n633 635\n634 636\n635 637\n636 638\n637 639\n638 640\n639 641\n640 642\n641 643\n642 644\n643 645\n644 646\n645 647\n646 648\n647 649\n648 650\n649 651\n650 652\n651 653\n652 654\n653 655\n654 656\n655 657\n656 658\n657 659\n658 660\n659 661\n660 662\n661 663\n662 664\n663 665\n664 666\n665 667\n666 668\n667 669\n668 670\n669 671\n670 672\n671 673\n672 674\n673 675\n674 676\n675 677\n676 678\n677 679\n678 680\n679 681\n680 682\n681 683\n682 684\n683 685\n684 686\n685 687\n686 688\n687 689\n688 690\n689 691\n690 692\n691 693\n692 694\n693 695\n694 696\n695 697\n696 698\n697 699\n698 700\n699 701\n700 702\n701 703\n702 704\n703 705\n704 706\n705 707\n706 708\n707 709\n708 710\n709 711\n710 712\n711 713\n712 714\n713 715\n714 716\n715 717\n716 718\n717 719\n718 720\n719 721\n720 722\n721 723\n722 724\n723 725\n724 726\n725 727\n726 728\n727 729\n728 730\n729 731\n730 732\n731 733\n732 734\n733 735\n734 736\n735 737\n736 738\n737 739\n738 740\n739 741\n740 742\n741 743\n742 744\n743 745\n744 746\n745 747\n746 748\n747 749\n748 750\n749 751\n750 752\n751 753\n752 754\n753 755\n754 756\n755 757\n756 758\n757 759\n758 760\n759 761\n760 762\n761 763\n762 764\n763 765\n764 766\n765 767\n766 768\n767 769\n768 770\n769 771\n770 772\n771 773\n772 774\n773 775\n774 776\n775 777\n776 778\n777 779\n778 780\n779 781\n780 782\n781 783\n782 784\n783 785\n784 786\n785 787\n786 788\n787 789\n788 790\n789 791\n790 792\n791 793\n792 794\n793 795\n794 796\n795 797\n796 798\n797 799\n798 800\n799 801\n800 802\n801 803\n802 804\n803 805\n804 806\n805 807\n806 808\n807 809\n808 810\n809 811\n810 812\n811 813\n812 814\n813 815\n814 816\n815 817\n816 818\n817 819\n818 820\n819 821\n820 822\n821 823\n822 824\n823 825\n824 826\n825 827\n826 828\n827 829\n828 830\n829 831\n830 832\n831 833\n832 834\n833 835\n834 836\n835 837\n836 838\n837 839\n838 840\n839 841\n840 842\n841 843\n842 844\n843 845\n844 846\n845 847\n846 848\n847 849\n848 850\n849 851\n850 852\n851 853\n852 854\n853 855\n854 856\n855 857\n856 858\n857 859\n858 860\n859 861\n860 862\n861 863\n862 864\n863 865\n864 866\n865 867\n866 868\n867 869\n868 870\n869 871\n870 872\n871 873\n872 874\n873 875\n874 876\n875 877\n876 878\n877 879\n878 880\n879 881\n880 882\n881 883\n882 884\n883 885\n884 886\n885 887\n886 888\n887 889\n888 890\n889 891\n890 892\n891 893\n892 894\n893 895\n894 896\n895 897\n896 898\n897 899\n898 900\n899 901\n900 902\n901 903\n902 904\n903 905\n904 906\n905 907\n906 908\n907 909\n908 910\n909 911\n910 912\n911 913\n912 914\n913 915\n914 916\n915 917\n916 918\n917 919\n918 920\n919 921\n920 922\n921 923\n922 924\n923 925\n924 926\n925 927\n926 928\n927 929\n928 930\n929 931\n930 932\n931 933\n932 934\n933 935\n934 936\n935 937\n936 938\n937 939\n938 940\n939 941\n940 942\n941 943\n942 944\n943 945\n944 946\n945 947\n946 948\n947 949\n948 950\n949 951\n950 952\n951 953\n952 954\n953 955\n954 956\n955 957\n956 958\n957 959\n958 960\n959 961\n960 962\n961 963\n962 964\n963 965\n964 966\n965 967\n966 968\n967 969\n968 970\n969 971\n970 972\n971 973\n972 974\n973 975\n974 976\n975 977\n976 978\n977 979\n978 980\n979 981\n980 982\n981 983\n982 984\n983 985\n984 986\n985 987\n986 988\n987 989\n988 990\n989 991\n990 992\n991 993\n992 994\n993 995\n994 996\n995 997\n996 998\n997 999\n998 1000\n999 1001\n1000 1002\n1001 1003\n1002 1004\n1003 1005\n1004 1006\n1005 1007\n1006 1008\n1007 1009\n1008 1010\n1009 1011\n1010 1012\n1011 1013\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n1 1000\n",
"3\n1 2\n1 3\n2 4\n",
"400\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n6 11\n7 12\n8 13\n9 14\n10 15\n11 16\n12 17\n13 18\n14 19\n15 20\n16 21\n17 22\n18 23\n19 24\n20 25\n21 26\n22 27\n23 28\n24 29\n25 30\n26 31\n27 32\n28 33\n29 34\n30 35\n31 36\n32 37\n33 38\n34 39\n35 40\n36 41\n37 42\n38 43\n39 44\n40 45\n41 46\n42 47\n43 48\n44 49\n45 50\n46 51\n47 52\n48 53\n49 54\n50 55\n51 56\n52 57\n53 58\n54 59\n55 60\n56 61\n57 62\n58 63\n59 64\n60 65\n61 66\n62 67\n63 68\n64 69\n65 70\n66 71\n67 72\n68 73\n69 74\n70 75\n71 76\n72 77\n73 78\n74 79\n75 80\n76 81\n77 82\n78 83\n79 84\n80 85\n81 86\n82 87\n83 88\n84 89\n85 90\n86 91\n87 92\n88 93\n89 94\n90 95\n91 96\n92 97\n93 98\n94 99\n95 100\n96 101\n97 102\n98 103\n99 104\n100 105\n101 106\n102 107\n103 108\n104 109\n105 110\n106 111\n107 112\n108 113\n109 114\n110 115\n111 116\n112 117\n113 118\n114 119\n115 120\n116 121\n117 122\n118 123\n119 124\n120 125\n121 126\n122 127\n123 128\n124 129\n125 130\n126 131\n127 132\n128 133\n129 134\n130 135\n131 136\n132 137\n133 138\n134 139\n135 140\n136 141\n137 142\n138 143\n139 144\n140 145\n141 146\n142 147\n143 148\n144 149\n145 150\n146 151\n147 152\n148 153\n149 154\n150 155\n151 156\n152 157\n153 158\n154 159\n155 160\n156 161\n157 162\n158 163\n159 164\n160 165\n161 166\n162 167\n163 168\n164 169\n165 170\n166 171\n167 172\n168 173\n169 174\n170 175\n171 176\n172 177\n173 178\n174 179\n175 180\n176 181\n177 182\n178 183\n179 184\n180 185\n181 186\n182 187\n183 188\n184 189\n185 190\n186 191\n187 192\n188 193\n189 194\n190 195\n191 196\n192 197\n193 198\n194 199\n195 200\n196 201\n197 202\n198 203\n199 204\n200 205\n201 206\n202 207\n203 208\n204 209\n205 210\n206 211\n207 212\n208 213\n209 214\n210 215\n211 216\n212 217\n213 218\n214 219\n215 220\n216 221\n217 222\n218 223\n219 224\n220 225\n221 226\n222 227\n223 228\n224 229\n225 230\n226 231\n227 232\n228 233\n229 234\n230 235\n231 236\n232 237\n233 238\n234 239\n235 240\n236 241\n237 242\n238 243\n239 244\n240 245\n241 246\n242 247\n243 248\n244 249\n245 250\n246 251\n247 252\n248 253\n249 254\n250 255\n251 256\n252 257\n253 258\n254 259\n255 260\n256 261\n257 262\n258 263\n259 264\n260 265\n261 266\n262 267\n263 268\n264 269\n265 270\n266 271\n267 272\n268 273\n269 274\n270 275\n271 276\n272 277\n273 278\n274 279\n275 280\n276 281\n277 282\n278 283\n279 284\n280 285\n281 286\n282 287\n283 288\n284 289\n285 290\n286 291\n287 292\n288 293\n289 294\n290 295\n291 296\n292 297\n293 298\n294 299\n295 300\n296 301\n297 302\n298 303\n299 304\n300 305\n301 306\n302 307\n303 308\n304 309\n305 310\n306 311\n307 312\n308 313\n309 314\n310 315\n311 316\n312 317\n313 318\n314 319\n315 320\n316 321\n317 322\n318 323\n319 324\n320 325\n321 326\n322 327\n323 328\n324 329\n325 330\n326 331\n327 332\n328 333\n329 334\n330 335\n331 336\n332 337\n333 338\n334 339\n335 340\n336 341\n337 342\n338 343\n339 344\n340 345\n341 346\n342 347\n343 348\n344 349\n345 350\n346 351\n347 352\n348 353\n349 354\n350 355\n351 356\n352 357\n353 358\n354 359\n355 360\n356 361\n357 362\n358 363\n359 364\n360 365\n361 366\n362 367\n363 368\n364 369\n365 370\n366 371\n367 372\n368 373\n369 374\n370 375\n371 376\n372 377\n373 378\n374 379\n375 380\n376 381\n377 382\n378 383\n379 384\n380 385\n381 386\n382 387\n383 388\n384 389\n385 390\n386 391\n387 392\n388 393\n389 394\n390 395\n391 396\n392 397\n393 398\n394 399\n395 400\n396 401\n397 402\n398 403\n399 404\n400 405\n401 406\n402 407\n403 408\n404 409\n405 410\n406 411\n407 412\n408 413\n409 414\n410 415\n411 416\n412 417\n413 418\n414 419\n415 420\n416 421\n417 422\n418 423\n419 424\n420 425\n421 426\n422 427\n423 428\n424 429\n425 430\n426 431\n427 432\n428 433\n429 434\n430 435\n431 436\n432 437\n433 438\n434 439\n435 440\n436 441\n437 442\n438 443\n439 444\n440 445\n441 446\n442 447\n443 448\n444 449\n445 450\n446 451\n447 452\n448 453\n449 454\n450 455\n451 456\n452 457\n453 458\n454 459\n455 460\n456 461\n457 462\n458 463\n459 464\n460 465\n461 466\n462 467\n463 468\n464 469\n465 470\n466 471\n467 472\n468 473\n469 474\n470 475\n471 476\n472 477\n473 478\n474 479\n475 480\n476 481\n477 482\n478 483\n479 484\n480 485\n481 486\n482 487\n483 488\n484 489\n485 490\n486 491\n487 492\n488 493\n489 494\n490 495\n491 496\n492 497\n493 498\n494 499\n495 500\n496 501\n497 502\n498 503\n499 504\n500 505\n501 506\n502 507\n503 508\n504 509\n505 510\n506 511\n507 512\n508 513\n509 514\n510 515\n511 516\n512 517\n513 518\n514 519\n515 520\n516 521\n517 522\n518 523\n519 524\n520 525\n521 526\n522 527\n523 528\n524 529\n525 530\n526 531\n527 532\n528 533\n529 534\n530 535\n531 536\n532 537\n533 538\n534 539\n535 540\n536 541\n537 542\n538 543\n539 544\n540 545\n541 546\n542 547\n543 548\n544 549\n545 550\n546 551\n547 552\n548 553\n549 554\n550 555\n551 556\n552 557\n553 558\n554 559\n555 560\n556 561\n557 562\n558 563\n559 564\n560 565\n561 566\n562 567\n563 568\n564 569\n565 570\n566 571\n567 572\n568 573\n569 574\n570 575\n571 576\n572 577\n573 578\n574 579\n575 580\n576 581\n577 582\n578 583\n579 584\n580 585\n581 586\n582 587\n583 588\n584 589\n585 590\n586 591\n587 592\n588 593\n589 594\n590 595\n591 596\n592 597\n593 598\n594 599\n595 600\n596 601\n597 602\n598 603\n599 604\n600 605\n601 606\n602 607\n603 608\n604 609\n605 610\n606 611\n607 612\n608 613\n609 614\n610 615\n611 616\n612 617\n613 618\n614 619\n615 620\n616 621\n617 622\n618 623\n619 624\n620 625\n621 626\n622 627\n623 628\n624 629\n625 630\n626 631\n627 632\n628 633\n629 634\n630 635\n631 636\n632 637\n633 638\n634 639\n635 640\n636 641\n637 642\n638 643\n639 644\n640 645\n641 646\n642 647\n643 648\n644 649\n645 650\n646 651\n647 652\n648 653\n649 654\n650 655\n651 656\n652 657\n653 658\n654 659\n655 660\n656 661\n657 662\n658 663\n659 664\n660 665\n661 666\n662 667\n663 668\n664 669\n665 670\n666 671\n667 672\n668 673\n669 674\n670 675\n671 676\n672 677\n673 678\n674 679\n675 680\n676 681\n677 682\n678 683\n679 684\n680 685\n681 686\n682 687\n683 688\n684 689\n685 690\n686 691\n687 692\n688 693\n689 694\n690 695\n691 696\n692 697\n693 698\n694 699\n695 700\n696 701\n697 702\n698 703\n699 704\n700 705\n701 706\n702 707\n703 708\n704 709\n705 710\n706 711\n707 712\n708 713\n709 714\n710 715\n711 716\n712 717\n713 718\n714 719\n715 720\n716 721\n717 722\n718 723\n719 724\n720 725\n721 726\n722 727\n723 728\n724 729\n725 730\n726 731\n727 732\n728 733\n729 734\n730 735\n731 736\n732 737\n733 738\n734 739\n735 740\n736 741\n737 742\n738 743\n739 744\n740 745\n741 746\n742 747\n743 748\n744 749\n745 750\n746 751\n747 752\n748 753\n749 754\n750 755\n751 756\n752 757\n753 758\n754 759\n755 760\n756 761\n757 762\n758 763\n759 764\n760 765\n761 766\n762 767\n763 768\n764 769\n765 770\n766 771\n767 772\n768 773\n769 774\n770 775\n771 776\n772 777\n773 778\n774 779\n775 780\n776 781\n777 782\n778 783\n779 784\n780 785\n781 786\n782 787\n783 788\n784 789\n785 790\n786 791\n787 792\n788 793\n789 794\n790 795\n791 796\n792 797\n793 798\n794 799\n795 800\n796 801\n797 802\n798 803\n799 804\n800 805\n801 806\n802 807\n803 808\n804 809\n805 810\n806 811\n807 812\n808 813\n809 814\n810 815\n811 816\n812 817\n813 818\n814 819\n815 820\n816 821\n817 822\n818 823\n819 824\n820 825\n821 826\n822 827\n823 828\n824 829\n825 830\n826 831\n827 832\n828 833\n829 834\n830 835\n831 836\n832 837\n833 838\n834 839\n835 840\n836 841\n837 842\n838 843\n839 844\n840 845\n841 846\n842 847\n843 848\n844 849\n845 850\n846 851\n847 852\n848 853\n849 854\n850 855\n851 856\n852 857\n853 858\n854 859\n855 860\n856 861\n857 862\n858 863\n859 864\n860 865\n861 866\n862 867\n863 868\n864 869\n865 870\n866 871\n867 872\n868 873\n869 874\n870 875\n871 876\n872 877\n873 878\n874 879\n875 880\n876 881\n877 882\n878 883\n879 884\n880 885\n881 886\n882 887\n883 888\n884 889\n885 890\n886 891\n887 892\n888 893\n889 894\n890 895\n891 896\n892 897\n893 898\n894 899\n895 900\n896 901\n897 902\n898 903\n899 904\n900 905\n901 906\n902 907\n903 908\n904 909\n905 910\n906 911\n907 912\n908 913\n909 914\n910 915\n911 916\n912 917\n913 918\n914 919\n915 920\n916 921\n917 922\n918 923\n919 924\n920 925\n921 926\n922 927\n923 928\n924 929\n925 930\n926 931\n927 932\n928 933\n929 934\n930 935\n931 936\n932 937\n933 938\n934 939\n935 940\n936 941\n937 942\n938 943\n939 944\n940 945\n941 946\n942 947\n943 948\n944 949\n945 950\n946 951\n947 952\n948 953\n949 954\n950 955\n951 956\n952 957\n953 958\n954 959\n955 960\n956 961\n957 962\n958 963\n959 964\n960 965\n961 966\n962 967\n963 968\n964 969\n965 970\n966 971\n967 972\n968 973\n969 974\n970 975\n971 976\n972 977\n973 978\n974 979\n975 980\n976 981\n977 982\n978 983\n979 984\n980 985\n981 986\n982 987\n983 988\n984 989\n985 990\n986 991\n987 992\n988 993\n989 994\n990 995\n991 996\n992 997\n993 998\n994 999\n995 1000\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n",
"5\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n2 513\n3 514\n4 515\n5 516\n6 517\n7 518\n8 519\n9 520\n10 521\n11 522\n12 523\n13 524\n14 525\n15 526\n16 527\n17 528\n18 529\n19 530\n20 531\n21 532\n22 533\n23 534\n24 535\n25 536\n26 537\n27 538\n28 539\n29 540\n30 541\n31 542\n32 543\n33 544\n34 545\n35 546\n36 547\n37 548\n38 549\n39 550\n40 551\n41 552\n42 553\n43 554\n44 555\n45 556\n46 557\n47 558\n48 559\n49 560\n50 561\n51 562\n52 563\n53 564\n54 565\n55 566\n56 567\n57 568\n58 569\n59 570\n60 571\n61 572\n62 573\n63 574\n64 575\n65 576\n66 577\n67 578\n68 579\n69 580\n70 581\n71 582\n72 583\n73 584\n74 585\n75 586\n76 587\n77 588\n78 589\n79 590\n80 591\n81 592\n82 593\n83 594\n84 595\n85 596\n86 597\n87 598\n88 599\n89 600\n90 601\n91 602\n92 603\n93 604\n94 605\n95 606\n96 607\n97 608\n98 609\n99 610\n100 611\n101 612\n102 613\n103 614\n104 615\n105 616\n106 617\n107 618\n108 619\n109 620\n110 621\n111 622\n112 623\n113 624\n114 625\n115 626\n116 627\n117 628\n118 629\n119 630\n120 631\n121 632\n122 633\n123 634\n124 635\n125 636\n126 637\n127 638\n128 639\n129 640\n130 641\n131 642\n132 643\n133 644\n134 645\n135 646\n136 647\n137 648\n138 649\n139 650\n140 651\n141 652\n142 653\n143 654\n144 655\n145 656\n146 657\n147 658\n148 659\n149 660\n150 661\n151 662\n152 663\n153 664\n154 665\n155 666\n156 667\n157 668\n158 669\n159 670\n160 671\n161 672\n162 673\n163 674\n164 675\n165 676\n166 677\n167 678\n168 679\n169 680\n170 681\n171 682\n172 683\n173 684\n174 685\n175 686\n176 687\n177 688\n178 689\n179 690\n180 691\n181 692\n182 693\n183 694\n184 695\n185 696\n186 697\n187 698\n188 699\n189 700\n190 701\n191 702\n192 703\n193 704\n194 705\n195 706\n196 707\n197 708\n198 709\n199 710\n200 711\n201 712\n202 713\n203 714\n204 715\n205 716\n206 717\n207 718\n208 719\n209 720\n210 721\n211 722\n212 723\n213 724\n214 725\n215 726\n216 727\n217 728\n218 729\n219 730\n220 731\n221 732\n222 733\n223 734\n224 735\n225 736\n226 737\n227 738\n228 739\n229 740\n230 741\n231 742\n232 743\n233 744\n234 745\n235 746\n236 747\n237 748\n238 749\n239 750\n240 751\n241 752\n242 753\n243 754\n244 755\n245 756\n246 757\n247 758\n248 759\n249 760\n250 761\n251 762\n252 763\n253 764\n254 765\n255 766\n256 767\n257 768\n258 769\n259 770\n260 771\n261 772\n262 773\n263 774\n264 775\n265 776\n266 777\n267 778\n268 779\n269 780\n270 781\n271 782\n272 783\n273 784\n274 785\n275 786\n276 787\n277 788\n278 789\n279 790\n280 791\n281 792\n282 793\n283 794\n284 795\n285 796\n286 797\n287 798\n288 799\n289 800\n290 801\n291 802\n292 803\n293 804\n294 805\n295 806\n296 807\n297 808\n298 809\n299 810\n300 811\n301 812\n302 813\n303 814\n304 815\n305 816\n306 817\n307 818\n308 819\n309 820\n310 821\n311 822\n312 823\n313 824\n314 825\n315 826\n316 827\n317 828\n318 829\n319 830\n320 831\n321 832\n322 833\n323 834\n324 835\n325 836\n326 837\n327 838\n328 839\n329 840\n330 841\n331 842\n332 843\n333 844\n334 845\n335 846\n336 847\n337 848\n338 849\n339 850\n340 851\n341 852\n342 853\n343 854\n344 855\n345 856\n346 857\n347 858\n348 859\n349 860\n350 861\n351 862\n352 863\n353 864\n354 865\n355 866\n356 867\n357 868\n358 869\n359 870\n360 871\n361 872\n362 873\n363 874\n364 875\n365 876\n366 877\n367 878\n368 879\n369 880\n370 881\n371 882\n372 883\n373 884\n374 885\n375 886\n376 887\n377 888\n378 889\n379 890\n380 891\n381 892\n382 893\n383 894\n384 895\n385 896\n386 897\n387 898\n388 899\n389 900\n390 901\n391 902\n392 903\n393 904\n394 905\n395 906\n396 907\n397 908\n398 909\n399 910\n400 911\n401 912\n402 913\n403 914\n404 915\n405 916\n406 917\n407 918\n408 919\n409 920\n410 921\n411 922\n412 923\n413 924\n414 925\n415 926\n416 927\n417 928\n418 929\n419 930\n420 931\n421 932\n422 933\n423 934\n424 935\n425 936\n426 937\n427 938\n428 939\n429 940\n430 941\n431 942\n432 943\n433 944\n434 945\n435 946\n436 947\n437 948\n438 949\n439 950\n440 951\n441 952\n442 953\n443 954\n444 955\n445 956\n446 957\n447 958\n448 959\n449 960\n450 961\n451 962\n452 963\n453 964\n454 965\n455 966\n456 967\n457 968\n458 969\n459 970\n460 971\n461 972\n462 973\n463 974\n464 975\n465 976\n466 977\n467 978\n468 979\n469 980\n470 981\n471 982\n472 983\n473 984\n474 985\n475 986\n476 987\n477 988\n478 989\n479 990\n480 991\n481 992\n482 993\n483 994\n484 995\n485 996\n486 997\n487 998\n488 999\n489 1000\n490 1001\n491 1002\n492 1003\n493 1004\n494 1005\n495 1006\n496 1007\n497 1008\n498 1009\n499 1010\n500 1011\n501 1012\n502 1013\n503 1014\n504 1015\n505 1016\n506 1017\n507 1018\n508 1019\n509 1020\n510 1021\n511 1022\n512 1023\n513 1024\n",
"3\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n2 514\n3 515\n4 516\n5 517\n6 518\n7 519\n8 520\n9 521\n10 522\n11 523\n12 524\n13 525\n14 526\n15 527\n16 528\n17 529\n18 530\n19 531\n20 532\n21 533\n22 534\n23 535\n24 536\n25 537\n26 538\n27 539\n28 540\n29 541\n30 542\n31 543\n32 544\n33 545\n34 546\n35 547\n36 548\n37 549\n38 550\n39 551\n40 552\n41 553\n42 554\n43 555\n44 556\n45 557\n46 558\n47 559\n48 560\n49 561\n50 562\n51 563\n52 564\n53 565\n54 566\n55 567\n56 568\n57 569\n58 570\n59 571\n60 572\n61 573\n62 574\n63 575\n64 576\n65 577\n66 578\n67 579\n68 580\n69 581\n70 582\n71 583\n72 584\n73 585\n74 586\n75 587\n76 588\n77 589\n78 590\n79 591\n80 592\n81 593\n82 594\n83 595\n84 596\n85 597\n86 598\n87 599\n88 600\n89 601\n90 602\n91 603\n92 604\n93 605\n94 606\n95 607\n96 608\n97 609\n98 610\n99 611\n100 612\n101 613\n102 614\n103 615\n104 616\n105 617\n106 618\n107 619\n108 620\n109 621\n110 622\n111 623\n112 624\n113 625\n114 626\n115 627\n116 628\n117 629\n118 630\n119 631\n120 632\n121 633\n122 634\n123 635\n124 636\n125 637\n126 638\n127 639\n128 640\n129 641\n130 642\n131 643\n132 644\n133 645\n134 646\n135 647\n136 648\n137 649\n138 650\n139 651\n140 652\n141 653\n142 654\n143 655\n144 656\n145 657\n146 658\n147 659\n148 660\n149 661\n150 662\n151 663\n152 664\n153 665\n154 666\n155 667\n156 668\n157 669\n158 670\n159 671\n160 672\n161 673\n162 674\n163 675\n164 676\n165 677\n166 678\n167 679\n168 680\n169 681\n170 682\n171 683\n172 684\n173 685\n174 686\n175 687\n176 688\n177 689\n178 690\n179 691\n180 692\n181 693\n182 694\n183 695\n184 696\n185 697\n186 698\n187 699\n188 700\n189 701\n190 702\n191 703\n192 704\n193 705\n194 706\n195 707\n196 708\n197 709\n198 710\n199 711\n200 712\n201 713\n202 714\n203 715\n204 716\n205 717\n206 718\n207 719\n208 720\n209 721\n210 722\n211 723\n212 724\n213 725\n214 726\n215 727\n216 728\n217 729\n218 730\n219 731\n220 732\n221 733\n222 734\n223 735\n224 736\n225 737\n226 738\n227 739\n228 740\n229 741\n230 742\n231 743\n232 744\n233 745\n234 746\n235 747\n236 748\n237 749\n238 750\n239 751\n240 752\n241 753\n242 754\n243 755\n244 756\n245 757\n246 758\n247 759\n248 760\n249 761\n250 762\n251 763\n252 764\n253 765\n254 766\n255 767\n256 768\n257 769\n258 770\n259 771\n260 772\n261 773\n262 774\n263 775\n264 776\n265 777\n266 778\n267 779\n268 780\n269 781\n270 782\n271 783\n272 784\n273 785\n274 786\n275 787\n276 788\n277 789\n278 790\n279 791\n280 792\n281 793\n282 794\n283 795\n284 796\n285 797\n286 798\n287 799\n288 800\n289 801\n290 802\n291 803\n292 804\n293 805\n294 806\n295 807\n296 808\n297 809\n298 810\n299 811\n300 812\n301 813\n302 814\n303 815\n304 816\n305 817\n306 818\n307 819\n308 820\n309 821\n310 822\n311 823\n312 824\n313 825\n314 826\n315 827\n316 828\n317 829\n318 830\n319 831\n320 832\n321 833\n322 834\n323 835\n324 836\n325 837\n326 838\n327 839\n328 840\n329 841\n330 842\n331 843\n332 844\n333 845\n334 846\n335 847\n336 848\n337 849\n338 850\n339 851\n340 852\n341 853\n342 854\n343 855\n344 856\n345 857\n346 858\n347 859\n348 860\n349 861\n350 862\n351 863\n352 864\n353 865\n354 866\n355 867\n356 868\n357 869\n358 870\n359 871\n360 872\n361 873\n362 874\n363 875\n364 876\n365 877\n366 878\n367 879\n368 880\n369 881\n370 882\n371 883\n372 884\n373 885\n374 886\n375 887\n376 888\n377 889\n378 890\n379 891\n380 892\n381 893\n382 894\n383 895\n384 896\n385 897\n386 898\n387 899\n388 900\n389 901\n390 902\n391 903\n392 904\n393 905\n394 906\n395 907\n396 908\n397 909\n398 910\n399 911\n400 912\n401 913\n402 914\n403 915\n404 916\n405 917\n406 918\n407 919\n408 920\n409 921\n410 922\n411 923\n412 924\n413 925\n414 926\n415 927\n416 928\n417 929\n418 930\n419 931\n420 932\n421 933\n422 934\n423 935\n424 936\n425 937\n426 938\n427 939\n428 940\n429 941\n430 942\n431 943\n432 944\n433 945\n434 946\n435 947\n436 948\n437 949\n438 950\n439 951\n440 952\n441 953\n442 954\n443 955\n444 956\n445 957\n446 958\n447 959\n448 960\n449 961\n450 962\n451 963\n452 964\n453 965\n454 966\n455 967\n456 968\n457 969\n458 970\n459 971\n460 972\n461 973\n462 974\n463 975\n464 976\n465 977\n466 978\n467 979\n468 980\n469 981\n470 982\n471 983\n472 984\n473 985\n474 986\n475 987\n476 988\n477 989\n478 990\n479 991\n480 992\n481 993\n482 994\n483 995\n484 996\n485 997\n486 998\n487 999\n488 1000\n489 1001\n490 1002\n491 1003\n492 1004\n493 1005\n494 1006\n495 1007\n496 1008\n497 1009\n498 1010\n499 1011\n500 1012\n501 1013\n502 1014\n503 1015\n504 1016\n505 1017\n506 1018\n507 1019\n508 1020\n509 1021\n510 1022\n511 1023\n512 1024\n",
"3\n1 2\n1 3\n1 4\n1 5\n2 6\n",
"4\n1 2\n1 3\n1 4\n1 5\n2 6\n3 7\n",
"128\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n2 18\n3 19\n4 20\n5 21\n6 22\n7 23\n8 24\n9 25\n10 26\n11 27\n12 28\n13 29\n14 30\n15 31\n16 32\n17 33\n18 34\n19 35\n20 36\n21 37\n22 38\n23 39\n24 40\n25 41\n26 42\n27 43\n28 44\n29 45\n30 46\n31 47\n32 48\n33 49\n34 50\n35 51\n36 52\n37 53\n38 54\n39 55\n40 56\n41 57\n42 58\n43 59\n44 60\n45 61\n46 62\n47 63\n48 64\n49 65\n50 66\n51 67\n52 68\n53 69\n54 70\n55 71\n56 72\n57 73\n58 74\n59 75\n60 76\n61 77\n62 78\n63 79\n64 80\n65 81\n66 82\n67 83\n68 84\n69 85\n70 86\n71 87\n72 88\n73 89\n74 90\n75 91\n76 92\n77 93\n78 94\n79 95\n80 96\n81 97\n82 98\n83 99\n84 100\n85 101\n86 102\n87 103\n88 104\n89 105\n90 106\n91 107\n92 108\n93 109\n94 110\n95 111\n96 112\n97 113\n98 114\n99 115\n100 116\n101 117\n102 118\n103 119\n104 120\n105 121\n106 122\n107 123\n108 124\n109 125\n110 126\n111 127\n112 128\n113 129\n114 130\n115 131\n116 132\n117 133\n118 134\n119 135\n120 136\n121 137\n122 138\n123 139\n124 140\n125 141\n126 142\n127 143\n128 144\n129 145\n130 146\n131 147\n132 148\n133 149\n134 150\n135 151\n136 152\n137 153\n138 154\n139 155\n140 156\n141 157\n142 158\n143 159\n144 160\n145 161\n146 162\n147 163\n148 164\n149 165\n150 166\n151 167\n152 168\n153 169\n154 170\n155 171\n156 172\n157 173\n158 174\n159 175\n160 176\n161 177\n162 178\n163 179\n164 180\n165 181\n166 182\n167 183\n168 184\n169 185\n170 186\n171 187\n172 188\n173 189\n174 190\n175 191\n176 192\n177 193\n178 194\n179 195\n180 196\n181 197\n182 198\n183 199\n184 200\n185 201\n186 202\n187 203\n188 204\n189 205\n190 206\n191 207\n192 208\n193 209\n194 210\n195 211\n196 212\n197 213\n198 214\n199 215\n200 216\n201 217\n202 218\n203 219\n204 220\n205 221\n206 222\n207 223\n208 224\n209 225\n210 226\n211 227\n212 228\n213 229\n214 230\n215 231\n216 232\n217 233\n218 234\n219 235\n220 236\n221 237\n222 238\n223 239\n224 240\n225 241\n226 242\n227 243\n228 244\n229 245\n230 246\n231 247\n232 248\n233 249\n234 250\n235 251\n236 252\n237 253\n238 254\n239 255\n240 256\n241 257\n242 258\n243 259\n244 260\n245 261\n246 262\n247 263\n248 264\n249 265\n250 266\n251 267\n252 268\n253 269\n254 270\n255 271\n256 272\n257 273\n258 274\n259 275\n260 276\n261 277\n262 278\n263 279\n264 280\n265 281\n266 282\n267 283\n268 284\n269 285\n270 286\n271 287\n272 288\n273 289\n274 290\n275 291\n276 292\n277 293\n278 294\n279 295\n280 296\n281 297\n282 298\n283 299\n284 300\n285 301\n286 302\n287 303\n288 304\n289 305\n290 306\n291 307\n292 308\n293 309\n294 310\n295 311\n296 312\n297 313\n298 314\n299 315\n300 316\n301 317\n302 318\n303 319\n304 320\n305 321\n306 322\n307 323\n308 324\n309 325\n310 326\n311 327\n312 328\n313 329\n314 330\n315 331\n316 332\n317 333\n318 334\n319 335\n320 336\n321 337\n322 338\n323 339\n324 340\n325 341\n326 342\n327 343\n328 344\n329 345\n330 346\n331 347\n332 348\n333 349\n334 350\n335 351\n336 352\n337 353\n338 354\n339 355\n340 356\n341 357\n342 358\n343 359\n344 360\n345 361\n346 362\n347 363\n348 364\n349 365\n350 366\n351 367\n352 368\n353 369\n354 370\n355 371\n356 372\n357 373\n358 374\n359 375\n360 376\n361 377\n362 378\n363 379\n364 380\n365 381\n366 382\n367 383\n368 384\n369 385\n370 386\n371 387\n372 388\n373 389\n374 390\n375 391\n376 392\n377 393\n378 394\n379 395\n380 396\n381 397\n382 398\n383 399\n384 400\n385 401\n386 402\n387 403\n388 404\n389 405\n390 406\n391 407\n392 408\n393 409\n394 410\n395 411\n396 412\n397 413\n398 414\n399 415\n400 416\n401 417\n402 418\n403 419\n404 420\n405 421\n406 422\n407 423\n408 424\n409 425\n410 426\n411 427\n412 428\n413 429\n414 430\n415 431\n416 432\n417 433\n418 434\n419 435\n420 436\n421 437\n422 438\n423 439\n424 440\n425 441\n426 442\n427 443\n428 444\n429 445\n430 446\n431 447\n432 448\n433 449\n434 450\n435 451\n436 452\n437 453\n438 454\n439 455\n440 456\n441 457\n442 458\n443 459\n444 460\n445 461\n446 462\n447 463\n448 464\n449 465\n450 466\n451 467\n452 468\n453 469\n454 470\n455 471\n456 472\n457 473\n458 474\n459 475\n460 476\n461 477\n462 478\n463 479\n464 480\n465 481\n466 482\n467 483\n468 484\n469 485\n470 486\n471 487\n472 488\n473 489\n474 490\n475 491\n476 492\n477 493\n478 494\n479 495\n480 496\n481 497\n482 498\n483 499\n484 500\n485 501\n486 502\n487 503\n488 504\n489 505\n490 506\n491 507\n492 508\n493 509\n494 510\n495 511\n496 512\n497 513\n498 514\n499 515\n500 516\n501 517\n502 518\n503 519\n504 520\n505 521\n506 522\n507 523\n508 524\n509 525\n510 526\n511 527\n512 528\n513 529\n514 530\n515 531\n516 532\n517 533\n518 534\n519 535\n520 536\n521 537\n522 538\n523 539\n524 540\n525 541\n526 542\n527 543\n528 544\n529 545\n530 546\n531 547\n532 548\n533 549\n534 550\n535 551\n536 552\n537 553\n538 554\n539 555\n540 556\n541 557\n542 558\n543 559\n544 560\n545 561\n546 562\n547 563\n548 564\n549 565\n550 566\n551 567\n552 568\n553 569\n554 570\n555 571\n556 572\n557 573\n558 574\n559 575\n560 576\n561 577\n562 578\n563 579\n564 580\n565 581\n566 582\n567 583\n568 584\n569 585\n570 586\n571 587\n572 588\n573 589\n574 590\n575 591\n576 592\n577 593\n578 594\n579 595\n580 596\n581 597\n582 598\n583 599\n584 600\n585 601\n586 602\n587 603\n588 604\n589 605\n590 606\n591 607\n592 608\n593 609\n594 610\n595 611\n596 612\n597 613\n598 614\n599 615\n600 616\n601 617\n602 618\n603 619\n604 620\n605 621\n606 622\n607 623\n608 624\n609 625\n610 626\n611 627\n612 628\n613 629\n614 630\n615 631\n616 632\n617 633\n618 634\n619 635\n620 636\n621 637\n622 638\n623 639\n624 640\n625 641\n626 642\n627 643\n628 644\n629 645\n630 646\n631 647\n632 648\n633 649\n634 650\n635 651\n636 652\n637 653\n638 654\n639 655\n640 656\n641 657\n642 658\n643 659\n644 660\n645 661\n646 662\n647 663\n648 664\n649 665\n650 666\n651 667\n652 668\n653 669\n654 670\n655 671\n656 672\n657 673\n658 674\n659 675\n660 676\n661 677\n662 678\n663 679\n664 680\n665 681\n666 682\n667 683\n668 684\n669 685\n670 686\n671 687\n672 688\n673 689\n674 690\n675 691\n676 692\n677 693\n678 694\n679 695\n680 696\n681 697\n682 698\n683 699\n684 700\n685 701\n686 702\n687 703\n688 704\n689 705\n690 706\n691 707\n692 708\n693 709\n694 710\n695 711\n696 712\n697 713\n698 714\n699 715\n700 716\n701 717\n702 718\n703 719\n704 720\n705 721\n706 722\n707 723\n708 724\n709 725\n710 726\n711 727\n712 728\n713 729\n714 730\n715 731\n716 732\n717 733\n718 734\n719 735\n720 736\n721 737\n722 738\n723 739\n724 740\n725 741\n726 742\n727 743\n728 744\n729 745\n730 746\n731 747\n732 748\n733 749\n734 750\n735 751\n736 752\n737 753\n738 754\n739 755\n740 756\n741 757\n742 758\n743 759\n744 760\n745 761\n746 762\n747 763\n748 764\n749 765\n750 766\n751 767\n752 768\n753 769\n754 770\n755 771\n756 772\n757 773\n758 774\n759 775\n760 776\n761 777\n762 778\n763 779\n764 780\n765 781\n766 782\n767 783\n768 784\n769 785\n770 786\n771 787\n772 788\n773 789\n774 790\n775 791\n776 792\n777 793\n778 794\n779 795\n780 796\n781 797\n782 798\n783 799\n784 800\n785 801\n786 802\n787 803\n788 804\n789 805\n790 806\n791 807\n792 808\n793 809\n794 810\n795 811\n796 812\n797 813\n798 814\n799 815\n800 816\n801 817\n802 818\n803 819\n804 820\n805 821\n806 822\n807 823\n808 824\n809 825\n810 826\n811 827\n812 828\n813 829\n814 830\n815 831\n816 832\n817 833\n818 834\n819 835\n820 836\n821 837\n822 838\n823 839\n824 840\n825 841\n826 842\n827 843\n828 844\n829 845\n830 846\n831 847\n832 848\n833 849\n834 850\n835 851\n836 852\n837 853\n838 854\n839 855\n840 856\n841 857\n842 858\n843 859\n844 860\n845 861\n846 862\n847 863\n848 864\n849 865\n850 866\n851 867\n852 868\n853 869\n854 870\n855 871\n856 872\n857 873\n858 874\n859 875\n860 876\n861 877\n862 878\n863 879\n864 880\n865 881\n866 882\n867 883\n868 884\n869 885\n870 886\n871 887\n872 888\n873 889\n874 890\n875 891\n876 892\n877 893\n878 894\n879 895\n880 896\n881 897\n882 898\n883 899\n884 900\n885 901\n886 902\n887 903\n888 904\n889 905\n890 906\n891 907\n892 908\n893 909\n894 910\n895 911\n896 912\n897 913\n898 914\n899 915\n900 916\n901 917\n902 918\n903 919\n904 920\n905 921\n906 922\n907 923\n908 924\n909 925\n910 926\n911 927\n912 928\n913 929\n914 930\n915 931\n916 932\n917 933\n918 934\n919 935\n920 936\n921 937\n922 938\n923 939\n924 940\n925 941\n926 942\n927 943\n928 944\n929 945\n930 946\n931 947\n932 948\n933 949\n934 950\n935 951\n936 952\n937 953\n938 954\n939 955\n940 956\n941 957\n942 958\n943 959\n944 960\n945 961\n946 962\n947 963\n948 964\n949 965\n950 966\n951 967\n952 968\n953 969\n954 970\n955 971\n956 972\n957 973\n958 974\n959 975\n960 976\n961 977\n962 978\n963 979\n964 980\n965 981\n966 982\n967 983\n968 984\n969 985\n970 986\n971 987\n972 988\n973 989\n974 990\n975 991\n976 992\n977 993\n978 994\n979 995\n980 996\n981 997\n982 998\n983 999\n984 1000\n985 1001\n986 1002\n987 1003\n988 1004\n989 1005\n990 1006\n991 1007\n992 1008\n993 1009\n994 1010\n995 1011\n996 1012\n997 1013\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n2 515\n3 516\n4 517\n5 518\n6 519\n7 520\n8 521\n9 522\n10 523\n11 524\n12 525\n13 526\n14 527\n15 528\n16 529\n17 530\n18 531\n19 532\n20 533\n21 534\n22 535\n23 536\n24 537\n25 538\n26 539\n27 540\n28 541\n29 542\n30 543\n31 544\n32 545\n33 546\n34 547\n35 548\n36 549\n37 550\n38 551\n39 552\n40 553\n41 554\n42 555\n43 556\n44 557\n45 558\n46 559\n47 560\n48 561\n49 562\n50 563\n51 564\n52 565\n53 566\n54 567\n55 568\n56 569\n57 570\n58 571\n59 572\n60 573\n61 574\n62 575\n63 576\n64 577\n65 578\n66 579\n67 580\n68 581\n69 582\n70 583\n71 584\n72 585\n73 586\n74 587\n75 588\n76 589\n77 590\n78 591\n79 592\n80 593\n81 594\n82 595\n83 596\n84 597\n85 598\n86 599\n87 600\n88 601\n89 602\n90 603\n91 604\n92 605\n93 606\n94 607\n95 608\n96 609\n97 610\n98 611\n99 612\n100 613\n101 614\n102 615\n103 616\n104 617\n105 618\n106 619\n107 620\n108 621\n109 622\n110 623\n111 624\n112 625\n113 626\n114 627\n115 628\n116 629\n117 630\n118 631\n119 632\n120 633\n121 634\n122 635\n123 636\n124 637\n125 638\n126 639\n127 640\n128 641\n129 642\n130 643\n131 644\n132 645\n133 646\n134 647\n135 648\n136 649\n137 650\n138 651\n139 652\n140 653\n141 654\n142 655\n143 656\n144 657\n145 658\n146 659\n147 660\n148 661\n149 662\n150 663\n151 664\n152 665\n153 666\n154 667\n155 668\n156 669\n157 670\n158 671\n159 672\n160 673\n161 674\n162 675\n163 676\n164 677\n165 678\n166 679\n167 680\n168 681\n169 682\n170 683\n171 684\n172 685\n173 686\n174 687\n175 688\n176 689\n177 690\n178 691\n179 692\n180 693\n181 694\n182 695\n183 696\n184 697\n185 698\n186 699\n187 700\n188 701\n189 702\n190 703\n191 704\n192 705\n193 706\n194 707\n195 708\n196 709\n197 710\n198 711\n199 712\n200 713\n201 714\n202 715\n203 716\n204 717\n205 718\n206 719\n207 720\n208 721\n209 722\n210 723\n211 724\n212 725\n213 726\n214 727\n215 728\n216 729\n217 730\n218 731\n219 732\n220 733\n221 734\n222 735\n223 736\n224 737\n225 738\n226 739\n227 740\n228 741\n229 742\n230 743\n231 744\n232 745\n233 746\n234 747\n235 748\n236 749\n237 750\n238 751\n239 752\n240 753\n241 754\n242 755\n243 756\n244 757\n245 758\n246 759\n247 760\n248 761\n249 762\n250 763\n251 764\n252 765\n253 766\n254 767\n255 768\n256 769\n257 770\n258 771\n259 772\n260 773\n261 774\n262 775\n263 776\n264 777\n265 778\n266 779\n267 780\n268 781\n269 782\n270 783\n271 784\n272 785\n273 786\n274 787\n275 788\n276 789\n277 790\n278 791\n279 792\n280 793\n281 794\n282 795\n283 796\n284 797\n285 798\n286 799\n287 800\n288 801\n289 802\n290 803\n291 804\n292 805\n293 806\n294 807\n295 808\n296 809\n297 810\n298 811\n299 812\n300 813\n301 814\n302 815\n303 816\n304 817\n305 818\n306 819\n307 820\n308 821\n309 822\n310 823\n311 824\n312 825\n313 826\n314 827\n315 828\n316 829\n317 830\n318 831\n319 832\n320 833\n321 834\n322 835\n323 836\n324 837\n325 838\n326 839\n327 840\n328 841\n329 842\n330 843\n331 844\n332 845\n333 846\n334 847\n335 848\n336 849\n337 850\n338 851\n339 852\n340 853\n341 854\n342 855\n343 856\n344 857\n345 858\n346 859\n347 860\n348 861\n349 862\n350 863\n351 864\n352 865\n353 866\n354 867\n355 868\n356 869\n357 870\n358 871\n359 872\n360 873\n361 874\n362 875\n363 876\n364 877\n365 878\n366 879\n367 880\n368 881\n369 882\n370 883\n371 884\n372 885\n373 886\n374 887\n375 888\n376 889\n377 890\n378 891\n379 892\n380 893\n381 894\n382 895\n383 896\n384 897\n385 898\n386 899\n387 900\n388 901\n389 902\n390 903\n391 904\n392 905\n393 906\n394 907\n395 908\n396 909\n397 910\n398 911\n399 912\n400 913\n401 914\n402 915\n403 916\n404 917\n405 918\n406 919\n407 920\n408 921\n409 922\n410 923\n411 924\n412 925\n413 926\n414 927\n415 928\n416 929\n417 930\n418 931\n419 932\n420 933\n421 934\n422 935\n423 936\n424 937\n425 938\n426 939\n427 940\n428 941\n429 942\n430 943\n431 944\n432 945\n433 946\n434 947\n435 948\n436 949\n437 950\n438 951\n439 952\n440 953\n441 954\n442 955\n443 956\n444 957\n445 958\n446 959\n447 960\n448 961\n449 962\n450 963\n451 964\n452 965\n453 966\n454 967\n455 968\n456 969\n457 970\n458 971\n459 972\n460 973\n461 974\n462 975\n463 976\n464 977\n465 978\n466 979\n467 980\n468 981\n469 982\n470 983\n471 984\n472 985\n473 986\n474 987\n475 988\n476 989\n477 990\n478 991\n479 992\n480 993\n481 994\n482 995\n483 996\n484 997\n485 998\n486 999\n487 1000\n488 1001\n489 1002\n490 1003\n491 1004\n492 1005\n493 1006\n494 1007\n495 1008\n496 1009\n497 1010\n498 1011\n499 1012\n500 1013\n501 1014\n502 1015\n503 1016\n504 1017\n505 1018\n506 1019\n507 1020\n508 1021\n509 1022\n510 1023\n511 1024\n",
"4\n1 2\n1 3\n1 4\n2 5\n3 6\n4 7\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n2 672\n3 673\n4 674\n5 675\n6 676\n7 677\n8 678\n9 679\n10 680\n11 681\n12 682\n13 683\n14 684\n15 685\n16 686\n17 687\n18 688\n19 689\n20 690\n21 691\n22 692\n23 693\n24 694\n25 695\n26 696\n27 697\n28 698\n29 699\n30 700\n31 701\n32 702\n33 703\n34 704\n35 705\n36 706\n37 707\n38 708\n39 709\n40 710\n41 711\n42 712\n43 713\n44 714\n45 715\n46 716\n47 717\n48 718\n49 719\n50 720\n51 721\n52 722\n53 723\n54 724\n55 725\n56 726\n57 727\n58 728\n59 729\n60 730\n61 731\n62 732\n63 733\n64 734\n65 735\n66 736\n67 737\n68 738\n69 739\n70 740\n71 741\n72 742\n73 743\n74 744\n75 745\n76 746\n77 747\n78 748\n79 749\n80 750\n81 751\n82 752\n83 753\n84 754\n85 755\n86 756\n87 757\n88 758\n89 759\n90 760\n91 761\n92 762\n93 763\n94 764\n95 765\n96 766\n97 767\n98 768\n99 769\n100 770\n101 771\n102 772\n103 773\n104 774\n105 775\n106 776\n107 777\n108 778\n109 779\n110 780\n111 781\n112 782\n113 783\n114 784\n115 785\n116 786\n117 787\n118 788\n119 789\n120 790\n121 791\n122 792\n123 793\n124 794\n125 795\n126 796\n127 797\n128 798\n129 799\n130 800\n131 801\n132 802\n133 803\n134 804\n135 805\n136 806\n137 807\n138 808\n139 809\n140 810\n141 811\n142 812\n143 813\n144 814\n145 815\n146 816\n147 817\n148 818\n149 819\n150 820\n151 821\n152 822\n153 823\n154 824\n155 825\n156 826\n157 827\n158 828\n159 829\n160 830\n161 831\n162 832\n163 833\n164 834\n165 835\n166 836\n167 837\n168 838\n169 839\n170 840\n171 841\n172 842\n173 843\n174 844\n175 845\n176 846\n177 847\n178 848\n179 849\n180 850\n181 851\n182 852\n183 853\n184 854\n185 855\n186 856\n187 857\n188 858\n189 859\n190 860\n191 861\n192 862\n193 863\n194 864\n195 865\n196 866\n197 867\n198 868\n199 869\n200 870\n201 871\n202 872\n203 873\n204 874\n205 875\n206 876\n207 877\n208 878\n209 879\n210 880\n211 881\n212 882\n213 883\n214 884\n215 885\n216 886\n217 887\n218 888\n219 889\n220 890\n221 891\n222 892\n223 893\n224 894\n225 895\n226 896\n227 897\n228 898\n229 899\n230 900\n231 901\n232 902\n233 903\n234 904\n235 905\n236 906\n237 907\n238 908\n239 909\n240 910\n241 911\n242 912\n243 913\n244 914\n245 915\n246 916\n247 917\n248 918\n249 919\n250 920\n251 921\n252 922\n253 923\n254 924\n255 925\n256 926\n257 927\n258 928\n259 929\n260 930\n261 931\n262 932\n263 933\n264 934\n265 935\n266 936\n267 937\n268 938\n269 939\n270 940\n271 941\n272 942\n273 943\n274 944\n275 945\n276 946\n277 947\n278 948\n279 949\n280 950\n281 951\n282 952\n283 953\n284 954\n285 955\n286 956\n287 957\n288 958\n289 959\n290 960\n291 961\n292 962\n293 963\n294 964\n295 965\n296 966\n297 967\n298 968\n299 969\n300 970\n301 971\n302 972\n303 973\n304 974\n305 975\n306 976\n307 977\n308 978\n309 979\n310 980\n311 981\n312 982\n313 983\n314 984\n315 985\n316 986\n317 987\n318 988\n319 989\n320 990\n321 991\n322 992\n323 993\n324 994\n325 995\n326 996\n327 997\n328 998\n329 999\n330 1000\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n2 8\n3 9\n4 10\n",
"88\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n2 25\n3 26\n4 27\n5 28\n6 29\n7 30\n8 31\n9 32\n10 33\n11 34\n12 35\n13 36\n14 37\n15 38\n16 39\n17 40\n18 41\n19 42\n20 43\n21 44\n22 45\n23 46\n24 47\n25 48\n26 49\n27 50\n28 51\n29 52\n30 53\n31 54\n32 55\n33 56\n34 57\n35 58\n36 59\n37 60\n38 61\n39 62\n40 63\n41 64\n42 65\n43 66\n44 67\n45 68\n46 69\n47 70\n48 71\n49 72\n50 73\n51 74\n52 75\n53 76\n54 77\n55 78\n56 79\n57 80\n58 81\n59 82\n60 83\n61 84\n62 85\n63 86\n64 87\n65 88\n66 89\n67 90\n68 91\n69 92\n70 93\n71 94\n72 95\n73 96\n74 97\n75 98\n76 99\n77 100\n78 101\n79 102\n80 103\n81 104\n82 105\n83 106\n84 107\n85 108\n86 109\n87 110\n88 111\n89 112\n90 113\n91 114\n92 115\n93 116\n94 117\n95 118\n96 119\n97 120\n98 121\n99 122\n100 123\n101 124\n102 125\n103 126\n104 127\n105 128\n106 129\n107 130\n108 131\n109 132\n110 133\n111 134\n112 135\n113 136\n114 137\n115 138\n116 139\n117 140\n118 141\n119 142\n120 143\n121 144\n122 145\n123 146\n124 147\n125 148\n126 149\n127 150\n128 151\n129 152\n130 153\n131 154\n132 155\n133 156\n134 157\n135 158\n136 159\n137 160\n138 161\n139 162\n140 163\n141 164\n142 165\n143 166\n144 167\n145 168\n146 169\n147 170\n148 171\n149 172\n150 173\n151 174\n152 175\n153 176\n154 177\n155 178\n156 179\n157 180\n158 181\n159 182\n160 183\n161 184\n162 185\n163 186\n164 187\n165 188\n166 189\n167 190\n168 191\n169 192\n170 193\n171 194\n172 195\n173 196\n174 197\n175 198\n176 199\n177 200\n178 201\n179 202\n180 203\n181 204\n182 205\n183 206\n184 207\n185 208\n186 209\n187 210\n188 211\n189 212\n190 213\n191 214\n192 215\n193 216\n194 217\n195 218\n196 219\n197 220\n198 221\n199 222\n200 223\n201 224\n202 225\n203 226\n204 227\n205 228\n206 229\n207 230\n208 231\n209 232\n210 233\n211 234\n212 235\n213 236\n214 237\n215 238\n216 239\n217 240\n218 241\n219 242\n220 243\n221 244\n222 245\n223 246\n224 247\n225 248\n226 249\n227 250\n228 251\n229 252\n230 253\n231 254\n232 255\n233 256\n234 257\n235 258\n236 259\n237 260\n238 261\n239 262\n240 263\n241 264\n242 265\n243 266\n244 267\n245 268\n246 269\n247 270\n248 271\n249 272\n250 273\n251 274\n252 275\n253 276\n254 277\n255 278\n256 279\n257 280\n258 281\n259 282\n260 283\n261 284\n262 285\n263 286\n264 287\n265 288\n266 289\n267 290\n268 291\n269 292\n270 293\n271 294\n272 295\n273 296\n274 297\n275 298\n276 299\n277 300\n278 301\n279 302\n280 303\n281 304\n282 305\n283 306\n284 307\n285 308\n286 309\n287 310\n288 311\n289 312\n290 313\n291 314\n292 315\n293 316\n294 317\n295 318\n296 319\n297 320\n298 321\n299 322\n300 323\n301 324\n302 325\n303 326\n304 327\n305 328\n306 329\n307 330\n308 331\n309 332\n310 333\n311 334\n312 335\n313 336\n314 337\n315 338\n316 339\n317 340\n318 341\n319 342\n320 343\n321 344\n322 345\n323 346\n324 347\n325 348\n326 349\n327 350\n328 351\n329 352\n330 353\n331 354\n332 355\n333 356\n334 357\n335 358\n336 359\n337 360\n338 361\n339 362\n340 363\n341 364\n342 365\n343 366\n344 367\n345 368\n346 369\n347 370\n348 371\n349 372\n350 373\n351 374\n352 375\n353 376\n354 377\n355 378\n356 379\n357 380\n358 381\n359 382\n360 383\n361 384\n362 385\n363 386\n364 387\n365 388\n366 389\n367 390\n368 391\n369 392\n370 393\n371 394\n372 395\n373 396\n374 397\n375 398\n376 399\n377 400\n378 401\n379 402\n380 403\n381 404\n382 405\n383 406\n384 407\n385 408\n386 409\n387 410\n388 411\n389 412\n390 413\n391 414\n392 415\n393 416\n394 417\n395 418\n396 419\n397 420\n398 421\n399 422\n400 423\n401 424\n402 425\n403 426\n404 427\n405 428\n406 429\n407 430\n408 431\n409 432\n410 433\n411 434\n412 435\n413 436\n414 437\n415 438\n416 439\n417 440\n418 441\n419 442\n420 443\n421 444\n422 445\n423 446\n424 447\n425 448\n426 449\n427 450\n428 451\n429 452\n430 453\n431 454\n432 455\n433 456\n434 457\n435 458\n436 459\n437 460\n438 461\n439 462\n440 463\n441 464\n442 465\n443 466\n444 467\n445 468\n446 469\n447 470\n448 471\n449 472\n450 473\n451 474\n452 475\n453 476\n454 477\n455 478\n456 479\n457 480\n458 481\n459 482\n460 483\n461 484\n462 485\n463 486\n464 487\n465 488\n466 489\n467 490\n468 491\n469 492\n470 493\n471 494\n472 495\n473 496\n474 497\n475 498\n476 499\n477 500\n478 501\n479 502\n480 503\n481 504\n482 505\n483 506\n484 507\n485 508\n486 509\n487 510\n488 511\n489 512\n490 513\n491 514\n492 515\n493 516\n494 517\n495 518\n496 519\n497 520\n498 521\n499 522\n500 523\n501 524\n502 525\n503 526\n504 527\n505 528\n506 529\n507 530\n508 531\n509 532\n510 533\n511 534\n512 535\n513 536\n514 537\n515 538\n516 539\n517 540\n518 541\n519 542\n520 543\n521 544\n522 545\n523 546\n524 547\n525 548\n526 549\n527 550\n528 551\n529 552\n530 553\n531 554\n532 555\n533 556\n534 557\n535 558\n536 559\n537 560\n538 561\n539 562\n540 563\n541 564\n542 565\n543 566\n544 567\n545 568\n546 569\n547 570\n548 571\n549 572\n550 573\n551 574\n552 575\n553 576\n554 577\n555 578\n556 579\n557 580\n558 581\n559 582\n560 583\n561 584\n562 585\n563 586\n564 587\n565 588\n566 589\n567 590\n568 591\n569 592\n570 593\n571 594\n572 595\n573 596\n574 597\n575 598\n576 599\n577 600\n578 601\n579 602\n580 603\n581 604\n582 605\n583 606\n584 607\n585 608\n586 609\n587 610\n588 611\n589 612\n590 613\n591 614\n592 615\n593 616\n594 617\n595 618\n596 619\n597 620\n598 621\n599 622\n600 623\n601 624\n602 625\n603 626\n604 627\n605 628\n606 629\n607 630\n608 631\n609 632\n610 633\n611 634\n612 635\n613 636\n614 637\n615 638\n616 639\n617 640\n618 641\n619 642\n620 643\n621 644\n622 645\n623 646\n624 647\n625 648\n626 649\n627 650\n628 651\n629 652\n630 653\n631 654\n632 655\n633 656\n634 657\n635 658\n636 659\n637 660\n638 661\n639 662\n640 663\n641 664\n642 665\n643 666\n644 667\n645 668\n646 669\n647 670\n648 671\n649 672\n650 673\n651 674\n652 675\n653 676\n654 677\n655 678\n656 679\n657 680\n658 681\n659 682\n660 683\n661 684\n662 685\n663 686\n664 687\n665 688\n666 689\n667 690\n668 691\n669 692\n670 693\n671 694\n672 695\n673 696\n674 697\n675 698\n676 699\n677 700\n678 701\n679 702\n680 703\n681 704\n682 705\n683 706\n684 707\n685 708\n686 709\n687 710\n688 711\n689 712\n690 713\n691 714\n692 715\n693 716\n694 717\n695 718\n696 719\n697 720\n698 721\n699 722\n700 723\n701 724\n702 725\n703 726\n704 727\n705 728\n706 729\n707 730\n708 731\n709 732\n710 733\n711 734\n712 735\n713 736\n714 737\n715 738\n716 739\n717 740\n718 741\n719 742\n720 743\n721 744\n722 745\n723 746\n724 747\n725 748\n726 749\n727 750\n728 751\n729 752\n730 753\n731 754\n732 755\n733 756\n734 757\n735 758\n736 759\n737 760\n738 761\n739 762\n740 763\n741 764\n742 765\n743 766\n744 767\n745 768\n746 769\n747 770\n748 771\n749 772\n750 773\n751 774\n752 775\n753 776\n754 777\n755 778\n756 779\n757 780\n758 781\n759 782\n760 783\n761 784\n762 785\n763 786\n764 787\n765 788\n766 789\n767 790\n768 791\n769 792\n770 793\n771 794\n772 795\n773 796\n774 797\n775 798\n776 799\n777 800\n778 801\n779 802\n780 803\n781 804\n782 805\n783 806\n784 807\n785 808\n786 809\n787 810\n788 811\n789 812\n790 813\n791 814\n792 815\n793 816\n794 817\n795 818\n796 819\n797 820\n798 821\n799 822\n800 823\n801 824\n802 825\n803 826\n804 827\n805 828\n806 829\n807 830\n808 831\n809 832\n810 833\n811 834\n812 835\n813 836\n814 837\n815 838\n816 839\n817 840\n818 841\n819 842\n820 843\n821 844\n822 845\n823 846\n824 847\n825 848\n826 849\n827 850\n828 851\n829 852\n830 853\n831 854\n832 855\n833 856\n834 857\n835 858\n836 859\n837 860\n838 861\n839 862\n840 863\n841 864\n842 865\n843 866\n844 867\n845 868\n846 869\n847 870\n848 871\n849 872\n850 873\n851 874\n852 875\n853 876\n854 877\n855 878\n856 879\n857 880\n858 881\n859 882\n860 883\n861 884\n862 885\n863 886\n864 887\n865 888\n866 889\n867 890\n868 891\n869 892\n870 893\n871 894\n872 895\n873 896\n874 897\n875 898\n876 899\n877 900\n878 901\n879 902\n880 903\n881 904\n882 905\n883 906\n884 907\n885 908\n886 909\n887 910\n888 911\n889 912\n890 913\n891 914\n892 915\n893 916\n894 917\n895 918\n896 919\n897 920\n898 921\n899 922\n900 923\n901 924\n902 925\n903 926\n904 927\n905 928\n906 929\n907 930\n908 931\n909 932\n910 933\n911 934\n912 935\n913 936\n914 937\n915 938\n916 939\n917 940\n918 941\n919 942\n920 943\n921 944\n922 945\n923 946\n924 947\n925 948\n926 949\n927 950\n928 951\n929 952\n930 953\n931 954\n932 955\n933 956\n934 957\n935 958\n936 959\n937 960\n938 961\n939 962\n940 963\n941 964\n942 965\n943 966\n944 967\n945 968\n946 969\n947 970\n948 971\n949 972\n950 973\n951 974\n952 975\n953 976\n954 977\n955 978\n956 979\n957 980\n958 981\n959 982\n960 983\n961 984\n962 985\n963 986\n964 987\n965 988\n966 989\n967 990\n968 991\n969 992\n970 993\n971 994\n972 995\n973 996\n974 997\n975 998\n976 999\n977 1000\n978 1001\n979 1002\n980 1003\n981 1004\n982 1005\n983 1006\n984 1007\n985 1008\n986 1009\n987 1010\n988 1011\n989 1012\n990 1013\n",
"6\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n1 1000\n1 1001\n1 1002\n1 1003\n1 1004\n1 1005\n1 1006\n1 1007\n1 1008\n1 1009\n1 1010\n1 1011\n1 1012\n1 1013\n1 1014\n1 1015\n1 1016\n1 1017\n1 1018\n1 1019\n1 1020\n1 1021\n1 1022\n1 1023\n1 1024\n",
"128\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n2 18\n3 19\n4 20\n5 21\n6 22\n7 23\n8 24\n9 25\n10 26\n11 27\n12 28\n13 29\n14 30\n15 31\n16 32\n17 33\n18 34\n19 35\n20 36\n21 37\n22 38\n23 39\n24 40\n25 41\n26 42\n27 43\n28 44\n29 45\n30 46\n31 47\n32 48\n33 49\n34 50\n35 51\n36 52\n37 53\n38 54\n39 55\n40 56\n41 57\n42 58\n43 59\n44 60\n45 61\n46 62\n47 63\n48 64\n49 65\n50 66\n51 67\n52 68\n53 69\n54 70\n55 71\n56 72\n57 73\n58 74\n59 75\n60 76\n61 77\n62 78\n63 79\n64 80\n65 81\n66 82\n67 83\n68 84\n69 85\n70 86\n71 87\n72 88\n73 89\n74 90\n75 91\n76 92\n77 93\n78 94\n79 95\n80 96\n81 97\n82 98\n83 99\n84 100\n85 101\n86 102\n87 103\n88 104\n89 105\n90 106\n91 107\n92 108\n93 109\n94 110\n95 111\n96 112\n97 113\n98 114\n99 115\n100 116\n101 117\n102 118\n103 119\n104 120\n105 121\n106 122\n107 123\n108 124\n109 125\n110 126\n111 127\n112 128\n113 129\n114 130\n115 131\n116 132\n117 133\n118 134\n119 135\n120 136\n121 137\n122 138\n123 139\n124 140\n125 141\n126 142\n127 143\n128 144\n129 145\n130 146\n131 147\n132 148\n133 149\n134 150\n135 151\n136 152\n137 153\n138 154\n139 155\n140 156\n141 157\n142 158\n143 159\n144 160\n145 161\n146 162\n147 163\n148 164\n149 165\n150 166\n151 167\n152 168\n153 169\n154 170\n155 171\n156 172\n157 173\n158 174\n159 175\n160 176\n161 177\n162 178\n163 179\n164 180\n165 181\n166 182\n167 183\n168 184\n169 185\n170 186\n171 187\n172 188\n173 189\n174 190\n175 191\n176 192\n177 193\n178 194\n179 195\n180 196\n181 197\n182 198\n183 199\n184 200\n185 201\n186 202\n187 203\n188 204\n189 205\n190 206\n191 207\n192 208\n193 209\n194 210\n195 211\n196 212\n197 213\n198 214\n199 215\n200 216\n201 217\n202 218\n203 219\n204 220\n205 221\n206 222\n207 223\n208 224\n209 225\n210 226\n211 227\n212 228\n213 229\n214 230\n215 231\n216 232\n217 233\n218 234\n219 235\n220 236\n221 237\n222 238\n223 239\n224 240\n225 241\n226 242\n227 243\n228 244\n229 245\n230 246\n231 247\n232 248\n233 249\n234 250\n235 251\n236 252\n237 253\n238 254\n239 255\n240 256\n241 257\n242 258\n243 259\n244 260\n245 261\n246 262\n247 263\n248 264\n249 265\n250 266\n251 267\n252 268\n253 269\n254 270\n255 271\n256 272\n257 273\n258 274\n259 275\n260 276\n261 277\n262 278\n263 279\n264 280\n265 281\n266 282\n267 283\n268 284\n269 285\n270 286\n271 287\n272 288\n273 289\n274 290\n275 291\n276 292\n277 293\n278 294\n279 295\n280 296\n281 297\n282 298\n283 299\n284 300\n285 301\n286 302\n287 303\n288 304\n289 305\n290 306\n291 307\n292 308\n293 309\n294 310\n295 311\n296 312\n297 313\n298 314\n299 315\n300 316\n301 317\n302 318\n303 319\n304 320\n305 321\n306 322\n307 323\n308 324\n309 325\n310 326\n311 327\n312 328\n313 329\n314 330\n315 331\n316 332\n317 333\n318 334\n319 335\n320 336\n321 337\n322 338\n323 339\n324 340\n325 341\n326 342\n327 343\n328 344\n329 345\n330 346\n331 347\n332 348\n333 349\n334 350\n335 351\n336 352\n337 353\n338 354\n339 355\n340 356\n341 357\n342 358\n343 359\n344 360\n345 361\n346 362\n347 363\n348 364\n349 365\n350 366\n351 367\n352 368\n353 369\n354 370\n355 371\n356 372\n357 373\n358 374\n359 375\n360 376\n361 377\n362 378\n363 379\n364 380\n365 381\n366 382\n367 383\n368 384\n369 385\n370 386\n371 387\n372 388\n373 389\n374 390\n375 391\n376 392\n377 393\n378 394\n379 395\n380 396\n381 397\n382 398\n383 399\n384 400\n385 401\n386 402\n387 403\n388 404\n389 405\n390 406\n391 407\n392 408\n393 409\n394 410\n395 411\n396 412\n397 413\n398 414\n399 415\n400 416\n401 417\n402 418\n403 419\n404 420\n405 421\n406 422\n407 423\n408 424\n409 425\n410 426\n411 427\n412 428\n413 429\n414 430\n415 431\n416 432\n417 433\n418 434\n419 435\n420 436\n421 437\n422 438\n423 439\n424 440\n425 441\n426 442\n427 443\n428 444\n429 445\n430 446\n431 447\n432 448\n433 449\n434 450\n435 451\n436 452\n437 453\n438 454\n439 455\n440 456\n441 457\n442 458\n443 459\n444 460\n445 461\n446 462\n447 463\n448 464\n449 465\n450 466\n451 467\n452 468\n453 469\n454 470\n455 471\n456 472\n457 473\n458 474\n459 475\n460 476\n461 477\n462 478\n463 479\n464 480\n465 481\n466 482\n467 483\n468 484\n469 485\n470 486\n471 487\n472 488\n473 489\n474 490\n475 491\n476 492\n477 493\n478 494\n479 495\n480 496\n481 497\n482 498\n483 499\n484 500\n485 501\n486 502\n487 503\n488 504\n489 505\n490 506\n491 507\n492 508\n493 509\n494 510\n495 511\n496 512\n497 513\n498 514\n499 515\n500 516\n501 517\n502 518\n503 519\n504 520\n505 521\n506 522\n507 523\n508 524\n509 525\n510 526\n511 527\n512 528\n513 529\n514 530\n515 531\n516 532\n517 533\n518 534\n519 535\n520 536\n521 537\n522 538\n523 539\n524 540\n525 541\n526 542\n527 543\n528 544\n529 545\n530 546\n531 547\n532 548\n533 549\n534 550\n535 551\n536 552\n537 553\n538 554\n539 555\n540 556\n541 557\n542 558\n543 559\n544 560\n545 561\n546 562\n547 563\n548 564\n549 565\n550 566\n551 567\n552 568\n553 569\n554 570\n555 571\n556 572\n557 573\n558 574\n559 575\n560 576\n561 577\n562 578\n563 579\n564 580\n565 581\n566 582\n567 583\n568 584\n569 585\n570 586\n571 587\n572 588\n573 589\n574 590\n575 591\n576 592\n577 593\n578 594\n579 595\n580 596\n581 597\n582 598\n583 599\n584 600\n585 601\n586 602\n587 603\n588 604\n589 605\n590 606\n591 607\n592 608\n593 609\n594 610\n595 611\n596 612\n597 613\n598 614\n599 615\n600 616\n601 617\n602 618\n603 619\n604 620\n605 621\n606 622\n607 623\n608 624\n609 625\n610 626\n611 627\n612 628\n613 629\n614 630\n615 631\n616 632\n617 633\n618 634\n619 635\n620 636\n621 637\n622 638\n623 639\n624 640\n625 641\n626 642\n627 643\n628 644\n629 645\n630 646\n631 647\n632 648\n633 649\n634 650\n635 651\n636 652\n637 653\n638 654\n639 655\n640 656\n641 657\n642 658\n643 659\n644 660\n645 661\n646 662\n647 663\n648 664\n649 665\n650 666\n651 667\n652 668\n653 669\n654 670\n655 671\n656 672\n657 673\n658 674\n659 675\n660 676\n661 677\n662 678\n663 679\n664 680\n665 681\n666 682\n667 683\n668 684\n669 685\n670 686\n671 687\n672 688\n673 689\n674 690\n675 691\n676 692\n677 693\n678 694\n679 695\n680 696\n681 697\n682 698\n683 699\n684 700\n685 701\n686 702\n687 703\n688 704\n689 705\n690 706\n691 707\n692 708\n693 709\n694 710\n695 711\n696 712\n697 713\n698 714\n699 715\n700 716\n701 717\n702 718\n703 719\n704 720\n705 721\n706 722\n707 723\n708 724\n709 725\n710 726\n711 727\n712 728\n713 729\n714 730\n715 731\n716 732\n717 733\n718 734\n719 735\n720 736\n721 737\n722 738\n723 739\n724 740\n725 741\n726 742\n727 743\n728 744\n729 745\n730 746\n731 747\n732 748\n733 749\n734 750\n735 751\n736 752\n737 753\n738 754\n739 755\n740 756\n741 757\n742 758\n743 759\n744 760\n745 761\n746 762\n747 763\n748 764\n749 765\n750 766\n751 767\n752 768\n753 769\n754 770\n755 771\n756 772\n757 773\n758 774\n759 775\n760 776\n761 777\n762 778\n763 779\n764 780\n765 781\n766 782\n767 783\n768 784\n769 785\n770 786\n771 787\n772 788\n773 789\n774 790\n775 791\n776 792\n777 793\n778 794\n779 795\n780 796\n781 797\n782 798\n783 799\n784 800\n785 801\n786 802\n787 803\n788 804\n789 805\n790 806\n791 807\n792 808\n793 809\n794 810\n795 811\n796 812\n797 813\n798 814\n799 815\n800 816\n801 817\n802 818\n803 819\n804 820\n805 821\n806 822\n807 823\n808 824\n809 825\n810 826\n811 827\n812 828\n813 829\n814 830\n815 831\n816 832\n817 833\n818 834\n819 835\n820 836\n821 837\n822 838\n823 839\n824 840\n825 841\n826 842\n827 843\n828 844\n829 845\n830 846\n831 847\n832 848\n833 849\n834 850\n835 851\n836 852\n837 853\n838 854\n839 855\n840 856\n841 857\n842 858\n843 859\n844 860\n845 861\n846 862\n847 863\n848 864\n849 865\n850 866\n851 867\n852 868\n853 869\n854 870\n855 871\n856 872\n857 873\n858 874\n859 875\n860 876\n861 877\n862 878\n863 879\n864 880\n865 881\n866 882\n867 883\n868 884\n869 885\n870 886\n871 887\n872 888\n873 889\n874 890\n875 891\n876 892\n877 893\n878 894\n879 895\n880 896\n881 897\n882 898\n883 899\n884 900\n885 901\n886 902\n887 903\n888 904\n889 905\n890 906\n891 907\n892 908\n893 909\n894 910\n895 911\n896 912\n897 913\n898 914\n899 915\n900 916\n901 917\n902 918\n903 919\n904 920\n905 921\n906 922\n907 923\n908 924\n909 925\n910 926\n911 927\n912 928\n913 929\n914 930\n915 931\n916 932\n917 933\n918 934\n919 935\n920 936\n921 937\n922 938\n923 939\n924 940\n925 941\n926 942\n927 943\n928 944\n929 945\n930 946\n931 947\n932 948\n933 949\n934 950\n935 951\n936 952\n937 953\n938 954\n939 955\n940 956\n941 957\n942 958\n943 959\n944 960\n945 961\n946 962\n947 963\n948 964\n949 965\n950 966\n951 967\n952 968\n953 969\n954 970\n955 971\n956 972\n957 973\n958 974\n959 975\n960 976\n961 977\n962 978\n963 979\n964 980\n965 981\n966 982\n967 983\n968 984\n969 985\n970 986\n971 987\n972 988\n973 989\n974 990\n975 991\n976 992\n977 993\n978 994\n979 995\n980 996\n981 997\n982 998\n983 999\n984 1000\n985 1001\n986 1002\n987 1003\n988 1004\n989 1005\n990 1006\n991 1007\n992 1008\n993 1009\n994 1010\n995 1011\n996 1012\n997 1013\n998 1014\n999 1015\n1000 1016\n1001 1017\n1002 1018\n1003 1019\n1004 1020\n1005 1021\n1006 1022\n1007 1023\n1008 1024\n",
"90\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n2 25\n3 26\n4 27\n5 28\n6 29\n7 30\n8 31\n9 32\n10 33\n11 34\n12 35\n13 36\n14 37\n15 38\n16 39\n17 40\n18 41\n19 42\n20 43\n21 44\n22 45\n23 46\n24 47\n25 48\n26 49\n27 50\n28 51\n29 52\n30 53\n31 54\n32 55\n33 56\n34 57\n35 58\n36 59\n37 60\n38 61\n39 62\n40 63\n41 64\n42 65\n43 66\n44 67\n45 68\n46 69\n47 70\n48 71\n49 72\n50 73\n51 74\n52 75\n53 76\n54 77\n55 78\n56 79\n57 80\n58 81\n59 82\n60 83\n61 84\n62 85\n63 86\n64 87\n65 88\n66 89\n67 90\n68 91\n69 92\n70 93\n71 94\n72 95\n73 96\n74 97\n75 98\n76 99\n77 100\n78 101\n79 102\n80 103\n81 104\n82 105\n83 106\n84 107\n85 108\n86 109\n87 110\n88 111\n89 112\n90 113\n91 114\n92 115\n93 116\n94 117\n95 118\n96 119\n97 120\n98 121\n99 122\n100 123\n101 124\n102 125\n103 126\n104 127\n105 128\n106 129\n107 130\n108 131\n109 132\n110 133\n111 134\n112 135\n113 136\n114 137\n115 138\n116 139\n117 140\n118 141\n119 142\n120 143\n121 144\n122 145\n123 146\n124 147\n125 148\n126 149\n127 150\n128 151\n129 152\n130 153\n131 154\n132 155\n133 156\n134 157\n135 158\n136 159\n137 160\n138 161\n139 162\n140 163\n141 164\n142 165\n143 166\n144 167\n145 168\n146 169\n147 170\n148 171\n149 172\n150 173\n151 174\n152 175\n153 176\n154 177\n155 178\n156 179\n157 180\n158 181\n159 182\n160 183\n161 184\n162 185\n163 186\n164 187\n165 188\n166 189\n167 190\n168 191\n169 192\n170 193\n171 194\n172 195\n173 196\n174 197\n175 198\n176 199\n177 200\n178 201\n179 202\n180 203\n181 204\n182 205\n183 206\n184 207\n185 208\n186 209\n187 210\n188 211\n189 212\n190 213\n191 214\n192 215\n193 216\n194 217\n195 218\n196 219\n197 220\n198 221\n199 222\n200 223\n201 224\n202 225\n203 226\n204 227\n205 228\n206 229\n207 230\n208 231\n209 232\n210 233\n211 234\n212 235\n213 236\n214 237\n215 238\n216 239\n217 240\n218 241\n219 242\n220 243\n221 244\n222 245\n223 246\n224 247\n225 248\n226 249\n227 250\n228 251\n229 252\n230 253\n231 254\n232 255\n233 256\n234 257\n235 258\n236 259\n237 260\n238 261\n239 262\n240 263\n241 264\n242 265\n243 266\n244 267\n245 268\n246 269\n247 270\n248 271\n249 272\n250 273\n251 274\n252 275\n253 276\n254 277\n255 278\n256 279\n257 280\n258 281\n259 282\n260 283\n261 284\n262 285\n263 286\n264 287\n265 288\n266 289\n267 290\n268 291\n269 292\n270 293\n271 294\n272 295\n273 296\n274 297\n275 298\n276 299\n277 300\n278 301\n279 302\n280 303\n281 304\n282 305\n283 306\n284 307\n285 308\n286 309\n287 310\n288 311\n289 312\n290 313\n291 314\n292 315\n293 316\n294 317\n295 318\n296 319\n297 320\n298 321\n299 322\n300 323\n301 324\n302 325\n303 326\n304 327\n305 328\n306 329\n307 330\n308 331\n309 332\n310 333\n311 334\n312 335\n313 336\n314 337\n315 338\n316 339\n317 340\n318 341\n319 342\n320 343\n321 344\n322 345\n323 346\n324 347\n325 348\n326 349\n327 350\n328 351\n329 352\n330 353\n331 354\n332 355\n333 356\n334 357\n335 358\n336 359\n337 360\n338 361\n339 362\n340 363\n341 364\n342 365\n343 366\n344 367\n345 368\n346 369\n347 370\n348 371\n349 372\n350 373\n351 374\n352 375\n353 376\n354 377\n355 378\n356 379\n357 380\n358 381\n359 382\n360 383\n361 384\n362 385\n363 386\n364 387\n365 388\n366 389\n367 390\n368 391\n369 392\n370 393\n371 394\n372 395\n373 396\n374 397\n375 398\n376 399\n377 400\n378 401\n379 402\n380 403\n381 404\n382 405\n383 406\n384 407\n385 408\n386 409\n387 410\n388 411\n389 412\n390 413\n391 414\n392 415\n393 416\n394 417\n395 418\n396 419\n397 420\n398 421\n399 422\n400 423\n401 424\n402 425\n403 426\n404 427\n405 428\n406 429\n407 430\n408 431\n409 432\n410 433\n411 434\n412 435\n413 436\n414 437\n415 438\n416 439\n417 440\n418 441\n419 442\n420 443\n421 444\n422 445\n423 446\n424 447\n425 448\n426 449\n427 450\n428 451\n429 452\n430 453\n431 454\n432 455\n433 456\n434 457\n435 458\n436 459\n437 460\n438 461\n439 462\n440 463\n441 464\n442 465\n443 466\n444 467\n445 468\n446 469\n447 470\n448 471\n449 472\n450 473\n451 474\n452 475\n453 476\n454 477\n455 478\n456 479\n457 480\n458 481\n459 482\n460 483\n461 484\n462 485\n463 486\n464 487\n465 488\n466 489\n467 490\n468 491\n469 492\n470 493\n471 494\n472 495\n473 496\n474 497\n475 498\n476 499\n477 500\n478 501\n479 502\n480 503\n481 504\n482 505\n483 506\n484 507\n485 508\n486 509\n487 510\n488 511\n489 512\n490 513\n491 514\n492 515\n493 516\n494 517\n495 518\n496 519\n497 520\n498 521\n499 522\n500 523\n501 524\n502 525\n503 526\n504 527\n505 528\n506 529\n507 530\n508 531\n509 532\n510 533\n511 534\n512 535\n513 536\n514 537\n515 538\n516 539\n517 540\n518 541\n519 542\n520 543\n521 544\n522 545\n523 546\n524 547\n525 548\n526 549\n527 550\n528 551\n529 552\n530 553\n531 554\n532 555\n533 556\n534 557\n535 558\n536 559\n537 560\n538 561\n539 562\n540 563\n541 564\n542 565\n543 566\n544 567\n545 568\n546 569\n547 570\n548 571\n549 572\n550 573\n551 574\n552 575\n553 576\n554 577\n555 578\n556 579\n557 580\n558 581\n559 582\n560 583\n561 584\n562 585\n563 586\n564 587\n565 588\n566 589\n567 590\n568 591\n569 592\n570 593\n571 594\n572 595\n573 596\n574 597\n575 598\n576 599\n577 600\n578 601\n579 602\n580 603\n581 604\n582 605\n583 606\n584 607\n585 608\n586 609\n587 610\n588 611\n589 612\n590 613\n591 614\n592 615\n593 616\n594 617\n595 618\n596 619\n597 620\n598 621\n599 622\n600 623\n601 624\n602 625\n603 626\n604 627\n605 628\n606 629\n607 630\n608 631\n609 632\n610 633\n611 634\n612 635\n613 636\n614 637\n615 638\n616 639\n617 640\n618 641\n619 642\n620 643\n621 644\n622 645\n623 646\n624 647\n625 648\n626 649\n627 650\n628 651\n629 652\n630 653\n631 654\n632 655\n633 656\n634 657\n635 658\n636 659\n637 660\n638 661\n639 662\n640 663\n641 664\n642 665\n643 666\n644 667\n645 668\n646 669\n647 670\n648 671\n649 672\n650 673\n651 674\n652 675\n653 676\n654 677\n655 678\n656 679\n657 680\n658 681\n659 682\n660 683\n661 684\n662 685\n663 686\n664 687\n665 688\n666 689\n667 690\n668 691\n669 692\n670 693\n671 694\n672 695\n673 696\n674 697\n675 698\n676 699\n677 700\n678 701\n679 702\n680 703\n681 704\n682 705\n683 706\n684 707\n685 708\n686 709\n687 710\n688 711\n689 712\n690 713\n691 714\n692 715\n693 716\n694 717\n695 718\n696 719\n697 720\n698 721\n699 722\n700 723\n701 724\n702 725\n703 726\n704 727\n705 728\n706 729\n707 730\n708 731\n709 732\n710 733\n711 734\n712 735\n713 736\n714 737\n715 738\n716 739\n717 740\n718 741\n719 742\n720 743\n721 744\n722 745\n723 746\n724 747\n725 748\n726 749\n727 750\n728 751\n729 752\n730 753\n731 754\n732 755\n733 756\n734 757\n735 758\n736 759\n737 760\n738 761\n739 762\n740 763\n741 764\n742 765\n743 766\n744 767\n745 768\n746 769\n747 770\n748 771\n749 772\n750 773\n751 774\n752 775\n753 776\n754 777\n755 778\n756 779\n757 780\n758 781\n759 782\n760 783\n761 784\n762 785\n763 786\n764 787\n765 788\n766 789\n767 790\n768 791\n769 792\n770 793\n771 794\n772 795\n773 796\n774 797\n775 798\n776 799\n777 800\n778 801\n779 802\n780 803\n781 804\n782 805\n783 806\n784 807\n785 808\n786 809\n787 810\n788 811\n789 812\n790 813\n791 814\n792 815\n793 816\n794 817\n795 818\n796 819\n797 820\n798 821\n799 822\n800 823\n801 824\n802 825\n803 826\n804 827\n805 828\n806 829\n807 830\n808 831\n809 832\n810 833\n811 834\n812 835\n813 836\n814 837\n815 838\n816 839\n817 840\n818 841\n819 842\n820 843\n821 844\n822 845\n823 846\n824 847\n825 848\n826 849\n827 850\n828 851\n829 852\n830 853\n831 854\n832 855\n833 856\n834 857\n835 858\n836 859\n837 860\n838 861\n839 862\n840 863\n841 864\n842 865\n843 866\n844 867\n845 868\n846 869\n847 870\n848 871\n849 872\n850 873\n851 874\n852 875\n853 876\n854 877\n855 878\n856 879\n857 880\n858 881\n859 882\n860 883\n861 884\n862 885\n863 886\n864 887\n865 888\n866 889\n867 890\n868 891\n869 892\n870 893\n871 894\n872 895\n873 896\n874 897\n875 898\n876 899\n877 900\n878 901\n879 902\n880 903\n881 904\n882 905\n883 906\n884 907\n885 908\n886 909\n887 910\n888 911\n889 912\n890 913\n891 914\n892 915\n893 916\n894 917\n895 918\n896 919\n897 920\n898 921\n899 922\n900 923\n901 924\n902 925\n903 926\n904 927\n905 928\n906 929\n907 930\n908 931\n909 932\n910 933\n911 934\n912 935\n913 936\n914 937\n915 938\n916 939\n917 940\n918 941\n919 942\n920 943\n921 944\n922 945\n923 946\n924 947\n925 948\n926 949\n927 950\n928 951\n929 952\n930 953\n931 954\n932 955\n933 956\n934 957\n935 958\n936 959\n937 960\n938 961\n939 962\n940 963\n941 964\n942 965\n943 966\n944 967\n945 968\n946 969\n947 970\n948 971\n949 972\n950 973\n951 974\n952 975\n953 976\n954 977\n955 978\n956 979\n957 980\n958 981\n959 982\n960 983\n961 984\n962 985\n963 986\n964 987\n965 988\n966 989\n967 990\n968 991\n969 992\n970 993\n971 994\n972 995\n973 996\n974 997\n975 998\n976 999\n977 1000\n978 1001\n979 1002\n980 1003\n981 1004\n982 1005\n983 1006\n984 1007\n985 1008\n986 1009\n987 1010\n988 1011\n989 1012\n990 1013\n991 1014\n992 1015\n993 1016\n994 1017\n995 1018\n996 1019\n997 1020\n998 1021\n999 1022\n1000 1023\n1001 1024\n",
"3\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n2 1000\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n2 510\n3 511\n4 512\n5 513\n6 514\n7 515\n8 516\n9 517\n10 518\n11 519\n12 520\n13 521\n14 522\n15 523\n16 524\n17 525\n18 526\n19 527\n20 528\n21 529\n22 530\n23 531\n24 532\n25 533\n26 534\n27 535\n28 536\n29 537\n30 538\n31 539\n32 540\n33 541\n34 542\n35 543\n36 544\n37 545\n38 546\n39 547\n40 548\n41 549\n42 550\n43 551\n44 552\n45 553\n46 554\n47 555\n48 556\n49 557\n50 558\n51 559\n52 560\n53 561\n54 562\n55 563\n56 564\n57 565\n58 566\n59 567\n60 568\n61 569\n62 570\n63 571\n64 572\n65 573\n66 574\n67 575\n68 576\n69 577\n70 578\n71 579\n72 580\n73 581\n74 582\n75 583\n76 584\n77 585\n78 586\n79 587\n80 588\n81 589\n82 590\n83 591\n84 592\n85 593\n86 594\n87 595\n88 596\n89 597\n90 598\n91 599\n92 600\n93 601\n94 602\n95 603\n96 604\n97 605\n98 606\n99 607\n100 608\n101 609\n102 610\n103 611\n104 612\n105 613\n106 614\n107 615\n108 616\n109 617\n110 618\n111 619\n112 620\n113 621\n114 622\n115 623\n116 624\n117 625\n118 626\n119 627\n120 628\n121 629\n122 630\n123 631\n124 632\n125 633\n126 634\n127 635\n128 636\n129 637\n130 638\n131 639\n132 640\n133 641\n134 642\n135 643\n136 644\n137 645\n138 646\n139 647\n140 648\n141 649\n142 650\n143 651\n144 652\n145 653\n146 654\n147 655\n148 656\n149 657\n150 658\n151 659\n152 660\n153 661\n154 662\n155 663\n156 664\n157 665\n158 666\n159 667\n160 668\n161 669\n162 670\n163 671\n164 672\n165 673\n166 674\n167 675\n168 676\n169 677\n170 678\n171 679\n172 680\n173 681\n174 682\n175 683\n176 684\n177 685\n178 686\n179 687\n180 688\n181 689\n182 690\n183 691\n184 692\n185 693\n186 694\n187 695\n188 696\n189 697\n190 698\n191 699\n192 700\n193 701\n194 702\n195 703\n196 704\n197 705\n198 706\n199 707\n200 708\n201 709\n202 710\n203 711\n204 712\n205 713\n206 714\n207 715\n208 716\n209 717\n210 718\n211 719\n212 720\n213 721\n214 722\n215 723\n216 724\n217 725\n218 726\n219 727\n220 728\n221 729\n222 730\n223 731\n224 732\n225 733\n226 734\n227 735\n228 736\n229 737\n230 738\n231 739\n232 740\n233 741\n234 742\n235 743\n236 744\n237 745\n238 746\n239 747\n240 748\n241 749\n242 750\n243 751\n244 752\n245 753\n246 754\n247 755\n248 756\n249 757\n250 758\n251 759\n252 760\n253 761\n254 762\n255 763\n256 764\n257 765\n258 766\n259 767\n260 768\n261 769\n262 770\n263 771\n264 772\n265 773\n266 774\n267 775\n268 776\n269 777\n270 778\n271 779\n272 780\n273 781\n274 782\n275 783\n276 784\n277 785\n278 786\n279 787\n280 788\n281 789\n282 790\n283 791\n284 792\n285 793\n286 794\n287 795\n288 796\n289 797\n290 798\n291 799\n292 800\n293 801\n294 802\n295 803\n296 804\n297 805\n298 806\n299 807\n300 808\n301 809\n302 810\n303 811\n304 812\n305 813\n306 814\n307 815\n308 816\n309 817\n310 818\n311 819\n312 820\n313 821\n314 822\n315 823\n316 824\n317 825\n318 826\n319 827\n320 828\n321 829\n322 830\n323 831\n324 832\n325 833\n326 834\n327 835\n328 836\n329 837\n330 838\n331 839\n332 840\n333 841\n334 842\n335 843\n336 844\n337 845\n338 846\n339 847\n340 848\n341 849\n342 850\n343 851\n344 852\n345 853\n346 854\n347 855\n348 856\n349 857\n350 858\n351 859\n352 860\n353 861\n354 862\n355 863\n356 864\n357 865\n358 866\n359 867\n360 868\n361 869\n362 870\n363 871\n364 872\n365 873\n366 874\n367 875\n368 876\n369 877\n370 878\n371 879\n372 880\n373 881\n374 882\n375 883\n376 884\n377 885\n378 886\n379 887\n380 888\n381 889\n382 890\n383 891\n384 892\n385 893\n386 894\n387 895\n388 896\n389 897\n390 898\n391 899\n392 900\n393 901\n394 902\n395 903\n396 904\n397 905\n398 906\n399 907\n400 908\n401 909\n402 910\n403 911\n404 912\n405 913\n406 914\n407 915\n408 916\n409 917\n410 918\n411 919\n412 920\n413 921\n414 922\n415 923\n416 924\n417 925\n418 926\n419 927\n420 928\n421 929\n422 930\n423 931\n424 932\n425 933\n426 934\n427 935\n428 936\n429 937\n430 938\n431 939\n432 940\n433 941\n434 942\n435 943\n436 944\n437 945\n438 946\n439 947\n440 948\n441 949\n442 950\n443 951\n444 952\n445 953\n446 954\n447 955\n448 956\n449 957\n450 958\n451 959\n452 960\n453 961\n454 962\n455 963\n456 964\n457 965\n458 966\n459 967\n460 968\n461 969\n462 970\n463 971\n464 972\n465 973\n466 974\n467 975\n468 976\n469 977\n470 978\n471 979\n472 980\n473 981\n474 982\n475 983\n476 984\n477 985\n478 986\n479 987\n480 988\n481 989\n482 990\n483 991\n484 992\n485 993\n486 994\n487 995\n488 996\n489 997\n490 998\n491 999\n492 1000\n493 1001\n494 1002\n495 1003\n496 1004\n497 1005\n498 1006\n499 1007\n500 1008\n501 1009\n502 1010\n503 1011\n504 1012\n505 1013\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n2 509\n3 510\n4 511\n5 512\n6 513\n7 514\n8 515\n9 516\n10 517\n11 518\n12 519\n13 520\n14 521\n15 522\n16 523\n17 524\n18 525\n19 526\n20 527\n21 528\n22 529\n23 530\n24 531\n25 532\n26 533\n27 534\n28 535\n29 536\n30 537\n31 538\n32 539\n33 540\n34 541\n35 542\n36 543\n37 544\n38 545\n39 546\n40 547\n41 548\n42 549\n43 550\n44 551\n45 552\n46 553\n47 554\n48 555\n49 556\n50 557\n51 558\n52 559\n53 560\n54 561\n55 562\n56 563\n57 564\n58 565\n59 566\n60 567\n61 568\n62 569\n63 570\n64 571\n65 572\n66 573\n67 574\n68 575\n69 576\n70 577\n71 578\n72 579\n73 580\n74 581\n75 582\n76 583\n77 584\n78 585\n79 586\n80 587\n81 588\n82 589\n83 590\n84 591\n85 592\n86 593\n87 594\n88 595\n89 596\n90 597\n91 598\n92 599\n93 600\n94 601\n95 602\n96 603\n97 604\n98 605\n99 606\n100 607\n101 608\n102 609\n103 610\n104 611\n105 612\n106 613\n107 614\n108 615\n109 616\n110 617\n111 618\n112 619\n113 620\n114 621\n115 622\n116 623\n117 624\n118 625\n119 626\n120 627\n121 628\n122 629\n123 630\n124 631\n125 632\n126 633\n127 634\n128 635\n129 636\n130 637\n131 638\n132 639\n133 640\n134 641\n135 642\n136 643\n137 644\n138 645\n139 646\n140 647\n141 648\n142 649\n143 650\n144 651\n145 652\n146 653\n147 654\n148 655\n149 656\n150 657\n151 658\n152 659\n153 660\n154 661\n155 662\n156 663\n157 664\n158 665\n159 666\n160 667\n161 668\n162 669\n163 670\n164 671\n165 672\n166 673\n167 674\n168 675\n169 676\n170 677\n171 678\n172 679\n173 680\n174 681\n175 682\n176 683\n177 684\n178 685\n179 686\n180 687\n181 688\n182 689\n183 690\n184 691\n185 692\n186 693\n187 694\n188 695\n189 696\n190 697\n191 698\n192 699\n193 700\n194 701\n195 702\n196 703\n197 704\n198 705\n199 706\n200 707\n201 708\n202 709\n203 710\n204 711\n205 712\n206 713\n207 714\n208 715\n209 716\n210 717\n211 718\n212 719\n213 720\n214 721\n215 722\n216 723\n217 724\n218 725\n219 726\n220 727\n221 728\n222 729\n223 730\n224 731\n225 732\n226 733\n227 734\n228 735\n229 736\n230 737\n231 738\n232 739\n233 740\n234 741\n235 742\n236 743\n237 744\n238 745\n239 746\n240 747\n241 748\n242 749\n243 750\n244 751\n245 752\n246 753\n247 754\n248 755\n249 756\n250 757\n251 758\n252 759\n253 760\n254 761\n255 762\n256 763\n257 764\n258 765\n259 766\n260 767\n261 768\n262 769\n263 770\n264 771\n265 772\n266 773\n267 774\n268 775\n269 776\n270 777\n271 778\n272 779\n273 780\n274 781\n275 782\n276 783\n277 784\n278 785\n279 786\n280 787\n281 788\n282 789\n283 790\n284 791\n285 792\n286 793\n287 794\n288 795\n289 796\n290 797\n291 798\n292 799\n293 800\n294 801\n295 802\n296 803\n297 804\n298 805\n299 806\n300 807\n301 808\n302 809\n303 810\n304 811\n305 812\n306 813\n307 814\n308 815\n309 816\n310 817\n311 818\n312 819\n313 820\n314 821\n315 822\n316 823\n317 824\n318 825\n319 826\n320 827\n321 828\n322 829\n323 830\n324 831\n325 832\n326 833\n327 834\n328 835\n329 836\n330 837\n331 838\n332 839\n333 840\n334 841\n335 842\n336 843\n337 844\n338 845\n339 846\n340 847\n341 848\n342 849\n343 850\n344 851\n345 852\n346 853\n347 854\n348 855\n349 856\n350 857\n351 858\n352 859\n353 860\n354 861\n355 862\n356 863\n357 864\n358 865\n359 866\n360 867\n361 868\n362 869\n363 870\n364 871\n365 872\n366 873\n367 874\n368 875\n369 876\n370 877\n371 878\n372 879\n373 880\n374 881\n375 882\n376 883\n377 884\n378 885\n379 886\n380 887\n381 888\n382 889\n383 890\n384 891\n385 892\n386 893\n387 894\n388 895\n389 896\n390 897\n391 898\n392 899\n393 900\n394 901\n395 902\n396 903\n397 904\n398 905\n399 906\n400 907\n401 908\n402 909\n403 910\n404 911\n405 912\n406 913\n407 914\n408 915\n409 916\n410 917\n411 918\n412 919\n413 920\n414 921\n415 922\n416 923\n417 924\n418 925\n419 926\n420 927\n421 928\n422 929\n423 930\n424 931\n425 932\n426 933\n427 934\n428 935\n429 936\n430 937\n431 938\n432 939\n433 940\n434 941\n435 942\n436 943\n437 944\n438 945\n439 946\n440 947\n441 948\n442 949\n443 950\n444 951\n445 952\n446 953\n447 954\n448 955\n449 956\n450 957\n451 958\n452 959\n453 960\n454 961\n455 962\n456 963\n457 964\n458 965\n459 966\n460 967\n461 968\n462 969\n463 970\n464 971\n465 972\n466 973\n467 974\n468 975\n469 976\n470 977\n471 978\n472 979\n473 980\n474 981\n475 982\n476 983\n477 984\n478 985\n479 986\n480 987\n481 988\n482 989\n483 990\n484 991\n485 992\n486 993\n487 994\n488 995\n489 996\n490 997\n491 998\n492 999\n493 1000\n494 1001\n495 1002\n496 1003\n497 1004\n498 1005\n499 1006\n500 1007\n501 1008\n502 1009\n503 1010\n504 1011\n505 1012\n506 1013\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n2 61\n3 62\n4 63\n5 64\n6 65\n7 66\n8 67\n9 68\n10 69\n11 70\n12 71\n13 72\n14 73\n15 74\n16 75\n17 76\n18 77\n19 78\n20 79\n21 80\n22 81\n23 82\n24 83\n25 84\n26 85\n27 86\n28 87\n29 88\n30 89\n31 90\n32 91\n33 92\n34 93\n35 94\n36 95\n37 96\n38 97\n39 98\n40 99\n41 100\n",
"3\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n2 100\n",
"2\n1 2\n1 3\n1 4\n",
"2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n1 1000\n1 1001\n1 1002\n1 1003\n1 1004\n1 1005\n1 1006\n1 1007\n1 1008\n1 1009\n1 1010\n1 1011\n1 1012\n1 1013\n",
"40\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n6 11\n7 12\n8 13\n9 14\n10 15\n11 16\n12 17\n13 18\n14 19\n15 20\n16 21\n17 22\n18 23\n19 24\n20 25\n21 26\n22 27\n23 28\n24 29\n25 30\n26 31\n27 32\n28 33\n29 34\n30 35\n31 36\n32 37\n33 38\n34 39\n35 40\n36 41\n37 42\n38 43\n39 44\n40 45\n41 46\n42 47\n43 48\n44 49\n45 50\n46 51\n47 52\n48 53\n49 54\n50 55\n51 56\n52 57\n53 58\n54 59\n55 60\n56 61\n57 62\n58 63\n59 64\n60 65\n61 66\n62 67\n63 68\n64 69\n65 70\n66 71\n67 72\n68 73\n69 74\n70 75\n71 76\n72 77\n73 78\n74 79\n75 80\n76 81\n77 82\n78 83\n79 84\n80 85\n81 86\n82 87\n83 88\n84 89\n85 90\n86 91\n87 92\n88 93\n89 94\n90 95\n91 96\n92 97\n93 98\n94 99\n95 100\n",
"2\n1 2\n1 3\n1 4\n1 5\n",
"5\n1 2\n1 3\n2 4\n3 5\n4 6\n",
"10\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n2 247\n3 248\n4 249\n5 250\n6 251\n7 252\n8 253\n9 254\n10 255\n11 256\n12 257\n13 258\n14 259\n15 260\n16 261\n17 262\n18 263\n19 264\n20 265\n21 266\n22 267\n23 268\n24 269\n25 270\n26 271\n27 272\n28 273\n29 274\n30 275\n31 276\n32 277\n33 278\n34 279\n35 280\n36 281\n37 282\n38 283\n39 284\n40 285\n41 286\n42 287\n43 288\n44 289\n45 290\n46 291\n47 292\n48 293\n49 294\n50 295\n51 296\n52 297\n53 298\n54 299\n55 300\n56 301\n57 302\n58 303\n59 304\n60 305\n61 306\n62 307\n63 308\n64 309\n65 310\n66 311\n67 312\n68 313\n69 314\n70 315\n71 316\n72 317\n73 318\n74 319\n75 320\n76 321\n77 322\n78 323\n79 324\n80 325\n81 326\n82 327\n83 328\n84 329\n85 330\n86 331\n87 332\n88 333\n89 334\n90 335\n91 336\n92 337\n93 338\n94 339\n95 340\n96 341\n97 342\n98 343\n99 344\n100 345\n101 346\n102 347\n103 348\n104 349\n105 350\n106 351\n107 352\n108 353\n109 354\n110 355\n111 356\n112 357\n113 358\n114 359\n115 360\n116 361\n117 362\n118 363\n119 364\n120 365\n121 366\n122 367\n123 368\n124 369\n125 370\n126 371\n127 372\n128 373\n129 374\n130 375\n131 376\n132 377\n133 378\n134 379\n135 380\n136 381\n137 382\n138 383\n139 384\n140 385\n141 386\n142 387\n143 388\n144 389\n145 390\n146 391\n147 392\n148 393\n149 394\n150 395\n151 396\n152 397\n153 398\n154 399\n155 400\n156 401\n157 402\n158 403\n159 404\n160 405\n161 406\n162 407\n163 408\n164 409\n165 410\n166 411\n167 412\n168 413\n169 414\n170 415\n171 416\n172 417\n173 418\n174 419\n175 420\n176 421\n177 422\n178 423\n179 424\n180 425\n181 426\n182 427\n183 428\n184 429\n185 430\n186 431\n187 432\n188 433\n189 434\n190 435\n191 436\n192 437\n193 438\n194 439\n195 440\n196 441\n197 442\n198 443\n199 444\n200 445\n201 446\n202 447\n203 448\n204 449\n205 450\n206 451\n207 452\n208 453\n209 454\n210 455\n211 456\n212 457\n213 458\n214 459\n215 460\n216 461\n217 462\n218 463\n219 464\n220 465\n221 466\n222 467\n223 468\n224 469\n225 470\n226 471\n227 472\n228 473\n229 474\n230 475\n231 476\n232 477\n233 478\n234 479\n235 480\n236 481\n237 482\n238 483\n239 484\n240 485\n241 486\n242 487\n243 488\n244 489\n245 490\n246 491\n247 492\n248 493\n249 494\n250 495\n251 496\n252 497\n253 498\n254 499\n255 500\n256 501\n257 502\n258 503\n259 504\n260 505\n261 506\n262 507\n263 508\n264 509\n265 510\n266 511\n267 512\n268 513\n269 514\n270 515\n271 516\n272 517\n273 518\n274 519\n275 520\n276 521\n277 522\n278 523\n279 524\n280 525\n281 526\n282 527\n283 528\n284 529\n285 530\n286 531\n287 532\n288 533\n289 534\n290 535\n291 536\n292 537\n293 538\n294 539\n295 540\n296 541\n297 542\n298 543\n299 544\n300 545\n301 546\n302 547\n303 548\n304 549\n305 550\n306 551\n307 552\n308 553\n309 554\n310 555\n311 556\n312 557\n313 558\n314 559\n315 560\n316 561\n317 562\n318 563\n319 564\n320 565\n321 566\n322 567\n323 568\n324 569\n325 570\n326 571\n327 572\n328 573\n329 574\n330 575\n331 576\n332 577\n333 578\n334 579\n335 580\n336 581\n337 582\n338 583\n339 584\n340 585\n341 586\n342 587\n343 588\n344 589\n345 590\n346 591\n347 592\n348 593\n349 594\n350 595\n351 596\n352 597\n353 598\n354 599\n355 600\n356 601\n357 602\n358 603\n359 604\n360 605\n361 606\n362 607\n363 608\n364 609\n365 610\n366 611\n367 612\n368 613\n369 614\n370 615\n371 616\n372 617\n373 618\n374 619\n375 620\n376 621\n377 622\n378 623\n379 624\n380 625\n381 626\n382 627\n383 628\n384 629\n385 630\n386 631\n387 632\n388 633\n389 634\n390 635\n391 636\n392 637\n393 638\n394 639\n395 640\n396 641\n397 642\n398 643\n399 644\n400 645\n401 646\n402 647\n403 648\n404 649\n405 650\n406 651\n407 652\n408 653\n409 654\n410 655\n411 656\n412 657\n413 658\n414 659\n415 660\n416 661\n417 662\n418 663\n419 664\n420 665\n421 666\n422 667\n423 668\n424 669\n425 670\n426 671\n427 672\n428 673\n429 674\n430 675\n431 676\n432 677\n433 678\n434 679\n435 680\n436 681\n437 682\n438 683\n439 684\n440 685\n441 686\n442 687\n443 688\n444 689\n445 690\n446 691\n447 692\n448 693\n449 694\n450 695\n451 696\n452 697\n453 698\n454 699\n455 700\n456 701\n457 702\n458 703\n459 704\n460 705\n461 706\n462 707\n463 708\n464 709\n465 710\n466 711\n467 712\n468 713\n469 714\n470 715\n471 716\n472 717\n473 718\n474 719\n475 720\n476 721\n477 722\n478 723\n479 724\n480 725\n481 726\n482 727\n483 728\n484 729\n485 730\n486 731\n487 732\n488 733\n489 734\n490 735\n491 736\n492 737\n493 738\n494 739\n495 740\n496 741\n497 742\n498 743\n499 744\n500 745\n501 746\n502 747\n503 748\n504 749\n505 750\n506 751\n507 752\n508 753\n509 754\n510 755\n511 756\n512 757\n513 758\n514 759\n515 760\n516 761\n517 762\n518 763\n519 764\n520 765\n521 766\n522 767\n523 768\n524 769\n525 770\n526 771\n527 772\n528 773\n529 774\n530 775\n531 776\n532 777\n533 778\n534 779\n535 780\n536 781\n537 782\n538 783\n539 784\n540 785\n541 786\n542 787\n543 788\n544 789\n545 790\n546 791\n547 792\n548 793\n549 794\n550 795\n551 796\n552 797\n553 798\n554 799\n555 800\n556 801\n557 802\n558 803\n559 804\n560 805\n561 806\n562 807\n563 808\n564 809\n565 810\n566 811\n567 812\n568 813\n569 814\n570 815\n571 816\n572 817\n573 818\n574 819\n575 820\n576 821\n577 822\n578 823\n579 824\n580 825\n581 826\n582 827\n583 828\n584 829\n585 830\n586 831\n587 832\n588 833\n589 834\n590 835\n591 836\n592 837\n593 838\n594 839\n595 840\n596 841\n597 842\n598 843\n599 844\n600 845\n601 846\n602 847\n603 848\n604 849\n605 850\n606 851\n607 852\n608 853\n609 854\n610 855\n611 856\n612 857\n613 858\n614 859\n615 860\n616 861\n617 862\n618 863\n619 864\n620 865\n621 866\n622 867\n623 868\n624 869\n625 870\n626 871\n627 872\n628 873\n629 874\n630 875\n631 876\n632 877\n633 878\n634 879\n635 880\n636 881\n637 882\n638 883\n639 884\n640 885\n641 886\n642 887\n643 888\n644 889\n645 890\n646 891\n647 892\n648 893\n649 894\n650 895\n651 896\n652 897\n653 898\n654 899\n655 900\n656 901\n657 902\n658 903\n659 904\n660 905\n661 906\n662 907\n663 908\n664 909\n665 910\n666 911\n667 912\n668 913\n669 914\n670 915\n671 916\n672 917\n673 918\n674 919\n675 920\n676 921\n677 922\n678 923\n679 924\n680 925\n681 926\n682 927\n683 928\n684 929\n685 930\n686 931\n687 932\n688 933\n689 934\n690 935\n691 936\n692 937\n693 938\n694 939\n695 940\n696 941\n697 942\n698 943\n699 944\n700 945\n701 946\n702 947\n703 948\n704 949\n705 950\n706 951\n707 952\n708 953\n709 954\n710 955\n711 956\n712 957\n713 958\n714 959\n715 960\n716 961\n717 962\n718 963\n719 964\n720 965\n721 966\n722 967\n723 968\n724 969\n725 970\n726 971\n727 972\n728 973\n729 974\n730 975\n731 976\n732 977\n733 978\n734 979\n735 980\n736 981\n737 982\n738 983\n739 984\n740 985\n741 986\n742 987\n743 988\n744 989\n745 990\n746 991\n747 992\n748 993\n749 994\n750 995\n751 996\n752 997\n753 998\n754 999\n755 1000\n",
"1023\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n554 556\n555 557\n556 558\n557 559\n558 560\n559 561\n560 562\n561 563\n562 564\n563 565\n564 566\n565 567\n566 568\n567 569\n568 570\n569 571\n570 572\n571 573\n572 574\n573 575\n574 576\n575 577\n576 578\n577 579\n578 580\n579 581\n580 582\n581 583\n582 584\n583 585\n584 586\n585 587\n586 588\n587 589\n588 590\n589 591\n590 592\n591 593\n592 594\n593 595\n594 596\n595 597\n596 598\n597 599\n598 600\n599 601\n600 602\n601 603\n602 604\n603 605\n604 606\n605 607\n606 608\n607 609\n608 610\n609 611\n610 612\n611 613\n612 614\n613 615\n614 616\n615 617\n616 618\n617 619\n618 620\n619 621\n620 622\n621 623\n622 624\n623 625\n624 626\n625 627\n626 628\n627 629\n628 630\n629 631\n630 632\n631 633\n632 634\n633 635\n634 636\n635 637\n636 638\n637 639\n638 640\n639 641\n640 642\n641 643\n642 644\n643 645\n644 646\n645 647\n646 648\n647 649\n648 650\n649 651\n650 652\n651 653\n652 654\n653 655\n654 656\n655 657\n656 658\n657 659\n658 660\n659 661\n660 662\n661 663\n662 664\n663 665\n664 666\n665 667\n666 668\n667 669\n668 670\n669 671\n670 672\n671 673\n672 674\n673 675\n674 676\n675 677\n676 678\n677 679\n678 680\n679 681\n680 682\n681 683\n682 684\n683 685\n684 686\n685 687\n686 688\n687 689\n688 690\n689 691\n690 692\n691 693\n692 694\n693 695\n694 696\n695 697\n696 698\n697 699\n698 700\n699 701\n700 702\n701 703\n702 704\n703 705\n704 706\n705 707\n706 708\n707 709\n708 710\n709 711\n710 712\n711 713\n712 714\n713 715\n714 716\n715 717\n716 718\n717 719\n718 720\n719 721\n720 722\n721 723\n722 724\n723 725\n724 726\n725 727\n726 728\n727 729\n728 730\n729 731\n730 732\n731 733\n732 734\n733 735\n734 736\n735 737\n736 738\n737 739\n738 740\n739 741\n740 742\n741 743\n742 744\n743 745\n744 746\n745 747\n746 748\n747 749\n748 750\n749 751\n750 752\n751 753\n752 754\n753 755\n754 756\n755 757\n756 758\n757 759\n758 760\n759 761\n760 762\n761 763\n762 764\n763 765\n764 766\n765 767\n766 768\n767 769\n768 770\n769 771\n770 772\n771 773\n772 774\n773 775\n774 776\n775 777\n776 778\n777 779\n778 780\n779 781\n780 782\n781 783\n782 784\n783 785\n784 786\n785 787\n786 788\n787 789\n788 790\n789 791\n790 792\n791 793\n792 794\n793 795\n794 796\n795 797\n796 798\n797 799\n798 800\n799 801\n800 802\n801 803\n802 804\n803 805\n804 806\n805 807\n806 808\n807 809\n808 810\n809 811\n810 812\n811 813\n812 814\n813 815\n814 816\n815 817\n816 818\n817 819\n818 820\n819 821\n820 822\n821 823\n822 824\n823 825\n824 826\n825 827\n826 828\n827 829\n828 830\n829 831\n830 832\n831 833\n832 834\n833 835\n834 836\n835 837\n836 838\n837 839\n838 840\n839 841\n840 842\n841 843\n842 844\n843 845\n844 846\n845 847\n846 848\n847 849\n848 850\n849 851\n850 852\n851 853\n852 854\n853 855\n854 856\n855 857\n856 858\n857 859\n858 860\n859 861\n860 862\n861 863\n862 864\n863 865\n864 866\n865 867\n866 868\n867 869\n868 870\n869 871\n870 872\n871 873\n872 874\n873 875\n874 876\n875 877\n876 878\n877 879\n878 880\n879 881\n880 882\n881 883\n882 884\n883 885\n884 886\n885 887\n886 888\n887 889\n888 890\n889 891\n890 892\n891 893\n892 894\n893 895\n894 896\n895 897\n896 898\n897 899\n898 900\n899 901\n900 902\n901 903\n902 904\n903 905\n904 906\n905 907\n906 908\n907 909\n908 910\n909 911\n910 912\n911 913\n912 914\n913 915\n914 916\n915 917\n916 918\n917 919\n918 920\n919 921\n920 922\n921 923\n922 924\n923 925\n924 926\n925 927\n926 928\n927 929\n928 930\n929 931\n930 932\n931 933\n932 934\n933 935\n934 936\n935 937\n936 938\n937 939\n938 940\n939 941\n940 942\n941 943\n942 944\n943 945\n944 946\n945 947\n946 948\n947 949\n948 950\n949 951\n950 952\n951 953\n952 954\n953 955\n954 956\n955 957\n956 958\n957 959\n958 960\n959 961\n960 962\n961 963\n962 964\n963 965\n964 966\n965 967\n966 968\n967 969\n968 970\n969 971\n970 972\n971 973\n972 974\n973 975\n974 976\n975 977\n976 978\n977 979\n978 980\n979 981\n980 982\n981 983\n982 984\n983 985\n984 986\n985 987\n986 988\n987 989\n988 990\n989 991\n990 992\n991 993\n992 994\n993 995\n994 996\n995 997\n996 998\n997 999\n998 1000\n999 1001\n1000 1002\n1001 1003\n1002 1004\n1003 1005\n1004 1006\n1005 1007\n1006 1008\n1007 1009\n1008 1010\n1009 1011\n1010 1012\n1011 1013\n1012 1014\n1013 1015\n1014 1016\n1015 1017\n1016 1018\n1017 1019\n1018 1020\n1019 1021\n1020 1022\n1021 1023\n1022 1024\n",
"999\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n554 556\n555 557\n556 558\n557 559\n558 560\n559 561\n560 562\n561 563\n562 564\n563 565\n564 566\n565 567\n566 568\n567 569\n568 570\n569 571\n570 572\n571 573\n572 574\n573 575\n574 576\n575 577\n576 578\n577 579\n578 580\n579 581\n580 582\n581 583\n582 584\n583 585\n584 586\n585 587\n586 588\n587 589\n588 590\n589 591\n590 592\n591 593\n592 594\n593 595\n594 596\n595 597\n596 598\n597 599\n598 600\n599 601\n600 602\n601 603\n602 604\n603 605\n604 606\n605 607\n606 608\n607 609\n608 610\n609 611\n610 612\n611 613\n612 614\n613 615\n614 616\n615 617\n616 618\n617 619\n618 620\n619 621\n620 622\n621 623\n622 624\n623 625\n624 626\n625 627\n626 628\n627 629\n628 630\n629 631\n630 632\n631 633\n632 634\n633 635\n634 636\n635 637\n636 638\n637 639\n638 640\n639 641\n640 642\n641 643\n642 644\n643 645\n644 646\n645 647\n646 648\n647 649\n648 650\n649 651\n650 652\n651 653\n652 654\n653 655\n654 656\n655 657\n656 658\n657 659\n658 660\n659 661\n660 662\n661 663\n662 664\n663 665\n664 666\n665 667\n666 668\n667 669\n668 670\n669 671\n670 672\n671 673\n672 674\n673 675\n674 676\n675 677\n676 678\n677 679\n678 680\n679 681\n680 682\n681 683\n682 684\n683 685\n684 686\n685 687\n686 688\n687 689\n688 690\n689 691\n690 692\n691 693\n692 694\n693 695\n694 696\n695 697\n696 698\n697 699\n698 700\n699 701\n700 702\n701 703\n702 704\n703 705\n704 706\n705 707\n706 708\n707 709\n708 710\n709 711\n710 712\n711 713\n712 714\n713 715\n714 716\n715 717\n716 718\n717 719\n718 720\n719 721\n720 722\n721 723\n722 724\n723 725\n724 726\n725 727\n726 728\n727 729\n728 730\n729 731\n730 732\n731 733\n732 734\n733 735\n734 736\n735 737\n736 738\n737 739\n738 740\n739 741\n740 742\n741 743\n742 744\n743 745\n744 746\n745 747\n746 748\n747 749\n748 750\n749 751\n750 752\n751 753\n752 754\n753 755\n754 756\n755 757\n756 758\n757 759\n758 760\n759 761\n760 762\n761 763\n762 764\n763 765\n764 766\n765 767\n766 768\n767 769\n768 770\n769 771\n770 772\n771 773\n772 774\n773 775\n774 776\n775 777\n776 778\n777 779\n778 780\n779 781\n780 782\n781 783\n782 784\n783 785\n784 786\n785 787\n786 788\n787 789\n788 790\n789 791\n790 792\n791 793\n792 794\n793 795\n794 796\n795 797\n796 798\n797 799\n798 800\n799 801\n800 802\n801 803\n802 804\n803 805\n804 806\n805 807\n806 808\n807 809\n808 810\n809 811\n810 812\n811 813\n812 814\n813 815\n814 816\n815 817\n816 818\n817 819\n818 820\n819 821\n820 822\n821 823\n822 824\n823 825\n824 826\n825 827\n826 828\n827 829\n828 830\n829 831\n830 832\n831 833\n832 834\n833 835\n834 836\n835 837\n836 838\n837 839\n838 840\n839 841\n840 842\n841 843\n842 844\n843 845\n844 846\n845 847\n846 848\n847 849\n848 850\n849 851\n850 852\n851 853\n852 854\n853 855\n854 856\n855 857\n856 858\n857 859\n858 860\n859 861\n860 862\n861 863\n862 864\n863 865\n864 866\n865 867\n866 868\n867 869\n868 870\n869 871\n870 872\n871 873\n872 874\n873 875\n874 876\n875 877\n876 878\n877 879\n878 880\n879 881\n880 882\n881 883\n882 884\n883 885\n884 886\n885 887\n886 888\n887 889\n888 890\n889 891\n890 892\n891 893\n892 894\n893 895\n894 896\n895 897\n896 898\n897 899\n898 900\n899 901\n900 902\n901 903\n902 904\n903 905\n904 906\n905 907\n906 908\n907 909\n908 910\n909 911\n910 912\n911 913\n912 914\n913 915\n914 916\n915 917\n916 918\n917 919\n918 920\n919 921\n920 922\n921 923\n922 924\n923 925\n924 926\n925 927\n926 928\n927 929\n928 930\n929 931\n930 932\n931 933\n932 934\n933 935\n934 936\n935 937\n936 938\n937 939\n938 940\n939 941\n940 942\n941 943\n942 944\n943 945\n944 946\n945 947\n946 948\n947 949\n948 950\n949 951\n950 952\n951 953\n952 954\n953 955\n954 956\n955 957\n956 958\n957 959\n958 960\n959 961\n960 962\n961 963\n962 964\n963 965\n964 966\n965 967\n966 968\n967 969\n968 970\n969 971\n970 972\n971 973\n972 974\n973 975\n974 976\n975 977\n976 978\n977 979\n978 980\n979 981\n980 982\n981 983\n982 984\n983 985\n984 986\n985 987\n986 988\n987 989\n988 990\n989 991\n990 992\n991 993\n992 994\n993 995\n994 996\n995 997\n996 998\n997 999\n998 1000\n",
"99\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n",
"4\n1 2\n1 3\n1 4\n2 5\n3 6\n",
"7\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n",
"554\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n1 1000\n2 1001\n3 1002\n4 1003\n5 1004\n6 1005\n7 1006\n8 1007\n9 1008\n10 1009\n11 1010\n",
"200\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n2 12\n3 13\n4 14\n5 15\n6 16\n7 17\n8 18\n9 19\n10 20\n11 21\n12 22\n13 23\n14 24\n15 25\n16 26\n17 27\n18 28\n19 29\n20 30\n21 31\n22 32\n23 33\n24 34\n25 35\n26 36\n27 37\n28 38\n29 39\n30 40\n31 41\n32 42\n33 43\n34 44\n35 45\n36 46\n37 47\n38 48\n39 49\n40 50\n41 51\n42 52\n43 53\n44 54\n45 55\n46 56\n47 57\n48 58\n49 59\n50 60\n51 61\n52 62\n53 63\n54 64\n55 65\n56 66\n57 67\n58 68\n59 69\n60 70\n61 71\n62 72\n63 73\n64 74\n65 75\n66 76\n67 77\n68 78\n69 79\n70 80\n71 81\n72 82\n73 83\n74 84\n75 85\n76 86\n77 87\n78 88\n79 89\n80 90\n81 91\n82 92\n83 93\n84 94\n85 95\n86 96\n87 97\n88 98\n89 99\n90 100\n91 101\n92 102\n93 103\n94 104\n95 105\n96 106\n97 107\n98 108\n99 109\n100 110\n101 111\n102 112\n103 113\n104 114\n105 115\n106 116\n107 117\n108 118\n109 119\n110 120\n111 121\n112 122\n113 123\n114 124\n115 125\n116 126\n117 127\n118 128\n119 129\n120 130\n121 131\n122 132\n123 133\n124 134\n125 135\n126 136\n127 137\n128 138\n129 139\n130 140\n131 141\n132 142\n133 143\n134 144\n135 145\n136 146\n137 147\n138 148\n139 149\n140 150\n141 151\n142 152\n143 153\n144 154\n145 155\n146 156\n147 157\n148 158\n149 159\n150 160\n151 161\n152 162\n153 163\n154 164\n155 165\n156 166\n157 167\n158 168\n159 169\n160 170\n161 171\n162 172\n163 173\n164 174\n165 175\n166 176\n167 177\n168 178\n169 179\n170 180\n171 181\n172 182\n173 183\n174 184\n175 185\n176 186\n177 187\n178 188\n179 189\n180 190\n181 191\n182 192\n183 193\n184 194\n185 195\n186 196\n187 197\n188 198\n189 199\n190 200\n191 201\n192 202\n193 203\n194 204\n195 205\n196 206\n197 207\n198 208\n199 209\n200 210\n201 211\n202 212\n203 213\n204 214\n205 215\n206 216\n207 217\n208 218\n209 219\n210 220\n211 221\n212 222\n213 223\n214 224\n215 225\n216 226\n217 227\n218 228\n219 229\n220 230\n221 231\n222 232\n223 233\n224 234\n225 235\n226 236\n227 237\n228 238\n229 239\n230 240\n231 241\n232 242\n233 243\n234 244\n235 245\n236 246\n237 247\n238 248\n239 249\n240 250\n241 251\n242 252\n243 253\n244 254\n245 255\n246 256\n247 257\n248 258\n249 259\n250 260\n251 261\n252 262\n253 263\n254 264\n255 265\n256 266\n257 267\n258 268\n259 269\n260 270\n261 271\n262 272\n263 273\n264 274\n265 275\n266 276\n267 277\n268 278\n269 279\n270 280\n271 281\n272 282\n273 283\n274 284\n275 285\n276 286\n277 287\n278 288\n279 289\n280 290\n281 291\n282 292\n283 293\n284 294\n285 295\n286 296\n287 297\n288 298\n289 299\n290 300\n291 301\n292 302\n293 303\n294 304\n295 305\n296 306\n297 307\n298 308\n299 309\n300 310\n301 311\n302 312\n303 313\n304 314\n305 315\n306 316\n307 317\n308 318\n309 319\n310 320\n311 321\n312 322\n313 323\n314 324\n315 325\n316 326\n317 327\n318 328\n319 329\n320 330\n321 331\n322 332\n323 333\n324 334\n325 335\n326 336\n327 337\n328 338\n329 339\n330 340\n331 341\n332 342\n333 343\n334 344\n335 345\n336 346\n337 347\n338 348\n339 349\n340 350\n341 351\n342 352\n343 353\n344 354\n345 355\n346 356\n347 357\n348 358\n349 359\n350 360\n351 361\n352 362\n353 363\n354 364\n355 365\n356 366\n357 367\n358 368\n359 369\n360 370\n361 371\n362 372\n363 373\n364 374\n365 375\n366 376\n367 377\n368 378\n369 379\n370 380\n371 381\n372 382\n373 383\n374 384\n375 385\n376 386\n377 387\n378 388\n379 389\n380 390\n381 391\n382 392\n383 393\n384 394\n385 395\n386 396\n387 397\n388 398\n389 399\n390 400\n391 401\n392 402\n393 403\n394 404\n395 405\n396 406\n397 407\n398 408\n399 409\n400 410\n401 411\n402 412\n403 413\n404 414\n405 415\n406 416\n407 417\n408 418\n409 419\n410 420\n411 421\n412 422\n413 423\n414 424\n415 425\n416 426\n417 427\n418 428\n419 429\n420 430\n421 431\n422 432\n423 433\n424 434\n425 435\n426 436\n427 437\n428 438\n429 439\n430 440\n431 441\n432 442\n433 443\n434 444\n435 445\n436 446\n437 447\n438 448\n439 449\n440 450\n441 451\n442 452\n443 453\n444 454\n445 455\n446 456\n447 457\n448 458\n449 459\n450 460\n451 461\n452 462\n453 463\n454 464\n455 465\n456 466\n457 467\n458 468\n459 469\n460 470\n461 471\n462 472\n463 473\n464 474\n465 475\n466 476\n467 477\n468 478\n469 479\n470 480\n471 481\n472 482\n473 483\n474 484\n475 485\n476 486\n477 487\n478 488\n479 489\n480 490\n481 491\n482 492\n483 493\n484 494\n485 495\n486 496\n487 497\n488 498\n489 499\n490 500\n491 501\n492 502\n493 503\n494 504\n495 505\n496 506\n497 507\n498 508\n499 509\n500 510\n501 511\n502 512\n503 513\n504 514\n505 515\n506 516\n507 517\n508 518\n509 519\n510 520\n511 521\n512 522\n513 523\n514 524\n515 525\n516 526\n517 527\n518 528\n519 529\n520 530\n521 531\n522 532\n523 533\n524 534\n525 535\n526 536\n527 537\n528 538\n529 539\n530 540\n531 541\n532 542\n533 543\n534 544\n535 545\n536 546\n537 547\n538 548\n539 549\n540 550\n541 551\n542 552\n543 553\n544 554\n545 555\n546 556\n547 557\n548 558\n549 559\n550 560\n551 561\n552 562\n553 563\n554 564\n555 565\n556 566\n557 567\n558 568\n559 569\n560 570\n561 571\n562 572\n563 573\n564 574\n565 575\n566 576\n567 577\n568 578\n569 579\n570 580\n571 581\n572 582\n573 583\n574 584\n575 585\n576 586\n577 587\n578 588\n579 589\n580 590\n581 591\n582 592\n583 593\n584 594\n585 595\n586 596\n587 597\n588 598\n589 599\n590 600\n591 601\n592 602\n593 603\n594 604\n595 605\n596 606\n597 607\n598 608\n599 609\n600 610\n601 611\n602 612\n603 613\n604 614\n605 615\n606 616\n607 617\n608 618\n609 619\n610 620\n611 621\n612 622\n613 623\n614 624\n615 625\n616 626\n617 627\n618 628\n619 629\n620 630\n621 631\n622 632\n623 633\n624 634\n625 635\n626 636\n627 637\n628 638\n629 639\n630 640\n631 641\n632 642\n633 643\n634 644\n635 645\n636 646\n637 647\n638 648\n639 649\n640 650\n641 651\n642 652\n643 653\n644 654\n645 655\n646 656\n647 657\n648 658\n649 659\n650 660\n651 661\n652 662\n653 663\n654 664\n655 665\n656 666\n657 667\n658 668\n659 669\n660 670\n661 671\n662 672\n663 673\n664 674\n665 675\n666 676\n667 677\n668 678\n669 679\n670 680\n671 681\n672 682\n673 683\n674 684\n675 685\n676 686\n677 687\n678 688\n679 689\n680 690\n681 691\n682 692\n683 693\n684 694\n685 695\n686 696\n687 697\n688 698\n689 699\n690 700\n691 701\n692 702\n693 703\n694 704\n695 705\n696 706\n697 707\n698 708\n699 709\n700 710\n701 711\n702 712\n703 713\n704 714\n705 715\n706 716\n707 717\n708 718\n709 719\n710 720\n711 721\n712 722\n713 723\n714 724\n715 725\n716 726\n717 727\n718 728\n719 729\n720 730\n721 731\n722 732\n723 733\n724 734\n725 735\n726 736\n727 737\n728 738\n729 739\n730 740\n731 741\n732 742\n733 743\n734 744\n735 745\n736 746\n737 747\n738 748\n739 749\n740 750\n741 751\n742 752\n743 753\n744 754\n745 755\n746 756\n747 757\n748 758\n749 759\n750 760\n751 761\n752 762\n753 763\n754 764\n755 765\n756 766\n757 767\n758 768\n759 769\n760 770\n761 771\n762 772\n763 773\n764 774\n765 775\n766 776\n767 777\n768 778\n769 779\n770 780\n771 781\n772 782\n773 783\n774 784\n775 785\n776 786\n777 787\n778 788\n779 789\n780 790\n781 791\n782 792\n783 793\n784 794\n785 795\n786 796\n787 797\n788 798\n789 799\n790 800\n791 801\n792 802\n793 803\n794 804\n795 805\n796 806\n797 807\n798 808\n799 809\n800 810\n801 811\n802 812\n803 813\n804 814\n805 815\n806 816\n807 817\n808 818\n809 819\n810 820\n811 821\n812 822\n813 823\n814 824\n815 825\n816 826\n817 827\n818 828\n819 829\n820 830\n821 831\n822 832\n823 833\n824 834\n825 835\n826 836\n827 837\n828 838\n829 839\n830 840\n831 841\n832 842\n833 843\n834 844\n835 845\n836 846\n837 847\n838 848\n839 849\n840 850\n841 851\n842 852\n843 853\n844 854\n845 855\n846 856\n847 857\n848 858\n849 859\n850 860\n851 861\n852 862\n853 863\n854 864\n855 865\n856 866\n857 867\n858 868\n859 869\n860 870\n861 871\n862 872\n863 873\n864 874\n865 875\n866 876\n867 877\n868 878\n869 879\n870 880\n871 881\n872 882\n873 883\n874 884\n875 885\n876 886\n877 887\n878 888\n879 889\n880 890\n881 891\n882 892\n883 893\n884 894\n885 895\n886 896\n887 897\n888 898\n889 899\n890 900\n891 901\n892 902\n893 903\n894 904\n895 905\n896 906\n897 907\n898 908\n899 909\n900 910\n901 911\n902 912\n903 913\n904 914\n905 915\n906 916\n907 917\n908 918\n909 919\n910 920\n911 921\n912 922\n913 923\n914 924\n915 925\n916 926\n917 927\n918 928\n919 929\n920 930\n921 931\n922 932\n923 933\n924 934\n925 935\n926 936\n927 937\n928 938\n929 939\n930 940\n931 941\n932 942\n933 943\n934 944\n935 945\n936 946\n937 947\n938 948\n939 949\n940 950\n941 951\n942 952\n943 953\n944 954\n945 955\n946 956\n947 957\n948 958\n949 959\n950 960\n951 961\n952 962\n953 963\n954 964\n955 965\n956 966\n957 967\n958 968\n959 969\n960 970\n961 971\n962 972\n963 973\n964 974\n965 975\n966 976\n967 977\n968 978\n969 979\n970 980\n971 981\n972 982\n973 983\n974 984\n975 985\n976 986\n977 987\n978 988\n979 989\n980 990\n981 991\n982 992\n983 993\n984 994\n985 995\n986 996\n987 997\n988 998\n989 999\n990 1000\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n2 727\n3 728\n4 729\n5 730\n6 731\n7 732\n8 733\n9 734\n10 735\n11 736\n12 737\n13 738\n14 739\n15 740\n16 741\n17 742\n18 743\n19 744\n20 745\n21 746\n22 747\n23 748\n24 749\n25 750\n26 751\n27 752\n28 753\n29 754\n30 755\n31 756\n32 757\n33 758\n34 759\n35 760\n36 761\n37 762\n38 763\n39 764\n40 765\n41 766\n42 767\n43 768\n44 769\n45 770\n46 771\n47 772\n48 773\n49 774\n50 775\n51 776\n52 777\n53 778\n54 779\n55 780\n56 781\n57 782\n58 783\n59 784\n60 785\n61 786\n62 787\n63 788\n64 789\n65 790\n66 791\n67 792\n68 793\n69 794\n70 795\n71 796\n72 797\n73 798\n74 799\n75 800\n76 801\n77 802\n78 803\n79 804\n80 805\n81 806\n82 807\n83 808\n84 809\n85 810\n86 811\n87 812\n88 813\n89 814\n90 815\n91 816\n92 817\n93 818\n94 819\n95 820\n96 821\n97 822\n98 823\n99 824\n100 825\n101 826\n102 827\n103 828\n104 829\n105 830\n106 831\n107 832\n108 833\n109 834\n110 835\n111 836\n112 837\n113 838\n114 839\n115 840\n116 841\n117 842\n118 843\n119 844\n120 845\n121 846\n122 847\n123 848\n124 849\n125 850\n126 851\n127 852\n128 853\n129 854\n130 855\n131 856\n132 857\n133 858\n134 859\n135 860\n136 861\n137 862\n138 863\n139 864\n140 865\n141 866\n142 867\n143 868\n144 869\n145 870\n146 871\n147 872\n148 873\n149 874\n150 875\n151 876\n152 877\n153 878\n154 879\n155 880\n156 881\n157 882\n158 883\n159 884\n160 885\n161 886\n162 887\n163 888\n164 889\n165 890\n166 891\n167 892\n168 893\n169 894\n170 895\n171 896\n172 897\n173 898\n174 899\n175 900\n176 901\n177 902\n178 903\n179 904\n180 905\n181 906\n182 907\n183 908\n184 909\n185 910\n186 911\n187 912\n188 913\n189 914\n190 915\n191 916\n192 917\n193 918\n194 919\n195 920\n196 921\n197 922\n198 923\n199 924\n200 925\n201 926\n202 927\n203 928\n204 929\n205 930\n206 931\n207 932\n208 933\n209 934\n210 935\n211 936\n212 937\n213 938\n214 939\n215 940\n216 941\n217 942\n218 943\n219 944\n220 945\n221 946\n222 947\n223 948\n224 949\n225 950\n226 951\n227 952\n228 953\n229 954\n230 955\n231 956\n232 957\n233 958\n234 959\n235 960\n236 961\n237 962\n238 963\n239 964\n240 965\n241 966\n242 967\n243 968\n244 969\n245 970\n246 971\n247 972\n248 973\n249 974\n250 975\n251 976\n252 977\n253 978\n254 979\n255 980\n256 981\n257 982\n258 983\n259 984\n260 985\n261 986\n262 987\n263 988\n264 989\n265 990\n266 991\n267 992\n268 993\n269 994\n270 995\n271 996\n272 997\n273 998\n274 999\n275 1000\n276 1001\n277 1002\n278 1003\n279 1004\n280 1005\n281 1006\n282 1007\n283 1008\n284 1009\n285 1010\n286 1011\n287 1012\n288 1013\n289 1014\n290 1015\n291 1016\n292 1017\n293 1018\n294 1019\n295 1020\n296 1021\n297 1022\n298 1023\n299 1024\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n2 559\n3 560\n4 561\n5 562\n6 563\n7 564\n8 565\n9 566\n10 567\n11 568\n12 569\n13 570\n14 571\n15 572\n16 573\n17 574\n18 575\n19 576\n20 577\n21 578\n22 579\n23 580\n24 581\n25 582\n26 583\n27 584\n28 585\n29 586\n30 587\n31 588\n32 589\n33 590\n34 591\n35 592\n36 593\n37 594\n38 595\n39 596\n40 597\n41 598\n42 599\n43 600\n44 601\n45 602\n46 603\n47 604\n48 605\n49 606\n50 607\n51 608\n52 609\n53 610\n54 611\n55 612\n56 613\n57 614\n58 615\n59 616\n60 617\n61 618\n62 619\n63 620\n64 621\n65 622\n66 623\n67 624\n68 625\n69 626\n70 627\n71 628\n72 629\n73 630\n74 631\n75 632\n76 633\n77 634\n78 635\n79 636\n80 637\n81 638\n82 639\n83 640\n84 641\n85 642\n86 643\n87 644\n88 645\n89 646\n90 647\n91 648\n92 649\n93 650\n94 651\n95 652\n96 653\n97 654\n98 655\n99 656\n100 657\n101 658\n102 659\n103 660\n104 661\n105 662\n106 663\n107 664\n108 665\n109 666\n110 667\n111 668\n112 669\n113 670\n114 671\n115 672\n116 673\n117 674\n118 675\n119 676\n120 677\n121 678\n122 679\n123 680\n124 681\n125 682\n126 683\n127 684\n128 685\n129 686\n130 687\n131 688\n132 689\n133 690\n134 691\n135 692\n136 693\n137 694\n138 695\n139 696\n140 697\n141 698\n142 699\n143 700\n144 701\n145 702\n146 703\n147 704\n148 705\n149 706\n150 707\n151 708\n152 709\n153 710\n154 711\n155 712\n156 713\n157 714\n158 715\n159 716\n160 717\n161 718\n162 719\n163 720\n164 721\n165 722\n166 723\n167 724\n168 725\n169 726\n170 727\n171 728\n172 729\n173 730\n174 731\n175 732\n176 733\n177 734\n178 735\n179 736\n180 737\n181 738\n182 739\n183 740\n184 741\n185 742\n186 743\n187 744\n188 745\n189 746\n190 747\n191 748\n192 749\n193 750\n194 751\n195 752\n196 753\n197 754\n198 755\n199 756\n200 757\n201 758\n202 759\n203 760\n204 761\n205 762\n206 763\n207 764\n208 765\n209 766\n210 767\n211 768\n212 769\n213 770\n214 771\n215 772\n216 773\n217 774\n218 775\n219 776\n220 777\n221 778\n222 779\n223 780\n224 781\n225 782\n226 783\n227 784\n228 785\n229 786\n230 787\n231 788\n232 789\n233 790\n234 791\n235 792\n236 793\n237 794\n238 795\n239 796\n240 797\n241 798\n242 799\n243 800\n244 801\n245 802\n246 803\n247 804\n248 805\n249 806\n250 807\n251 808\n252 809\n253 810\n254 811\n255 812\n256 813\n257 814\n258 815\n259 816\n260 817\n261 818\n262 819\n263 820\n264 821\n265 822\n266 823\n267 824\n268 825\n269 826\n270 827\n271 828\n272 829\n273 830\n274 831\n275 832\n276 833\n277 834\n278 835\n279 836\n280 837\n281 838\n282 839\n283 840\n284 841\n285 842\n286 843\n287 844\n288 845\n289 846\n290 847\n291 848\n292 849\n293 850\n294 851\n295 852\n296 853\n297 854\n298 855\n299 856\n300 857\n301 858\n302 859\n303 860\n304 861\n305 862\n306 863\n307 864\n308 865\n309 866\n310 867\n311 868\n312 869\n313 870\n314 871\n315 872\n316 873\n317 874\n318 875\n319 876\n320 877\n321 878\n322 879\n323 880\n324 881\n325 882\n326 883\n327 884\n328 885\n329 886\n330 887\n331 888\n332 889\n333 890\n334 891\n335 892\n336 893\n337 894\n338 895\n339 896\n340 897\n341 898\n342 899\n343 900\n344 901\n345 902\n346 903\n347 904\n348 905\n349 906\n350 907\n351 908\n352 909\n353 910\n354 911\n355 912\n356 913\n357 914\n358 915\n359 916\n360 917\n361 918\n362 919\n363 920\n364 921\n365 922\n366 923\n367 924\n368 925\n369 926\n370 927\n371 928\n372 929\n373 930\n374 931\n375 932\n376 933\n377 934\n378 935\n379 936\n380 937\n381 938\n382 939\n383 940\n384 941\n385 942\n386 943\n387 944\n388 945\n389 946\n390 947\n391 948\n392 949\n393 950\n394 951\n395 952\n396 953\n397 954\n398 955\n399 956\n400 957\n401 958\n402 959\n403 960\n404 961\n405 962\n406 963\n407 964\n408 965\n409 966\n410 967\n411 968\n412 969\n413 970\n414 971\n415 972\n416 973\n417 974\n418 975\n419 976\n420 977\n421 978\n422 979\n423 980\n424 981\n425 982\n426 983\n427 984\n428 985\n429 986\n430 987\n431 988\n432 989\n433 990\n434 991\n435 992\n436 993\n437 994\n438 995\n439 996\n440 997\n441 998\n442 999\n443 1000\n444 1001\n445 1002\n446 1003\n447 1004\n448 1005\n449 1006\n450 1007\n451 1008\n452 1009\n453 1010\n454 1011\n455 1012\n456 1013\n457 1014\n458 1015\n459 1016\n460 1017\n461 1018\n462 1019\n463 1020\n464 1021\n465 1022\n466 1023\n467 1024\n",
"5\n1 2\n1 3\n1 4\n1 5\n2 6\n3 7\n4 8\n5 9\n6 10\n",
"240\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n2 18\n3 19\n4 20\n5 21\n6 22\n7 23\n8 24\n9 25\n10 26\n11 27\n12 28\n13 29\n14 30\n15 31\n16 32\n17 33\n18 34\n19 35\n20 36\n21 37\n22 38\n23 39\n24 40\n25 41\n26 42\n27 43\n28 44\n29 45\n30 46\n31 47\n32 48\n33 49\n34 50\n35 51\n36 52\n37 53\n38 54\n39 55\n40 56\n41 57\n42 58\n43 59\n44 60\n45 61\n46 62\n47 63\n48 64\n49 65\n50 66\n51 67\n52 68\n53 69\n54 70\n55 71\n56 72\n57 73\n58 74\n59 75\n60 76\n61 77\n62 78\n63 79\n64 80\n65 81\n66 82\n67 83\n68 84\n69 85\n70 86\n71 87\n72 88\n73 89\n74 90\n75 91\n76 92\n77 93\n78 94\n79 95\n80 96\n81 97\n82 98\n83 99\n84 100\n85 101\n86 102\n87 103\n88 104\n89 105\n90 106\n91 107\n92 108\n93 109\n94 110\n95 111\n96 112\n97 113\n98 114\n99 115\n100 116\n101 117\n102 118\n103 119\n104 120\n105 121\n106 122\n107 123\n108 124\n109 125\n110 126\n111 127\n112 128\n113 129\n114 130\n115 131\n116 132\n117 133\n118 134\n119 135\n120 136\n121 137\n122 138\n123 139\n124 140\n125 141\n126 142\n127 143\n128 144\n129 145\n130 146\n131 147\n132 148\n133 149\n134 150\n135 151\n136 152\n137 153\n138 154\n139 155\n140 156\n141 157\n142 158\n143 159\n144 160\n145 161\n146 162\n147 163\n148 164\n149 165\n150 166\n151 167\n152 168\n153 169\n154 170\n155 171\n156 172\n157 173\n158 174\n159 175\n160 176\n161 177\n162 178\n163 179\n164 180\n165 181\n166 182\n167 183\n168 184\n169 185\n170 186\n171 187\n172 188\n173 189\n174 190\n175 191\n176 192\n177 193\n178 194\n179 195\n180 196\n181 197\n182 198\n183 199\n184 200\n185 201\n186 202\n187 203\n188 204\n189 205\n190 206\n191 207\n192 208\n193 209\n194 210\n195 211\n196 212\n197 213\n198 214\n199 215\n200 216\n201 217\n202 218\n203 219\n204 220\n205 221\n206 222\n207 223\n208 224\n209 225\n210 226\n211 227\n212 228\n213 229\n214 230\n215 231\n216 232\n217 233\n218 234\n219 235\n220 236\n221 237\n222 238\n223 239\n224 240\n225 241\n226 242\n227 243\n228 244\n229 245\n230 246\n231 247\n232 248\n233 249\n234 250\n235 251\n236 252\n237 253\n238 254\n239 255\n240 256\n241 257\n242 258\n243 259\n244 260\n245 261\n246 262\n247 263\n248 264\n249 265\n250 266\n251 267\n252 268\n253 269\n254 270\n255 271\n256 272\n257 273\n258 274\n259 275\n260 276\n261 277\n262 278\n263 279\n264 280\n265 281\n266 282\n267 283\n268 284\n269 285\n270 286\n271 287\n272 288\n273 289\n274 290\n275 291\n276 292\n277 293\n278 294\n279 295\n280 296\n281 297\n282 298\n283 299\n284 300\n285 301\n286 302\n287 303\n288 304\n289 305\n290 306\n291 307\n292 308\n293 309\n294 310\n295 311\n296 312\n297 313\n298 314\n299 315\n300 316\n301 317\n302 318\n303 319\n304 320\n305 321\n306 322\n307 323\n308 324\n309 325\n310 326\n311 327\n312 328\n313 329\n314 330\n315 331\n316 332\n317 333\n318 334\n319 335\n320 336\n321 337\n322 338\n323 339\n324 340\n325 341\n326 342\n327 343\n328 344\n329 345\n330 346\n331 347\n332 348\n333 349\n334 350\n335 351\n336 352\n337 353\n338 354\n339 355\n340 356\n341 357\n342 358\n343 359\n344 360\n345 361\n346 362\n347 363\n348 364\n349 365\n350 366\n351 367\n352 368\n353 369\n354 370\n355 371\n356 372\n357 373\n358 374\n359 375\n360 376\n361 377\n362 378\n363 379\n364 380\n365 381\n366 382\n367 383\n368 384\n369 385\n370 386\n371 387\n372 388\n373 389\n374 390\n375 391\n376 392\n377 393\n378 394\n379 395\n380 396\n381 397\n382 398\n383 399\n384 400\n385 401\n386 402\n387 403\n388 404\n389 405\n390 406\n391 407\n392 408\n393 409\n394 410\n395 411\n396 412\n397 413\n398 414\n399 415\n400 416\n401 417\n402 418\n403 419\n404 420\n405 421\n406 422\n407 423\n408 424\n409 425\n410 426\n411 427\n412 428\n413 429\n414 430\n415 431\n416 432\n417 433\n418 434\n419 435\n420 436\n421 437\n422 438\n423 439\n424 440\n425 441\n426 442\n427 443\n428 444\n429 445\n430 446\n431 447\n432 448\n433 449\n434 450\n435 451\n436 452\n437 453\n438 454\n439 455\n440 456\n441 457\n442 458\n443 459\n444 460\n445 461\n446 462\n447 463\n448 464\n449 465\n450 466\n451 467\n452 468\n453 469\n454 470\n455 471\n456 472\n457 473\n458 474\n459 475\n460 476\n461 477\n462 478\n463 479\n464 480\n465 481\n466 482\n467 483\n468 484\n469 485\n470 486\n471 487\n472 488\n473 489\n474 490\n475 491\n476 492\n477 493\n478 494\n479 495\n480 496\n481 497\n482 498\n483 499\n484 500\n485 501\n486 502\n487 503\n488 504\n489 505\n490 506\n491 507\n492 508\n493 509\n494 510\n495 511\n496 512\n497 513\n498 514\n499 515\n500 516\n501 517\n502 518\n503 519\n504 520\n505 521\n506 522\n507 523\n508 524\n509 525\n510 526\n511 527\n512 528\n513 529\n514 530\n515 531\n516 532\n517 533\n518 534\n519 535\n520 536\n521 537\n522 538\n523 539\n524 540\n525 541\n526 542\n527 543\n528 544\n529 545\n530 546\n531 547\n532 548\n533 549\n534 550\n535 551\n536 552\n537 553\n538 554\n539 555\n540 556\n541 557\n542 558\n543 559\n544 560\n545 561\n546 562\n547 563\n548 564\n549 565\n550 566\n551 567\n552 568\n553 569\n554 570\n555 571\n556 572\n557 573\n558 574\n559 575\n560 576\n561 577\n562 578\n563 579\n564 580\n565 581\n566 582\n567 583\n568 584\n569 585\n570 586\n571 587\n572 588\n573 589\n574 590\n575 591\n576 592\n577 593\n578 594\n579 595\n580 596\n581 597\n582 598\n583 599\n584 600\n585 601\n586 602\n587 603\n588 604\n589 605\n590 606\n591 607\n592 608\n593 609\n594 610\n595 611\n596 612\n597 613\n598 614\n599 615\n600 616\n601 617\n602 618\n603 619\n604 620\n605 621\n606 622\n607 623\n608 624\n609 625\n610 626\n611 627\n612 628\n613 629\n614 630\n615 631\n616 632\n617 633\n618 634\n619 635\n620 636\n621 637\n622 638\n623 639\n624 640\n625 641\n626 642\n627 643\n628 644\n629 645\n630 646\n631 647\n632 648\n633 649\n634 650\n635 651\n636 652\n637 653\n638 654\n639 655\n640 656\n641 657\n642 658\n643 659\n644 660\n645 661\n646 662\n647 663\n648 664\n649 665\n650 666\n651 667\n652 668\n653 669\n654 670\n655 671\n656 672\n657 673\n658 674\n659 675\n660 676\n661 677\n662 678\n663 679\n664 680\n665 681\n666 682\n667 683\n668 684\n669 685\n670 686\n671 687\n672 688\n673 689\n674 690\n675 691\n676 692\n677 693\n678 694\n679 695\n680 696\n681 697\n682 698\n683 699\n684 700\n685 701\n686 702\n687 703\n688 704\n689 705\n690 706\n691 707\n692 708\n693 709\n694 710\n695 711\n696 712\n697 713\n698 714\n699 715\n700 716\n701 717\n702 718\n703 719\n704 720\n705 721\n706 722\n707 723\n708 724\n709 725\n710 726\n711 727\n712 728\n713 729\n714 730\n715 731\n716 732\n717 733\n718 734\n719 735\n720 736\n721 737\n722 738\n723 739\n724 740\n725 741\n726 742\n727 743\n728 744\n729 745\n730 746\n731 747\n732 748\n733 749\n734 750\n735 751\n736 752\n737 753\n738 754\n739 755\n740 756\n741 757\n742 758\n743 759\n744 760\n745 761\n746 762\n747 763\n748 764\n749 765\n750 766\n751 767\n752 768\n753 769\n754 770\n755 771\n756 772\n757 773\n758 774\n759 775\n760 776\n761 777\n762 778\n763 779\n764 780\n765 781\n766 782\n767 783\n768 784\n769 785\n770 786\n771 787\n772 788\n773 789\n774 790\n775 791\n776 792\n777 793\n778 794\n779 795\n780 796\n781 797\n782 798\n783 799\n784 800\n785 801\n786 802\n787 803\n788 804\n789 805\n790 806\n791 807\n792 808\n793 809\n794 810\n795 811\n796 812\n797 813\n798 814\n799 815\n800 816\n801 817\n802 818\n803 819\n804 820\n805 821\n806 822\n807 823\n808 824\n809 825\n810 826\n811 827\n812 828\n813 829\n814 830\n815 831\n816 832\n817 833\n818 834\n819 835\n820 836\n821 837\n822 838\n823 839\n824 840\n825 841\n826 842\n827 843\n828 844\n829 845\n830 846\n831 847\n832 848\n833 849\n834 850\n835 851\n836 852\n837 853\n838 854\n839 855\n840 856\n841 857\n842 858\n843 859\n844 860\n845 861\n846 862\n847 863\n848 864\n849 865\n850 866\n851 867\n852 868\n853 869\n854 870\n855 871\n856 872\n857 873\n858 874\n859 875\n860 876\n861 877\n862 878\n863 879\n864 880\n865 881\n866 882\n867 883\n868 884\n869 885\n870 886\n871 887\n872 888\n873 889\n874 890\n875 891\n876 892\n877 893\n878 894\n879 895\n880 896\n881 897\n882 898\n883 899\n884 900\n885 901\n886 902\n887 903\n888 904\n889 905\n890 906\n891 907\n892 908\n893 909\n894 910\n895 911\n896 912\n897 913\n898 914\n899 915\n900 916\n901 917\n902 918\n903 919\n904 920\n905 921\n906 922\n907 923\n908 924\n909 925\n910 926\n911 927\n912 928\n913 929\n914 930\n915 931\n916 932\n917 933\n918 934\n919 935\n920 936\n921 937\n922 938\n923 939\n924 940\n925 941\n926 942\n927 943\n928 944\n929 945\n930 946\n931 947\n932 948\n933 949\n934 950\n935 951\n936 952\n937 953\n938 954\n939 955\n940 956\n941 957\n942 958\n943 959\n944 960\n945 961\n946 962\n947 963\n948 964\n949 965\n950 966\n951 967\n952 968\n953 969\n954 970\n955 971\n956 972\n957 973\n958 974\n959 975\n960 976\n961 977\n962 978\n963 979\n964 980\n965 981\n966 982\n967 983\n968 984\n969 985\n970 986\n971 987\n972 988\n973 989\n974 990\n975 991\n976 992\n977 993\n978 994\n979 995\n980 996\n981 997\n982 998\n983 999\n984 1000\n985 1001\n986 1002\n987 1003\n988 1004\n989 1005\n990 1006\n991 1007\n992 1008\n993 1009\n994 1010\n995 1011\n996 1012\n997 1013\n998 1014\n999 1015\n1000 1016\n1001 1017\n1002 1018\n1003 1019\n1004 1020\n1005 1021\n1006 1022\n1007 1023\n1008 1024\n1009 1025\n1010 1026\n1011 1027\n1012 1028\n1013 1029\n1014 1030\n1015 1031\n1016 1032\n1017 1033\n1018 1034\n1019 1035\n1020 1036\n1021 1037\n1022 1038\n1023 1039\n1024 1040\n1025 1041\n1026 1042\n1027 1043\n1028 1044\n1029 1045\n1030 1046\n1031 1047\n1032 1048\n1033 1049\n1034 1050\n1035 1051\n1036 1052\n1037 1053\n1038 1054\n1039 1055\n1040 1056\n1041 1057\n1042 1058\n1043 1059\n1044 1060\n1045 1061\n1046 1062\n1047 1063\n1048 1064\n1049 1065\n1050 1066\n1051 1067\n1052 1068\n1053 1069\n1054 1070\n1055 1071\n1056 1072\n1057 1073\n1058 1074\n1059 1075\n1060 1076\n1061 1077\n1062 1078\n1063 1079\n1064 1080\n1065 1081\n1066 1082\n1067 1083\n1068 1084\n1069 1085\n1070 1086\n1071 1087\n1072 1088\n1073 1089\n1074 1090\n1075 1091\n1076 1092\n1077 1093\n1078 1094\n1079 1095\n1080 1096\n1081 1097\n1082 1098\n1083 1099\n1084 1100\n1085 1101\n1086 1102\n1087 1103\n1088 1104\n1089 1105\n1090 1106\n1091 1107\n1092 1108\n1093 1109\n1094 1110\n1095 1111\n1096 1112\n1097 1113\n1098 1114\n1099 1115\n1100 1116\n1101 1117\n1102 1118\n1103 1119\n1104 1120\n1105 1121\n1106 1122\n1107 1123\n1108 1124\n1109 1125\n1110 1126\n1111 1127\n1112 1128\n1113 1129\n1114 1130\n1115 1131\n1116 1132\n1117 1133\n1118 1134\n1119 1135\n1120 1136\n1121 1137\n1122 1138\n1123 1139\n1124 1140\n1125 1141\n1126 1142\n1127 1143\n1128 1144\n1129 1145\n1130 1146\n1131 1147\n1132 1148\n1133 1149\n1134 1150\n1135 1151\n1136 1152\n1137 1153\n1138 1154\n1139 1155\n1140 1156\n1141 1157\n1142 1158\n1143 1159\n1144 1160\n1145 1161\n1146 1162\n1147 1163\n1148 1164\n1149 1165\n1150 1166\n1151 1167\n1152 1168\n1153 1169\n1154 1170\n1155 1171\n1156 1172\n1157 1173\n1158 1174\n1159 1175\n1160 1176\n1161 1177\n1162 1178\n1163 1179\n1164 1180\n1165 1181\n1166 1182\n1167 1183\n1168 1184\n1169 1185\n1170 1186\n1171 1187\n1172 1188\n1173 1189\n1174 1190\n1175 1191\n1176 1192\n1177 1193\n1178 1194\n1179 1195\n1180 1196\n1181 1197\n1182 1198\n1183 1199\n1184 1200\n1185 1201\n1186 1202\n1187 1203\n1188 1204\n1189 1205\n1190 1206\n1191 1207\n1192 1208\n1193 1209\n1194 1210\n1195 1211\n1196 1212\n1197 1213\n1198 1214\n1199 1215\n1200 1216\n1201 1217\n1202 1218\n1203 1219\n1204 1220\n1205 1221\n1206 1222\n1207 1223\n1208 1224\n1209 1225\n1210 1226\n1211 1227\n1212 1228\n1213 1229\n1214 1230\n1215 1231\n1216 1232\n1217 1233\n1218 1234\n1219 1235\n1220 1236\n1221 1237\n1222 1238\n1223 1239\n1224 1240\n1225 1241\n1226 1242\n1227 1243\n1228 1244\n1229 1245\n1230 1246\n1231 1247\n1232 1248\n1233 1249\n1234 1250\n1235 1251\n1236 1252\n1237 1253\n1238 1254\n1239 1255\n1240 1256\n1241 1257\n1242 1258\n1243 1259\n1244 1260\n1245 1261\n1246 1262\n1247 1263\n1248 1264\n1249 1265\n1250 1266\n1251 1267\n1252 1268\n1253 1269\n1254 1270\n1255 1271\n1256 1272\n1257 1273\n1258 1274\n1259 1275\n1260 1276\n1261 1277\n1262 1278\n1263 1279\n1264 1280\n1265 1281\n1266 1282\n1267 1283\n1268 1284\n1269 1285\n1270 1286\n1271 1287\n1272 1288\n1273 1289\n1274 1290\n1275 1291\n1276 1292\n1277 1293\n1278 1294\n1279 1295\n1280 1296\n1281 1297\n1282 1298\n1283 1299\n1284 1300\n1285 1301\n1286 1302\n1287 1303\n1288 1304\n1289 1305\n1290 1306\n1291 1307\n1292 1308\n1293 1309\n1294 1310\n1295 1311\n1296 1312\n1297 1313\n1298 1314\n1299 1315\n1300 1316\n1301 1317\n1302 1318\n1303 1319\n1304 1320\n1305 1321\n1306 1322\n1307 1323\n1308 1324\n1309 1325\n1310 1326\n1311 1327\n1312 1328\n1313 1329\n1314 1330\n1315 1331\n1316 1332\n1317 1333\n1318 1334\n1319 1335\n1320 1336\n1321 1337\n1322 1338\n1323 1339\n1324 1340\n1325 1341\n1326 1342\n1327 1343\n1328 1344\n1329 1345\n1330 1346\n1331 1347\n1332 1348\n1333 1349\n1334 1350\n1335 1351\n1336 1352\n1337 1353\n1338 1354\n1339 1355\n1340 1356\n1341 1357\n1342 1358\n1343 1359\n1344 1360\n1345 1361\n1346 1362\n1347 1363\n1348 1364\n1349 1365\n1350 1366\n1351 1367\n1352 1368\n1353 1369\n1354 1370\n1355 1371\n1356 1372\n1357 1373\n1358 1374\n1359 1375\n1360 1376\n1361 1377\n1362 1378\n1363 1379\n1364 1380\n1365 1381\n1366 1382\n1367 1383\n1368 1384\n1369 1385\n1370 1386\n1371 1387\n1372 1388\n1373 1389\n1374 1390\n1375 1391\n1376 1392\n1377 1393\n1378 1394\n1379 1395\n1380 1396\n1381 1397\n1382 1398\n1383 1399\n1384 1400\n1385 1401\n1386 1402\n1387 1403\n1388 1404\n1389 1405\n1390 1406\n1391 1407\n1392 1408\n1393 1409\n1394 1410\n1395 1411\n1396 1412\n1397 1413\n1398 1414\n1399 1415\n1400 1416\n1401 1417\n1402 1418\n1403 1419\n1404 1420\n1405 1421\n1406 1422\n1407 1423\n1408 1424\n1409 1425\n1410 1426\n1411 1427\n1412 1428\n1413 1429\n1414 1430\n1415 1431\n1416 1432\n1417 1433\n1418 1434\n1419 1435\n1420 1436\n1421 1437\n1422 1438\n1423 1439\n1424 1440\n1425 1441\n1426 1442\n1427 1443\n1428 1444\n1429 1445\n1430 1446\n1431 1447\n1432 1448\n1433 1449\n1434 1450\n1435 1451\n1436 1452\n1437 1453\n1438 1454\n1439 1455\n1440 1456\n1441 1457\n1442 1458\n1443 1459\n1444 1460\n1445 1461\n1446 1462\n1447 1463\n1448 1464\n1449 1465\n1450 1466\n1451 1467\n1452 1468\n1453 1469\n1454 1470\n1455 1471\n1456 1472\n1457 1473\n1458 1474\n1459 1475\n1460 1476\n1461 1477\n1462 1478\n1463 1479\n1464 1480\n1465 1481\n1466 1482\n1467 1483\n1468 1484\n1469 1485\n1470 1486\n1471 1487\n1472 1488\n1473 1489\n1474 1490\n1475 1491\n1476 1492\n1477 1493\n1478 1494\n1479 1495\n1480 1496\n1481 1497\n1482 1498\n1483 1499\n1484 1500\n1485 1501\n1486 1502\n1487 1503\n1488 1504\n1489 1505\n1490 1506\n1491 1507\n1492 1508\n1493 1509\n1494 1510\n1495 1511\n1496 1512\n1497 1513\n1498 1514\n1499 1515\n1500 1516\n1501 1517\n1502 1518\n1503 1519\n1504 1520\n1505 1521\n1506 1522\n1507 1523\n1508 1524\n1509 1525\n1510 1526\n1511 1527\n1512 1528\n1513 1529\n1514 1530\n1515 1531\n1516 1532\n1517 1533\n1518 1534\n1519 1535\n1520 1536\n1521 1537\n1522 1538\n1523 1539\n1524 1540\n1525 1541\n1526 1542\n1527 1543\n1528 1544\n1529 1545\n1530 1546\n1531 1547\n1532 1548\n1533 1549\n1534 1550\n1535 1551\n1536 1552\n1537 1553\n1538 1554\n1539 1555\n1540 1556\n1541 1557\n1542 1558\n1543 1559\n1544 1560\n1545 1561\n1546 1562\n1547 1563\n1548 1564\n1549 1565\n1550 1566\n1551 1567\n1552 1568\n1553 1569\n1554 1570\n1555 1571\n1556 1572\n1557 1573\n1558 1574\n1559 1575\n1560 1576\n1561 1577\n1562 1578\n1563 1579\n1564 1580\n1565 1581\n1566 1582\n1567 1583\n1568 1584\n1569 1585\n1570 1586\n1571 1587\n1572 1588\n1573 1589\n1574 1590\n1575 1591\n1576 1592\n1577 1593\n1578 1594\n1579 1595\n1580 1596\n1581 1597\n1582 1598\n1583 1599\n1584 1600\n1585 1601\n1586 1602\n1587 1603\n1588 1604\n1589 1605\n1590 1606\n1591 1607\n1592 1608\n1593 1609\n1594 1610\n1595 1611\n1596 1612\n1597 1613\n1598 1614\n1599 1615\n1600 1616\n1601 1617\n1602 1618\n1603 1619\n1604 1620\n1605 1621\n1606 1622\n1607 1623\n1608 1624\n1609 1625\n1610 1626\n1611 1627\n1612 1628\n1613 1629\n1614 1630\n1615 1631\n1616 1632\n1617 1633\n1618 1634\n1619 1635\n1620 1636\n1621 1637\n1622 1638\n1623 1639\n1624 1640\n1625 1641\n1626 1642\n1627 1643\n1628 1644\n1629 1645\n1630 1646\n1631 1647\n1632 1648\n1633 1649\n1634 1650\n1635 1651\n1636 1652\n1637 1653\n1638 1654\n1639 1655\n1640 1656\n1641 1657\n1642 1658\n1643 1659\n1644 1660\n1645 1661\n1646 1662\n1647 1663\n1648 1664\n1649 1665\n1650 1666\n1651 1667\n1652 1668\n1653 1669\n1654 1670\n1655 1671\n1656 1672\n1657 1673\n1658 1674\n1659 1675\n1660 1676\n1661 1677\n1662 1678\n1663 1679\n1664 1680\n1665 1681\n1666 1682\n1667 1683\n1668 1684\n1669 1685\n1670 1686\n1671 1687\n1672 1688\n1673 1689\n1674 1690\n1675 1691\n1676 1692\n1677 1693\n1678 1694\n1679 1695\n1680 1696\n1681 1697\n1682 1698\n1683 1699\n1684 1700\n1685 1701\n1686 1702\n1687 1703\n1688 1704\n1689 1705\n1690 1706\n1691 1707\n1692 1708\n1693 1709\n1694 1710\n1695 1711\n1696 1712\n1697 1713\n1698 1714\n1699 1715\n1700 1716\n1701 1717\n1702 1718\n1703 1719\n1704 1720\n1705 1721\n1706 1722\n1707 1723\n1708 1724\n1709 1725\n1710 1726\n1711 1727\n1712 1728\n1713 1729\n1714 1730\n1715 1731\n1716 1732\n1717 1733\n1718 1734\n1719 1735\n1720 1736\n1721 1737\n1722 1738\n1723 1739\n1724 1740\n1725 1741\n1726 1742\n1727 1743\n1728 1744\n1729 1745\n1730 1746\n1731 1747\n1732 1748\n1733 1749\n1734 1750\n1735 1751\n1736 1752\n1737 1753\n1738 1754\n1739 1755\n1740 1756\n1741 1757\n1742 1758\n1743 1759\n1744 1760\n1745 1761\n1746 1762\n1747 1763\n1748 1764\n1749 1765\n1750 1766\n1751 1767\n1752 1768\n1753 1769\n1754 1770\n1755 1771\n1756 1772\n1757 1773\n1758 1774\n1759 1775\n1760 1776\n1761 1777\n1762 1778\n1763 1779\n1764 1780\n1765 1781\n1766 1782\n1767 1783\n1768 1784\n1769 1785\n1770 1786\n1771 1787\n1772 1788\n1773 1789\n1774 1790\n1775 1791\n1776 1792\n1777 1793\n1778 1794\n1779 1795\n1780 1796\n1781 1797\n1782 1798\n1783 1799\n1784 1800\n1785 1801\n1786 1802\n1787 1803\n1788 1804\n1789 1805\n1790 1806\n1791 1807\n1792 1808\n1793 1809\n1794 1810\n1795 1811\n1796 1812\n1797 1813\n1798 1814\n1799 1815\n1800 1816\n1801 1817\n1802 1818\n1803 1819\n1804 1820\n1805 1821\n1806 1822\n1807 1823\n1808 1824\n1809 1825\n1810 1826\n1811 1827\n1812 1828\n1813 1829\n1814 1830\n1815 1831\n1816 1832\n1817 1833\n1818 1834\n1819 1835\n1820 1836\n1821 1837\n1822 1838\n1823 1839\n1824 1840\n1825 1841\n1826 1842\n1827 1843\n1828 1844\n1829 1845\n1830 1846\n1831 1847\n1832 1848\n1833 1849\n1834 1850\n1835 1851\n1836 1852\n1837 1853\n1838 1854\n1839 1855\n1840 1856\n1841 1857\n1842 1858\n1843 1859\n1844 1860\n1845 1861\n1846 1862\n1847 1863\n1848 1864\n1849 1865\n1850 1866\n1851 1867\n1852 1868\n1853 1869\n1854 1870\n1855 1871\n1856 1872\n1857 1873\n1858 1874\n1859 1875\n1860 1876\n1861 1877\n1862 1878\n1863 1879\n1864 1880\n1865 1881\n1866 1882\n1867 1883\n1868 1884\n1869 1885\n1870 1886\n1871 1887\n1872 1888\n1873 1889\n1874 1890\n1875 1891\n1876 1892\n1877 1893\n1878 1894\n1879 1895\n1880 1896\n1881 1897\n1882 1898\n1883 1899\n1884 1900\n1885 1901\n1886 1902\n1887 1903\n1888 1904\n1889 1905\n1890 1906\n1891 1907\n1892 1908\n1893 1909\n1894 1910\n1895 1911\n1896 1912\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n2 515\n3 516\n4 517\n5 518\n6 519\n7 520\n8 521\n9 522\n10 523\n11 524\n12 525\n13 526\n14 527\n15 528\n16 529\n17 530\n18 531\n19 532\n20 533\n21 534\n22 535\n23 536\n24 537\n25 538\n26 539\n27 540\n28 541\n29 542\n30 543\n31 544\n32 545\n33 546\n34 547\n35 548\n36 549\n37 550\n38 551\n39 552\n40 553\n41 554\n42 555\n43 556\n44 557\n45 558\n46 559\n47 560\n48 561\n49 562\n50 563\n51 564\n52 565\n53 566\n54 567\n55 568\n56 569\n57 570\n58 571\n59 572\n60 573\n61 574\n62 575\n63 576\n64 577\n65 578\n66 579\n67 580\n68 581\n69 582\n70 583\n71 584\n72 585\n73 586\n74 587\n75 588\n76 589\n77 590\n78 591\n79 592\n80 593\n81 594\n82 595\n83 596\n84 597\n85 598\n86 599\n87 600\n88 601\n89 602\n90 603\n91 604\n92 605\n93 606\n94 607\n95 608\n96 609\n97 610\n98 611\n99 612\n100 613\n101 614\n102 615\n103 616\n104 617\n105 618\n106 619\n107 620\n108 621\n109 622\n110 623\n111 624\n112 625\n113 626\n114 627\n115 628\n116 629\n117 630\n118 631\n119 632\n120 633\n121 634\n122 635\n123 636\n124 637\n125 638\n126 639\n127 640\n128 641\n129 642\n130 643\n131 644\n132 645\n133 646\n134 647\n135 648\n136 649\n137 650\n138 651\n139 652\n140 653\n141 654\n142 655\n143 656\n144 657\n145 658\n146 659\n147 660\n148 661\n149 662\n150 663\n151 664\n152 665\n153 666\n154 667\n155 668\n156 669\n157 670\n158 671\n159 672\n160 673\n161 674\n162 675\n163 676\n164 677\n165 678\n166 679\n167 680\n168 681\n169 682\n170 683\n171 684\n172 685\n173 686\n174 687\n175 688\n176 689\n177 690\n178 691\n179 692\n180 693\n181 694\n182 695\n183 696\n184 697\n185 698\n186 699\n187 700\n188 701\n189 702\n190 703\n191 704\n192 705\n193 706\n194 707\n195 708\n196 709\n197 710\n198 711\n199 712\n200 713\n201 714\n202 715\n203 716\n204 717\n205 718\n206 719\n207 720\n208 721\n209 722\n210 723\n211 724\n212 725\n213 726\n214 727\n215 728\n216 729\n217 730\n218 731\n219 732\n220 733\n221 734\n222 735\n223 736\n224 737\n225 738\n226 739\n227 740\n228 741\n229 742\n230 743\n231 744\n232 745\n233 746\n234 747\n235 748\n236 749\n237 750\n238 751\n239 752\n240 753\n241 754\n242 755\n243 756\n244 757\n245 758\n246 759\n247 760\n248 761\n249 762\n250 763\n251 764\n252 765\n253 766\n254 767\n255 768\n256 769\n257 770\n258 771\n259 772\n260 773\n261 774\n262 775\n263 776\n264 777\n265 778\n266 779\n267 780\n268 781\n269 782\n270 783\n271 784\n272 785\n273 786\n274 787\n275 788\n276 789\n277 790\n278 791\n279 792\n280 793\n281 794\n282 795\n283 796\n284 797\n285 798\n286 799\n287 800\n288 801\n289 802\n290 803\n291 804\n292 805\n293 806\n294 807\n295 808\n296 809\n297 810\n298 811\n299 812\n300 813\n301 814\n302 815\n303 816\n304 817\n305 818\n306 819\n307 820\n308 821\n309 822\n310 823\n311 824\n312 825\n313 826\n314 827\n315 828\n316 829\n317 830\n318 831\n319 832\n320 833\n321 834\n322 835\n323 836\n324 837\n325 838\n326 839\n327 840\n328 841\n329 842\n330 843\n331 844\n332 845\n333 846\n334 847\n335 848\n336 849\n337 850\n338 851\n339 852\n340 853\n341 854\n342 855\n343 856\n344 857\n345 858\n346 859\n347 860\n348 861\n349 862\n350 863\n351 864\n352 865\n353 866\n354 867\n355 868\n356 869\n357 870\n358 871\n359 872\n360 873\n361 874\n362 875\n363 876\n364 877\n365 878\n366 879\n367 880\n368 881\n369 882\n370 883\n371 884\n372 885\n373 886\n374 887\n375 888\n376 889\n377 890\n378 891\n379 892\n380 893\n381 894\n382 895\n383 896\n384 897\n385 898\n386 899\n387 900\n388 901\n389 902\n390 903\n391 904\n392 905\n393 906\n394 907\n395 908\n396 909\n397 910\n398 911\n399 912\n400 913\n401 914\n402 915\n403 916\n404 917\n405 918\n406 919\n407 920\n408 921\n409 922\n410 923\n411 924\n412 925\n413 926\n414 927\n415 928\n416 929\n417 930\n418 931\n419 932\n420 933\n421 934\n422 935\n423 936\n424 937\n425 938\n426 939\n427 940\n428 941\n429 942\n430 943\n431 944\n432 945\n433 946\n434 947\n435 948\n436 949\n437 950\n438 951\n439 952\n440 953\n441 954\n442 955\n443 956\n444 957\n445 958\n446 959\n447 960\n448 961\n449 962\n450 963\n451 964\n452 965\n453 966\n454 967\n455 968\n456 969\n457 970\n458 971\n459 972\n460 973\n461 974\n462 975\n463 976\n464 977\n465 978\n466 979\n467 980\n468 981\n469 982\n470 983\n471 984\n472 985\n473 986\n474 987\n475 988\n476 989\n477 990\n478 991\n479 992\n480 993\n481 994\n482 995\n483 996\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n2 672\n3 673\n4 674\n5 675\n6 676\n7 677\n8 678\n9 679\n10 680\n11 681\n12 682\n13 683\n14 684\n15 685\n16 686\n17 687\n18 688\n19 689\n20 690\n21 691\n22 692\n23 693\n24 694\n25 695\n26 696\n27 697\n28 698\n29 699\n30 700\n31 701\n32 702\n33 703\n34 704\n35 705\n36 706\n37 707\n38 708\n39 709\n40 710\n41 711\n42 712\n43 713\n44 714\n45 715\n46 716\n47 717\n48 718\n49 719\n50 720\n51 721\n52 722\n53 723\n54 724\n55 725\n56 726\n57 727\n58 728\n59 729\n60 730\n61 731\n62 732\n63 733\n64 734\n65 735\n66 736\n67 737\n68 738\n69 739\n70 740\n71 741\n72 742\n73 743\n74 744\n75 745\n76 746\n77 747\n78 748\n79 749\n80 750\n81 751\n82 752\n83 753\n84 754\n85 755\n86 756\n87 757\n88 758\n89 759\n90 760\n91 761\n92 762\n93 763\n94 764\n95 765\n96 766\n97 767\n98 768\n99 769\n100 770\n101 771\n102 772\n103 773\n104 774\n105 775\n106 776\n107 777\n108 778\n109 779\n110 780\n111 781\n112 782\n113 783\n114 784\n115 785\n116 786\n117 787\n118 788\n119 789\n120 790\n121 791\n122 792\n123 793\n124 794\n125 795\n126 796\n127 797\n128 798\n129 799\n130 800\n131 801\n132 802\n133 803\n134 804\n135 805\n136 806\n137 807\n138 808\n139 809\n140 810\n141 811\n142 812\n143 813\n144 814\n145 815\n146 816\n147 817\n148 818\n149 819\n150 820\n151 821\n152 822\n153 823\n154 824\n155 825\n156 826\n157 827\n158 828\n159 829\n160 830\n161 831\n162 832\n163 833\n164 834\n165 835\n166 836\n167 837\n168 838\n169 839\n170 840\n171 841\n172 842\n173 843\n174 844\n175 845\n176 846\n177 847\n178 848\n179 849\n180 850\n181 851\n182 852\n183 853\n184 854\n185 855\n186 856\n187 857\n188 858\n189 859\n190 860\n191 861\n192 862\n193 863\n194 864\n195 865\n196 866\n197 867\n198 868\n199 869\n200 870\n201 871\n202 872\n203 873\n204 874\n205 875\n206 876\n207 877\n208 878\n209 879\n210 880\n211 881\n212 882\n213 883\n214 884\n215 885\n216 886\n217 887\n218 888\n219 889\n220 890\n221 891\n222 892\n223 893\n224 894\n225 895\n226 896\n227 897\n228 898\n229 899\n230 900\n231 901\n232 902\n233 903\n234 904\n235 905\n236 906\n237 907\n238 908\n239 909\n240 910\n241 911\n242 912\n243 913\n244 914\n245 915\n246 916\n247 917\n248 918\n249 919\n250 920\n251 921\n252 922\n253 923\n254 924\n255 925\n256 926\n257 927\n258 928\n259 929\n260 930\n261 931\n262 932\n263 933\n264 934\n265 935\n266 936\n267 937\n268 938\n269 939\n270 940\n271 941\n272 942\n273 943\n274 944\n275 945\n276 946\n277 947\n278 948\n279 949\n280 950\n281 951\n282 952\n283 953\n284 954\n285 955\n286 956\n287 957\n288 958\n289 959\n290 960\n291 961\n292 962\n293 963\n294 964\n295 965\n296 966\n297 967\n298 968\n299 969\n300 970\n301 971\n302 972\n303 973\n304 974\n305 975\n306 976\n307 977\n308 978\n309 979\n310 980\n311 981\n312 982\n313 983\n314 984\n315 985\n316 986\n317 987\n318 988\n319 989\n320 990\n321 991\n322 992\n323 993\n324 994\n325 995\n326 996\n327 997\n328 998\n329 999\n330 1000\n331 1001\n332 1002\n333 1003\n334 1004\n335 1005\n336 1006\n337 1007\n338 1008\n339 1009\n340 1010\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n2 101\n3 102\n4 103\n5 104\n6 105\n7 106\n8 107\n9 108\n10 109\n11 110\n",
"146\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n2 16\n3 17\n4 18\n5 19\n6 20\n7 21\n8 22\n9 23\n10 24\n11 25\n12 26\n13 27\n14 28\n15 29\n16 30\n17 31\n18 32\n19 33\n20 34\n21 35\n22 36\n23 37\n24 38\n25 39\n26 40\n27 41\n28 42\n29 43\n30 44\n31 45\n32 46\n33 47\n34 48\n35 49\n36 50\n37 51\n38 52\n39 53\n40 54\n41 55\n42 56\n43 57\n44 58\n45 59\n46 60\n47 61\n48 62\n49 63\n50 64\n51 65\n52 66\n53 67\n54 68\n55 69\n56 70\n57 71\n58 72\n59 73\n60 74\n61 75\n62 76\n63 77\n64 78\n65 79\n66 80\n67 81\n68 82\n69 83\n70 84\n71 85\n72 86\n73 87\n74 88\n75 89\n76 90\n77 91\n78 92\n79 93\n80 94\n81 95\n82 96\n83 97\n84 98\n85 99\n86 100\n87 101\n88 102\n89 103\n90 104\n91 105\n92 106\n93 107\n94 108\n95 109\n96 110\n97 111\n98 112\n99 113\n100 114\n101 115\n102 116\n103 117\n104 118\n105 119\n106 120\n107 121\n108 122\n109 123\n110 124\n111 125\n112 126\n113 127\n114 128\n115 129\n116 130\n117 131\n118 132\n119 133\n120 134\n121 135\n122 136\n123 137\n124 138\n125 139\n126 140\n127 141\n128 142\n129 143\n130 144\n131 145\n132 146\n133 147\n134 148\n135 149\n136 150\n137 151\n138 152\n139 153\n140 154\n141 155\n142 156\n143 157\n144 158\n145 159\n146 160\n147 161\n148 162\n149 163\n150 164\n151 165\n152 166\n153 167\n154 168\n155 169\n156 170\n157 171\n158 172\n159 173\n160 174\n161 175\n162 176\n163 177\n164 178\n165 179\n166 180\n167 181\n168 182\n169 183\n170 184\n171 185\n172 186\n173 187\n174 188\n175 189\n176 190\n177 191\n178 192\n179 193\n180 194\n181 195\n182 196\n183 197\n184 198\n185 199\n186 200\n187 201\n188 202\n189 203\n190 204\n191 205\n192 206\n193 207\n194 208\n195 209\n196 210\n197 211\n198 212\n199 213\n200 214\n201 215\n202 216\n203 217\n204 218\n205 219\n206 220\n207 221\n208 222\n209 223\n210 224\n211 225\n212 226\n213 227\n214 228\n215 229\n216 230\n217 231\n218 232\n219 233\n220 234\n221 235\n222 236\n223 237\n224 238\n225 239\n226 240\n227 241\n228 242\n229 243\n230 244\n231 245\n232 246\n233 247\n234 248\n235 249\n236 250\n237 251\n238 252\n239 253\n240 254\n241 255\n242 256\n243 257\n244 258\n245 259\n246 260\n247 261\n248 262\n249 263\n250 264\n251 265\n252 266\n253 267\n254 268\n255 269\n256 270\n257 271\n258 272\n259 273\n260 274\n261 275\n262 276\n263 277\n264 278\n265 279\n266 280\n267 281\n268 282\n269 283\n270 284\n271 285\n272 286\n273 287\n274 288\n275 289\n276 290\n277 291\n278 292\n279 293\n280 294\n281 295\n282 296\n283 297\n284 298\n285 299\n286 300\n287 301\n288 302\n289 303\n290 304\n291 305\n292 306\n293 307\n294 308\n295 309\n296 310\n297 311\n298 312\n299 313\n300 314\n301 315\n302 316\n303 317\n304 318\n305 319\n306 320\n307 321\n308 322\n309 323\n310 324\n311 325\n312 326\n313 327\n314 328\n315 329\n316 330\n317 331\n318 332\n319 333\n320 334\n321 335\n322 336\n323 337\n324 338\n325 339\n326 340\n327 341\n328 342\n329 343\n330 344\n331 345\n332 346\n333 347\n334 348\n335 349\n336 350\n337 351\n338 352\n339 353\n340 354\n341 355\n342 356\n343 357\n344 358\n345 359\n346 360\n347 361\n348 362\n349 363\n350 364\n351 365\n352 366\n353 367\n354 368\n355 369\n356 370\n357 371\n358 372\n359 373\n360 374\n361 375\n362 376\n363 377\n364 378\n365 379\n366 380\n367 381\n368 382\n369 383\n370 384\n371 385\n372 386\n373 387\n374 388\n375 389\n376 390\n377 391\n378 392\n379 393\n380 394\n381 395\n382 396\n383 397\n384 398\n385 399\n386 400\n387 401\n388 402\n389 403\n390 404\n391 405\n392 406\n393 407\n394 408\n395 409\n396 410\n397 411\n398 412\n399 413\n400 414\n401 415\n402 416\n403 417\n404 418\n405 419\n406 420\n407 421\n408 422\n409 423\n410 424\n411 425\n412 426\n413 427\n414 428\n415 429\n416 430\n417 431\n418 432\n419 433\n420 434\n421 435\n422 436\n423 437\n424 438\n425 439\n426 440\n427 441\n428 442\n429 443\n430 444\n431 445\n432 446\n433 447\n434 448\n435 449\n436 450\n437 451\n438 452\n439 453\n440 454\n441 455\n442 456\n443 457\n444 458\n445 459\n446 460\n447 461\n448 462\n449 463\n450 464\n451 465\n452 466\n453 467\n454 468\n455 469\n456 470\n457 471\n458 472\n459 473\n460 474\n461 475\n462 476\n463 477\n464 478\n465 479\n466 480\n467 481\n468 482\n469 483\n470 484\n471 485\n472 486\n473 487\n474 488\n475 489\n476 490\n477 491\n478 492\n479 493\n480 494\n481 495\n482 496\n483 497\n484 498\n485 499\n486 500\n487 501\n488 502\n489 503\n490 504\n491 505\n492 506\n493 507\n494 508\n495 509\n496 510\n497 511\n498 512\n499 513\n500 514\n501 515\n502 516\n503 517\n504 518\n505 519\n506 520\n507 521\n508 522\n509 523\n510 524\n511 525\n512 526\n513 527\n514 528\n515 529\n516 530\n517 531\n518 532\n519 533\n520 534\n521 535\n522 536\n523 537\n524 538\n525 539\n526 540\n527 541\n528 542\n529 543\n530 544\n531 545\n532 546\n533 547\n534 548\n535 549\n536 550\n537 551\n538 552\n539 553\n540 554\n541 555\n542 556\n543 557\n544 558\n545 559\n546 560\n547 561\n548 562\n549 563\n550 564\n551 565\n552 566\n553 567\n554 568\n555 569\n556 570\n557 571\n558 572\n559 573\n560 574\n561 575\n562 576\n563 577\n564 578\n565 579\n566 580\n567 581\n568 582\n569 583\n570 584\n571 585\n572 586\n573 587\n574 588\n575 589\n576 590\n577 591\n578 592\n579 593\n580 594\n581 595\n582 596\n583 597\n584 598\n585 599\n586 600\n587 601\n588 602\n589 603\n590 604\n591 605\n592 606\n593 607\n594 608\n595 609\n596 610\n597 611\n598 612\n599 613\n600 614\n601 615\n602 616\n603 617\n604 618\n605 619\n606 620\n607 621\n608 622\n609 623\n610 624\n611 625\n612 626\n613 627\n614 628\n615 629\n616 630\n617 631\n618 632\n619 633\n620 634\n621 635\n622 636\n623 637\n624 638\n625 639\n626 640\n627 641\n628 642\n629 643\n630 644\n631 645\n632 646\n633 647\n634 648\n635 649\n636 650\n637 651\n638 652\n639 653\n640 654\n641 655\n642 656\n643 657\n644 658\n645 659\n646 660\n647 661\n648 662\n649 663\n650 664\n651 665\n652 666\n653 667\n654 668\n655 669\n656 670\n657 671\n658 672\n659 673\n660 674\n661 675\n662 676\n663 677\n664 678\n665 679\n666 680\n667 681\n668 682\n669 683\n670 684\n671 685\n672 686\n673 687\n674 688\n675 689\n676 690\n677 691\n678 692\n679 693\n680 694\n681 695\n682 696\n683 697\n684 698\n685 699\n686 700\n687 701\n688 702\n689 703\n690 704\n691 705\n692 706\n693 707\n694 708\n695 709\n696 710\n697 711\n698 712\n699 713\n700 714\n701 715\n702 716\n703 717\n704 718\n705 719\n706 720\n707 721\n708 722\n709 723\n710 724\n711 725\n712 726\n713 727\n714 728\n715 729\n716 730\n717 731\n718 732\n719 733\n720 734\n721 735\n722 736\n723 737\n724 738\n725 739\n726 740\n727 741\n728 742\n729 743\n730 744\n731 745\n732 746\n733 747\n734 748\n735 749\n736 750\n737 751\n738 752\n739 753\n740 754\n741 755\n742 756\n743 757\n744 758\n745 759\n746 760\n747 761\n748 762\n749 763\n750 764\n751 765\n752 766\n753 767\n754 768\n755 769\n756 770\n757 771\n758 772\n759 773\n760 774\n761 775\n762 776\n763 777\n764 778\n765 779\n766 780\n767 781\n768 782\n769 783\n770 784\n771 785\n772 786\n773 787\n774 788\n775 789\n776 790\n777 791\n778 792\n779 793\n780 794\n781 795\n782 796\n783 797\n784 798\n785 799\n786 800\n787 801\n788 802\n789 803\n790 804\n791 805\n792 806\n793 807\n794 808\n795 809\n796 810\n797 811\n798 812\n799 813\n800 814\n801 815\n802 816\n803 817\n804 818\n805 819\n806 820\n807 821\n808 822\n809 823\n810 824\n811 825\n812 826\n813 827\n814 828\n815 829\n816 830\n817 831\n818 832\n819 833\n820 834\n821 835\n822 836\n823 837\n824 838\n825 839\n826 840\n827 841\n828 842\n829 843\n830 844\n831 845\n832 846\n833 847\n834 848\n835 849\n836 850\n837 851\n838 852\n839 853\n840 854\n841 855\n842 856\n843 857\n844 858\n845 859\n846 860\n847 861\n848 862\n849 863\n850 864\n851 865\n852 866\n853 867\n854 868\n855 869\n856 870\n857 871\n858 872\n859 873\n860 874\n861 875\n862 876\n863 877\n864 878\n865 879\n866 880\n867 881\n868 882\n869 883\n870 884\n871 885\n872 886\n873 887\n874 888\n875 889\n876 890\n877 891\n878 892\n879 893\n880 894\n881 895\n882 896\n883 897\n884 898\n885 899\n886 900\n887 901\n888 902\n889 903\n890 904\n891 905\n892 906\n893 907\n894 908\n895 909\n896 910\n897 911\n898 912\n899 913\n900 914\n901 915\n902 916\n903 917\n904 918\n905 919\n906 920\n907 921\n908 922\n909 923\n910 924\n911 925\n912 926\n913 927\n914 928\n915 929\n916 930\n917 931\n918 932\n919 933\n920 934\n921 935\n922 936\n923 937\n924 938\n925 939\n926 940\n927 941\n928 942\n929 943\n930 944\n931 945\n932 946\n933 947\n934 948\n935 949\n936 950\n937 951\n938 952\n939 953\n940 954\n941 955\n942 956\n943 957\n944 958\n945 959\n946 960\n947 961\n948 962\n949 963\n950 964\n951 965\n952 966\n953 967\n954 968\n955 969\n956 970\n957 971\n958 972\n959 973\n960 974\n961 975\n962 976\n963 977\n964 978\n965 979\n966 980\n967 981\n968 982\n969 983\n970 984\n971 985\n972 986\n973 987\n974 988\n975 989\n976 990\n977 991\n978 992\n979 993\n980 994\n981 995\n982 996\n983 997\n984 998\n985 999\n986 1000\n987 1001\n988 1002\n989 1003\n990 1004\n991 1005\n992 1006\n993 1007\n994 1008\n995 1009\n996 1010\n997 1011\n998 1012\n999 1013\n",
"18\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n2 18\n3 19\n4 20\n5 21\n6 22\n7 23\n8 24\n9 25\n10 26\n11 27\n12 28\n13 29\n14 30\n15 31\n16 32\n17 33\n18 34\n19 35\n20 36\n21 37\n22 38\n23 39\n24 40\n25 41\n26 42\n27 43\n28 44\n29 45\n30 46\n31 47\n32 48\n33 49\n34 50\n35 51\n36 52\n37 53\n38 54\n39 55\n40 56\n41 57\n42 58\n43 59\n44 60\n45 61\n46 62\n47 63\n48 64\n49 65\n50 66\n51 67\n52 68\n53 69\n54 70\n55 71\n56 72\n57 73\n58 74\n59 75\n60 76\n61 77\n62 78\n63 79\n64 80\n65 81\n66 82\n67 83\n68 84\n69 85\n70 86\n71 87\n72 88\n73 89\n74 90\n75 91\n76 92\n77 93\n78 94\n79 95\n80 96\n81 97\n82 98\n83 99\n84 100\n85 101\n86 102\n87 103\n88 104\n89 105\n90 106\n91 107\n92 108\n93 109\n94 110\n95 111\n96 112\n97 113\n98 114\n99 115\n100 116\n101 117\n102 118\n103 119\n104 120\n105 121\n106 122\n107 123\n108 124\n109 125\n110 126\n111 127\n112 128\n113 129\n114 130\n115 131\n116 132\n117 133\n118 134\n119 135\n120 136\n121 137\n122 138\n123 139\n124 140\n",
"166\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n2 25\n3 26\n4 27\n5 28\n6 29\n7 30\n8 31\n9 32\n10 33\n11 34\n12 35\n13 36\n14 37\n15 38\n16 39\n17 40\n18 41\n19 42\n20 43\n21 44\n22 45\n23 46\n24 47\n25 48\n26 49\n27 50\n28 51\n29 52\n30 53\n31 54\n32 55\n33 56\n34 57\n35 58\n36 59\n37 60\n38 61\n39 62\n40 63\n41 64\n42 65\n43 66\n44 67\n45 68\n46 69\n47 70\n48 71\n49 72\n50 73\n51 74\n52 75\n53 76\n54 77\n55 78\n56 79\n57 80\n58 81\n59 82\n60 83\n61 84\n62 85\n63 86\n64 87\n65 88\n66 89\n67 90\n68 91\n69 92\n70 93\n71 94\n72 95\n73 96\n74 97\n75 98\n76 99\n77 100\n78 101\n79 102\n80 103\n81 104\n82 105\n83 106\n84 107\n85 108\n86 109\n87 110\n88 111\n89 112\n90 113\n91 114\n92 115\n93 116\n94 117\n95 118\n96 119\n97 120\n98 121\n99 122\n100 123\n101 124\n102 125\n103 126\n104 127\n105 128\n106 129\n107 130\n108 131\n109 132\n110 133\n111 134\n112 135\n113 136\n114 137\n115 138\n116 139\n117 140\n118 141\n119 142\n120 143\n121 144\n122 145\n123 146\n124 147\n125 148\n126 149\n127 150\n128 151\n129 152\n130 153\n131 154\n132 155\n133 156\n134 157\n135 158\n136 159\n137 160\n138 161\n139 162\n140 163\n141 164\n142 165\n143 166\n144 167\n145 168\n146 169\n147 170\n148 171\n149 172\n150 173\n151 174\n152 175\n153 176\n154 177\n155 178\n156 179\n157 180\n158 181\n159 182\n160 183\n161 184\n162 185\n163 186\n164 187\n165 188\n166 189\n167 190\n168 191\n169 192\n170 193\n171 194\n172 195\n173 196\n174 197\n175 198\n176 199\n177 200\n178 201\n179 202\n180 203\n181 204\n182 205\n183 206\n184 207\n185 208\n186 209\n187 210\n188 211\n189 212\n190 213\n191 214\n192 215\n193 216\n194 217\n195 218\n196 219\n197 220\n198 221\n199 222\n200 223\n201 224\n202 225\n203 226\n204 227\n205 228\n206 229\n207 230\n208 231\n209 232\n210 233\n211 234\n212 235\n213 236\n214 237\n215 238\n216 239\n217 240\n218 241\n219 242\n220 243\n221 244\n222 245\n223 246\n224 247\n225 248\n226 249\n227 250\n228 251\n229 252\n230 253\n231 254\n232 255\n233 256\n234 257\n235 258\n236 259\n237 260\n238 261\n239 262\n240 263\n241 264\n242 265\n243 266\n244 267\n245 268\n246 269\n247 270\n248 271\n249 272\n250 273\n251 274\n252 275\n253 276\n254 277\n255 278\n256 279\n257 280\n258 281\n259 282\n260 283\n261 284\n262 285\n263 286\n264 287\n265 288\n266 289\n267 290\n268 291\n269 292\n270 293\n271 294\n272 295\n273 296\n274 297\n275 298\n276 299\n277 300\n278 301\n279 302\n280 303\n281 304\n282 305\n283 306\n284 307\n285 308\n286 309\n287 310\n288 311\n289 312\n290 313\n291 314\n292 315\n293 316\n294 317\n295 318\n296 319\n297 320\n298 321\n299 322\n300 323\n301 324\n302 325\n303 326\n304 327\n305 328\n306 329\n307 330\n308 331\n309 332\n310 333\n311 334\n312 335\n313 336\n314 337\n315 338\n316 339\n317 340\n318 341\n319 342\n320 343\n321 344\n322 345\n323 346\n324 347\n325 348\n326 349\n327 350\n328 351\n329 352\n330 353\n331 354\n332 355\n333 356\n334 357\n335 358\n336 359\n337 360\n338 361\n339 362\n340 363\n341 364\n342 365\n343 366\n344 367\n345 368\n346 369\n347 370\n348 371\n349 372\n350 373\n351 374\n352 375\n353 376\n354 377\n355 378\n356 379\n357 380\n358 381\n359 382\n360 383\n361 384\n362 385\n363 386\n364 387\n365 388\n366 389\n367 390\n368 391\n369 392\n370 393\n371 394\n372 395\n373 396\n374 397\n375 398\n376 399\n377 400\n378 401\n379 402\n380 403\n381 404\n382 405\n383 406\n384 407\n385 408\n386 409\n387 410\n388 411\n389 412\n390 413\n391 414\n392 415\n393 416\n394 417\n395 418\n396 419\n397 420\n398 421\n399 422\n400 423\n401 424\n402 425\n403 426\n404 427\n405 428\n406 429\n407 430\n408 431\n409 432\n410 433\n411 434\n412 435\n413 436\n414 437\n415 438\n416 439\n417 440\n418 441\n419 442\n420 443\n421 444\n422 445\n423 446\n424 447\n425 448\n426 449\n427 450\n428 451\n429 452\n430 453\n431 454\n432 455\n433 456\n434 457\n435 458\n436 459\n437 460\n438 461\n439 462\n440 463\n441 464\n442 465\n443 466\n444 467\n445 468\n446 469\n447 470\n448 471\n449 472\n450 473\n451 474\n452 475\n453 476\n454 477\n455 478\n456 479\n457 480\n458 481\n459 482\n460 483\n461 484\n462 485\n463 486\n464 487\n465 488\n466 489\n467 490\n468 491\n469 492\n470 493\n471 494\n472 495\n473 496\n474 497\n475 498\n476 499\n477 500\n478 501\n479 502\n480 503\n481 504\n482 505\n483 506\n484 507\n485 508\n486 509\n487 510\n488 511\n489 512\n490 513\n491 514\n492 515\n493 516\n494 517\n495 518\n496 519\n497 520\n498 521\n499 522\n500 523\n501 524\n502 525\n503 526\n504 527\n505 528\n506 529\n507 530\n508 531\n509 532\n510 533\n511 534\n512 535\n513 536\n514 537\n515 538\n516 539\n517 540\n518 541\n519 542\n520 543\n521 544\n522 545\n523 546\n524 547\n525 548\n526 549\n527 550\n528 551\n529 552\n530 553\n531 554\n532 555\n533 556\n534 557\n535 558\n536 559\n537 560\n538 561\n539 562\n540 563\n541 564\n542 565\n543 566\n544 567\n545 568\n546 569\n547 570\n548 571\n549 572\n550 573\n551 574\n552 575\n553 576\n554 577\n555 578\n556 579\n557 580\n558 581\n559 582\n560 583\n561 584\n562 585\n563 586\n564 587\n565 588\n566 589\n567 590\n568 591\n569 592\n570 593\n571 594\n572 595\n573 596\n574 597\n575 598\n576 599\n577 600\n578 601\n579 602\n580 603\n581 604\n582 605\n583 606\n584 607\n585 608\n586 609\n587 610\n588 611\n589 612\n590 613\n591 614\n592 615\n593 616\n594 617\n595 618\n596 619\n597 620\n598 621\n599 622\n600 623\n601 624\n602 625\n603 626\n604 627\n605 628\n606 629\n607 630\n608 631\n609 632\n610 633\n611 634\n612 635\n613 636\n614 637\n615 638\n616 639\n617 640\n618 641\n619 642\n620 643\n621 644\n622 645\n623 646\n624 647\n625 648\n626 649\n627 650\n628 651\n629 652\n630 653\n631 654\n632 655\n633 656\n634 657\n635 658\n636 659\n637 660\n638 661\n639 662\n640 663\n641 664\n642 665\n643 666\n644 667\n645 668\n646 669\n647 670\n648 671\n649 672\n650 673\n651 674\n652 675\n653 676\n654 677\n655 678\n656 679\n657 680\n658 681\n659 682\n660 683\n661 684\n662 685\n663 686\n664 687\n665 688\n666 689\n667 690\n668 691\n669 692\n670 693\n671 694\n672 695\n673 696\n674 697\n675 698\n676 699\n677 700\n678 701\n679 702\n680 703\n681 704\n682 705\n683 706\n684 707\n685 708\n686 709\n687 710\n688 711\n689 712\n690 713\n691 714\n692 715\n693 716\n694 717\n695 718\n696 719\n697 720\n698 721\n699 722\n700 723\n701 724\n702 725\n703 726\n704 727\n705 728\n706 729\n707 730\n708 731\n709 732\n710 733\n711 734\n712 735\n713 736\n714 737\n715 738\n716 739\n717 740\n718 741\n719 742\n720 743\n721 744\n722 745\n723 746\n724 747\n725 748\n726 749\n727 750\n728 751\n729 752\n730 753\n731 754\n732 755\n733 756\n734 757\n735 758\n736 759\n737 760\n738 761\n739 762\n740 763\n741 764\n742 765\n743 766\n744 767\n745 768\n746 769\n747 770\n748 771\n749 772\n750 773\n751 774\n752 775\n753 776\n754 777\n755 778\n756 779\n757 780\n758 781\n759 782\n760 783\n761 784\n762 785\n763 786\n764 787\n765 788\n766 789\n767 790\n768 791\n769 792\n770 793\n771 794\n772 795\n773 796\n774 797\n775 798\n776 799\n777 800\n778 801\n779 802\n780 803\n781 804\n782 805\n783 806\n784 807\n785 808\n786 809\n787 810\n788 811\n789 812\n790 813\n791 814\n792 815\n793 816\n794 817\n795 818\n796 819\n797 820\n798 821\n799 822\n800 823\n801 824\n802 825\n803 826\n804 827\n805 828\n806 829\n807 830\n808 831\n809 832\n810 833\n811 834\n812 835\n813 836\n814 837\n815 838\n816 839\n817 840\n818 841\n819 842\n820 843\n821 844\n822 845\n823 846\n824 847\n825 848\n826 849\n827 850\n828 851\n829 852\n830 853\n831 854\n832 855\n833 856\n834 857\n835 858\n836 859\n837 860\n838 861\n839 862\n840 863\n841 864\n842 865\n843 866\n844 867\n845 868\n846 869\n847 870\n848 871\n849 872\n850 873\n851 874\n852 875\n853 876\n854 877\n855 878\n856 879\n857 880\n858 881\n859 882\n860 883\n861 884\n862 885\n863 886\n864 887\n865 888\n866 889\n867 890\n868 891\n869 892\n870 893\n871 894\n872 895\n873 896\n874 897\n875 898\n876 899\n877 900\n878 901\n879 902\n880 903\n881 904\n882 905\n883 906\n884 907\n885 908\n886 909\n887 910\n888 911\n889 912\n890 913\n891 914\n892 915\n893 916\n894 917\n895 918\n896 919\n897 920\n898 921\n899 922\n900 923\n901 924\n902 925\n903 926\n904 927\n905 928\n906 929\n907 930\n908 931\n909 932\n910 933\n911 934\n912 935\n913 936\n914 937\n915 938\n916 939\n917 940\n918 941\n919 942\n920 943\n921 944\n922 945\n923 946\n924 947\n925 948\n926 949\n927 950\n928 951\n929 952\n930 953\n931 954\n932 955\n933 956\n934 957\n935 958\n936 959\n937 960\n938 961\n939 962\n940 963\n941 964\n942 965\n943 966\n944 967\n945 968\n946 969\n947 970\n948 971\n949 972\n950 973\n951 974\n952 975\n953 976\n954 977\n955 978\n956 979\n957 980\n958 981\n959 982\n960 983\n961 984\n962 985\n963 986\n964 987\n965 988\n966 989\n967 990\n968 991\n969 992\n970 993\n971 994\n972 995\n973 996\n974 997\n975 998\n976 999\n977 1000\n978 1001\n979 1002\n980 1003\n981 1004\n982 1005\n983 1006\n984 1007\n985 1008\n986 1009\n987 1010\n988 1011\n989 1012\n990 1013\n991 1014\n992 1015\n993 1016\n994 1017\n995 1018\n996 1019\n997 1020\n998 1021\n999 1022\n1000 1023\n1001 1024\n1002 1025\n1003 1026\n1004 1027\n1005 1028\n1006 1029\n1007 1030\n1008 1031\n1009 1032\n1010 1033\n1011 1034\n1012 1035\n1013 1036\n1014 1037\n1015 1038\n1016 1039\n1017 1040\n1018 1041\n1019 1042\n1020 1043\n1021 1044\n1022 1045\n1023 1046\n1024 1047\n1025 1048\n1026 1049\n1027 1050\n1028 1051\n1029 1052\n1030 1053\n1031 1054\n1032 1055\n1033 1056\n1034 1057\n1035 1058\n1036 1059\n1037 1060\n1038 1061\n1039 1062\n1040 1063\n1041 1064\n1042 1065\n1043 1066\n1044 1067\n1045 1068\n1046 1069\n1047 1070\n1048 1071\n1049 1072\n1050 1073\n1051 1074\n1052 1075\n1053 1076\n1054 1077\n1055 1078\n1056 1079\n1057 1080\n1058 1081\n1059 1082\n1060 1083\n1061 1084\n1062 1085\n1063 1086\n1064 1087\n1065 1088\n1066 1089\n1067 1090\n1068 1091\n1069 1092\n1070 1093\n1071 1094\n1072 1095\n1073 1096\n1074 1097\n1075 1098\n1076 1099\n1077 1100\n1078 1101\n1079 1102\n1080 1103\n1081 1104\n1082 1105\n1083 1106\n1084 1107\n1085 1108\n1086 1109\n1087 1110\n1088 1111\n1089 1112\n1090 1113\n1091 1114\n1092 1115\n1093 1116\n1094 1117\n1095 1118\n1096 1119\n1097 1120\n1098 1121\n1099 1122\n1100 1123\n1101 1124\n1102 1125\n1103 1126\n1104 1127\n1105 1128\n1106 1129\n1107 1130\n1108 1131\n1109 1132\n1110 1133\n1111 1134\n1112 1135\n1113 1136\n1114 1137\n1115 1138\n1116 1139\n1117 1140\n1118 1141\n1119 1142\n1120 1143\n1121 1144\n1122 1145\n1123 1146\n1124 1147\n1125 1148\n1126 1149\n1127 1150\n1128 1151\n1129 1152\n1130 1153\n1131 1154\n1132 1155\n1133 1156\n1134 1157\n1135 1158\n1136 1159\n1137 1160\n1138 1161\n1139 1162\n1140 1163\n1141 1164\n1142 1165\n1143 1166\n1144 1167\n1145 1168\n1146 1169\n1147 1170\n1148 1171\n1149 1172\n1150 1173\n1151 1174\n1152 1175\n1153 1176\n1154 1177\n1155 1178\n1156 1179\n1157 1180\n1158 1181\n1159 1182\n1160 1183\n1161 1184\n1162 1185\n1163 1186\n1164 1187\n1165 1188\n1166 1189\n1167 1190\n1168 1191\n1169 1192\n1170 1193\n1171 1194\n1172 1195\n1173 1196\n1174 1197\n1175 1198\n1176 1199\n1177 1200\n1178 1201\n1179 1202\n1180 1203\n1181 1204\n1182 1205\n1183 1206\n1184 1207\n1185 1208\n1186 1209\n1187 1210\n1188 1211\n1189 1212\n1190 1213\n1191 1214\n1192 1215\n1193 1216\n1194 1217\n1195 1218\n1196 1219\n1197 1220\n1198 1221\n1199 1222\n1200 1223\n1201 1224\n1202 1225\n1203 1226\n1204 1227\n1205 1228\n1206 1229\n1207 1230\n1208 1231\n1209 1232\n1210 1233\n1211 1234\n1212 1235\n1213 1236\n1214 1237\n1215 1238\n1216 1239\n1217 1240\n1218 1241\n1219 1242\n1220 1243\n1221 1244\n1222 1245\n1223 1246\n1224 1247\n1225 1248\n1226 1249\n1227 1250\n1228 1251\n1229 1252\n1230 1253\n1231 1254\n1232 1255\n1233 1256\n1234 1257\n1235 1258\n1236 1259\n1237 1260\n1238 1261\n1239 1262\n1240 1263\n1241 1264\n1242 1265\n1243 1266\n1244 1267\n1245 1268\n1246 1269\n1247 1270\n1248 1271\n1249 1272\n1250 1273\n1251 1274\n1252 1275\n1253 1276\n1254 1277\n1255 1278\n1256 1279\n1257 1280\n1258 1281\n1259 1282\n1260 1283\n1261 1284\n1262 1285\n1263 1286\n1264 1287\n1265 1288\n1266 1289\n1267 1290\n1268 1291\n1269 1292\n1270 1293\n1271 1294\n1272 1295\n1273 1296\n1274 1297\n1275 1298\n1276 1299\n1277 1300\n1278 1301\n1279 1302\n1280 1303\n1281 1304\n1282 1305\n1283 1306\n1284 1307\n1285 1308\n1286 1309\n1287 1310\n1288 1311\n1289 1312\n1290 1313\n1291 1314\n1292 1315\n1293 1316\n1294 1317\n1295 1318\n1296 1319\n1297 1320\n1298 1321\n1299 1322\n1300 1323\n1301 1324\n1302 1325\n1303 1326\n1304 1327\n1305 1328\n1306 1329\n1307 1330\n1308 1331\n1309 1332\n1310 1333\n1311 1334\n1312 1335\n1313 1336\n1314 1337\n1315 1338\n1316 1339\n1317 1340\n1318 1341\n1319 1342\n1320 1343\n1321 1344\n1322 1345\n1323 1346\n1324 1347\n1325 1348\n1326 1349\n1327 1350\n1328 1351\n1329 1352\n1330 1353\n1331 1354\n1332 1355\n1333 1356\n1334 1357\n1335 1358\n1336 1359\n1337 1360\n1338 1361\n1339 1362\n1340 1363\n1341 1364\n1342 1365\n1343 1366\n1344 1367\n1345 1368\n1346 1369\n1347 1370\n1348 1371\n1349 1372\n1350 1373\n1351 1374\n1352 1375\n1353 1376\n1354 1377\n1355 1378\n1356 1379\n1357 1380\n1358 1381\n1359 1382\n1360 1383\n1361 1384\n1362 1385\n1363 1386\n1364 1387\n1365 1388\n1366 1389\n1367 1390\n1368 1391\n1369 1392\n1370 1393\n1371 1394\n1372 1395\n1373 1396\n1374 1397\n1375 1398\n1376 1399\n1377 1400\n1378 1401\n1379 1402\n1380 1403\n1381 1404\n1382 1405\n1383 1406\n1384 1407\n1385 1408\n1386 1409\n1387 1410\n1388 1411\n1389 1412\n1390 1413\n1391 1414\n1392 1415\n1393 1416\n1394 1417\n1395 1418\n1396 1419\n1397 1420\n1398 1421\n1399 1422\n1400 1423\n1401 1424\n1402 1425\n1403 1426\n1404 1427\n1405 1428\n1406 1429\n1407 1430\n1408 1431\n1409 1432\n1410 1433\n1411 1434\n1412 1435\n1413 1436\n1414 1437\n1415 1438\n1416 1439\n1417 1440\n1418 1441\n1419 1442\n1420 1443\n1421 1444\n1422 1445\n1423 1446\n1424 1447\n1425 1448\n1426 1449\n1427 1450\n1428 1451\n1429 1452\n1430 1453\n1431 1454\n1432 1455\n1433 1456\n1434 1457\n1435 1458\n1436 1459\n1437 1460\n1438 1461\n1439 1462\n1440 1463\n1441 1464\n1442 1465\n1443 1466\n1444 1467\n1445 1468\n1446 1469\n1447 1470\n1448 1471\n1449 1472\n1450 1473\n1451 1474\n1452 1475\n1453 1476\n1454 1477\n1455 1478\n1456 1479\n1457 1480\n1458 1481\n1459 1482\n1460 1483\n1461 1484\n1462 1485\n1463 1486\n1464 1487\n1465 1488\n1466 1489\n1467 1490\n1468 1491\n1469 1492\n1470 1493\n1471 1494\n1472 1495\n1473 1496\n1474 1497\n1475 1498\n1476 1499\n1477 1500\n1478 1501\n1479 1502\n1480 1503\n1481 1504\n1482 1505\n1483 1506\n1484 1507\n1485 1508\n1486 1509\n1487 1510\n1488 1511\n1489 1512\n1490 1513\n1491 1514\n1492 1515\n1493 1516\n1494 1517\n1495 1518\n1496 1519\n1497 1520\n1498 1521\n1499 1522\n1500 1523\n1501 1524\n1502 1525\n1503 1526\n1504 1527\n1505 1528\n1506 1529\n1507 1530\n1508 1531\n1509 1532\n1510 1533\n1511 1534\n1512 1535\n1513 1536\n1514 1537\n1515 1538\n1516 1539\n1517 1540\n1518 1541\n1519 1542\n1520 1543\n1521 1544\n1522 1545\n1523 1546\n1524 1547\n1525 1548\n1526 1549\n1527 1550\n1528 1551\n1529 1552\n1530 1553\n1531 1554\n1532 1555\n1533 1556\n1534 1557\n1535 1558\n1536 1559\n1537 1560\n1538 1561\n1539 1562\n1540 1563\n1541 1564\n1542 1565\n1543 1566\n1544 1567\n1545 1568\n1546 1569\n1547 1570\n1548 1571\n1549 1572\n1550 1573\n1551 1574\n1552 1575\n1553 1576\n1554 1577\n1555 1578\n1556 1579\n1557 1580\n1558 1581\n1559 1582\n1560 1583\n1561 1584\n1562 1585\n1563 1586\n1564 1587\n1565 1588\n1566 1589\n1567 1590\n1568 1591\n1569 1592\n1570 1593\n1571 1594\n1572 1595\n1573 1596\n1574 1597\n1575 1598\n1576 1599\n1577 1600\n1578 1601\n1579 1602\n1580 1603\n1581 1604\n1582 1605\n1583 1606\n1584 1607\n1585 1608\n1586 1609\n1587 1610\n1588 1611\n1589 1612\n1590 1613\n1591 1614\n1592 1615\n1593 1616\n1594 1617\n1595 1618\n1596 1619\n1597 1620\n1598 1621\n1599 1622\n1600 1623\n1601 1624\n1602 1625\n1603 1626\n1604 1627\n1605 1628\n1606 1629\n1607 1630\n1608 1631\n1609 1632\n1610 1633\n1611 1634\n1612 1635\n1613 1636\n1614 1637\n1615 1638\n1616 1639\n1617 1640\n1618 1641\n1619 1642\n1620 1643\n1621 1644\n1622 1645\n1623 1646\n1624 1647\n1625 1648\n1626 1649\n1627 1650\n1628 1651\n1629 1652\n1630 1653\n1631 1654\n1632 1655\n1633 1656\n1634 1657\n1635 1658\n1636 1659\n1637 1660\n1638 1661\n1639 1662\n1640 1663\n1641 1664\n1642 1665\n1643 1666\n1644 1667\n1645 1668\n1646 1669\n1647 1670\n1648 1671\n1649 1672\n1650 1673\n1651 1674\n1652 1675\n1653 1676\n1654 1677\n1655 1678\n1656 1679\n1657 1680\n1658 1681\n1659 1682\n1660 1683\n1661 1684\n1662 1685\n1663 1686\n1664 1687\n1665 1688\n1666 1689\n1667 1690\n1668 1691\n1669 1692\n1670 1693\n1671 1694\n1672 1695\n1673 1696\n1674 1697\n1675 1698\n1676 1699\n1677 1700\n1678 1701\n1679 1702\n1680 1703\n1681 1704\n1682 1705\n1683 1706\n1684 1707\n1685 1708\n1686 1709\n1687 1710\n1688 1711\n1689 1712\n1690 1713\n1691 1714\n1692 1715\n1693 1716\n1694 1717\n1695 1718\n1696 1719\n1697 1720\n1698 1721\n1699 1722\n1700 1723\n1701 1724\n1702 1725\n1703 1726\n1704 1727\n1705 1728\n1706 1729\n1707 1730\n1708 1731\n1709 1732\n1710 1733\n1711 1734\n1712 1735\n1713 1736\n1714 1737\n1715 1738\n1716 1739\n1717 1740\n1718 1741\n1719 1742\n1720 1743\n1721 1744\n1722 1745\n1723 1746\n1724 1747\n1725 1748\n1726 1749\n1727 1750\n1728 1751\n1729 1752\n1730 1753\n1731 1754\n1732 1755\n1733 1756\n1734 1757\n1735 1758\n1736 1759\n1737 1760\n1738 1761\n1739 1762\n1740 1763\n1741 1764\n1742 1765\n1743 1766\n1744 1767\n1745 1768\n1746 1769\n1747 1770\n1748 1771\n1749 1772\n1750 1773\n1751 1774\n1752 1775\n1753 1776\n1754 1777\n1755 1778\n1756 1779\n1757 1780\n1758 1781\n1759 1782\n1760 1783\n1761 1784\n1762 1785\n1763 1786\n1764 1787\n1765 1788\n1766 1789\n1767 1790\n1768 1791\n1769 1792\n1770 1793\n1771 1794\n1772 1795\n1773 1796\n1774 1797\n1775 1798\n1776 1799\n1777 1800\n1778 1801\n1779 1802\n1780 1803\n1781 1804\n1782 1805\n1783 1806\n1784 1807\n1785 1808\n1786 1809\n1787 1810\n1788 1811\n1789 1812\n1790 1813\n1791 1814\n1792 1815\n1793 1816\n1794 1817\n1795 1818\n1796 1819\n1797 1820\n1798 1821\n1799 1822\n1800 1823\n1801 1824\n1802 1825\n1803 1826\n1804 1827\n1805 1828\n1806 1829\n1807 1830\n1808 1831\n1809 1832\n1810 1833\n1811 1834\n1812 1835\n1813 1836\n1814 1837\n1815 1838\n1816 1839\n1817 1840\n1818 1841\n1819 1842\n1820 1843\n1821 1844\n1822 1845\n1823 1846\n1824 1847\n1825 1848\n1826 1849\n1827 1850\n1828 1851\n1829 1852\n1830 1853\n1831 1854\n1832 1855\n1833 1856\n1834 1857\n1835 1858\n1836 1859\n1837 1860\n1838 1861\n1839 1862\n1840 1863\n1841 1864\n1842 1865\n1843 1866\n1844 1867\n1845 1868\n1846 1869\n1847 1870\n1848 1871\n1849 1872\n1850 1873\n1851 1874\n1852 1875\n1853 1876\n1854 1877\n1855 1878\n1856 1879\n1857 1880\n1858 1881\n1859 1882\n1860 1883\n1861 1884\n1862 1885\n1863 1886\n1864 1887\n1865 1888\n1866 1889\n1867 1890\n1868 1891\n1869 1892\n",
"8\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n2 287\n3 288\n4 289\n5 290\n6 291\n7 292\n8 293\n9 294\n10 295\n11 296\n12 297\n13 298\n14 299\n15 300\n16 301\n17 302\n18 303\n19 304\n20 305\n21 306\n22 307\n23 308\n24 309\n25 310\n26 311\n27 312\n28 313\n29 314\n30 315\n31 316\n32 317\n33 318\n34 319\n35 320\n36 321\n37 322\n38 323\n39 324\n40 325\n41 326\n42 327\n43 328\n44 329\n45 330\n46 331\n47 332\n48 333\n49 334\n50 335\n51 336\n52 337\n53 338\n54 339\n55 340\n56 341\n57 342\n58 343\n59 344\n60 345\n61 346\n62 347\n63 348\n64 349\n65 350\n66 351\n67 352\n68 353\n69 354\n70 355\n71 356\n72 357\n73 358\n74 359\n75 360\n76 361\n77 362\n78 363\n79 364\n80 365\n81 366\n82 367\n83 368\n84 369\n85 370\n86 371\n87 372\n88 373\n89 374\n90 375\n91 376\n92 377\n93 378\n94 379\n95 380\n96 381\n97 382\n98 383\n99 384\n100 385\n101 386\n102 387\n103 388\n104 389\n105 390\n106 391\n107 392\n108 393\n109 394\n110 395\n111 396\n112 397\n113 398\n114 399\n115 400\n116 401\n117 402\n118 403\n119 404\n120 405\n121 406\n122 407\n123 408\n124 409\n125 410\n126 411\n127 412\n128 413\n129 414\n130 415\n131 416\n132 417\n133 418\n134 419\n135 420\n136 421\n137 422\n138 423\n139 424\n140 425\n141 426\n142 427\n143 428\n144 429\n145 430\n146 431\n147 432\n148 433\n149 434\n150 435\n151 436\n152 437\n153 438\n154 439\n155 440\n156 441\n157 442\n158 443\n159 444\n160 445\n161 446\n162 447\n163 448\n164 449\n165 450\n166 451\n167 452\n168 453\n169 454\n170 455\n171 456\n172 457\n173 458\n174 459\n175 460\n176 461\n177 462\n178 463\n179 464\n180 465\n181 466\n182 467\n183 468\n184 469\n185 470\n186 471\n187 472\n188 473\n189 474\n190 475\n191 476\n192 477\n193 478\n194 479\n195 480\n196 481\n197 482\n198 483\n199 484\n200 485\n201 486\n202 487\n203 488\n204 489\n205 490\n206 491\n207 492\n208 493\n209 494\n210 495\n211 496\n212 497\n213 498\n214 499\n215 500\n216 501\n217 502\n218 503\n219 504\n220 505\n221 506\n222 507\n223 508\n224 509\n225 510\n226 511\n227 512\n228 513\n229 514\n230 515\n231 516\n232 517\n233 518\n234 519\n235 520\n236 521\n237 522\n238 523\n239 524\n240 525\n241 526\n242 527\n243 528\n244 529\n245 530\n246 531\n247 532\n248 533\n249 534\n250 535\n251 536\n252 537\n253 538\n254 539\n255 540\n256 541\n257 542\n258 543\n259 544\n260 545\n261 546\n262 547\n263 548\n264 549\n265 550\n266 551\n267 552\n268 553\n269 554\n270 555\n271 556\n272 557\n273 558\n274 559\n275 560\n276 561\n277 562\n278 563\n279 564\n280 565\n281 566\n282 567\n283 568\n284 569\n285 570\n286 571\n287 572\n288 573\n289 574\n290 575\n291 576\n292 577\n293 578\n294 579\n295 580\n296 581\n297 582\n298 583\n299 584\n300 585\n301 586\n302 587\n303 588\n304 589\n305 590\n306 591\n307 592\n308 593\n309 594\n310 595\n311 596\n312 597\n313 598\n314 599\n315 600\n316 601\n317 602\n318 603\n319 604\n320 605\n321 606\n322 607\n323 608\n324 609\n325 610\n326 611\n327 612\n328 613\n329 614\n330 615\n331 616\n332 617\n333 618\n334 619\n335 620\n336 621\n337 622\n338 623\n339 624\n340 625\n341 626\n342 627\n343 628\n344 629\n345 630\n346 631\n347 632\n348 633\n349 634\n350 635\n351 636\n352 637\n353 638\n354 639\n355 640\n356 641\n357 642\n358 643\n359 644\n360 645\n361 646\n362 647\n363 648\n364 649\n365 650\n366 651\n367 652\n368 653\n369 654\n370 655\n371 656\n372 657\n373 658\n374 659\n375 660\n376 661\n377 662\n378 663\n379 664\n380 665\n381 666\n382 667\n383 668\n384 669\n385 670\n386 671\n387 672\n388 673\n389 674\n390 675\n391 676\n392 677\n393 678\n394 679\n395 680\n396 681\n397 682\n398 683\n399 684\n400 685\n401 686\n402 687\n403 688\n404 689\n405 690\n406 691\n407 692\n408 693\n409 694\n410 695\n411 696\n412 697\n413 698\n414 699\n415 700\n416 701\n417 702\n418 703\n419 704\n420 705\n421 706\n422 707\n423 708\n424 709\n425 710\n426 711\n427 712\n428 713\n429 714\n430 715\n431 716\n432 717\n433 718\n434 719\n435 720\n436 721\n437 722\n438 723\n439 724\n440 725\n441 726\n442 727\n443 728\n444 729\n445 730\n446 731\n447 732\n448 733\n449 734\n450 735\n451 736\n452 737\n453 738\n454 739\n455 740\n456 741\n457 742\n458 743\n459 744\n460 745\n461 746\n462 747\n463 748\n464 749\n465 750\n466 751\n467 752\n468 753\n469 754\n470 755\n471 756\n472 757\n473 758\n474 759\n475 760\n476 761\n477 762\n478 763\n479 764\n480 765\n481 766\n482 767\n483 768\n484 769\n485 770\n486 771\n487 772\n488 773\n489 774\n490 775\n491 776\n492 777\n493 778\n494 779\n495 780\n496 781\n497 782\n498 783\n499 784\n500 785\n501 786\n502 787\n503 788\n504 789\n505 790\n506 791\n507 792\n508 793\n509 794\n510 795\n511 796\n512 797\n513 798\n514 799\n515 800\n516 801\n517 802\n518 803\n519 804\n520 805\n521 806\n522 807\n523 808\n524 809\n525 810\n526 811\n527 812\n528 813\n529 814\n530 815\n531 816\n532 817\n533 818\n534 819\n535 820\n536 821\n537 822\n538 823\n539 824\n540 825\n541 826\n542 827\n543 828\n544 829\n545 830\n546 831\n547 832\n548 833\n549 834\n550 835\n551 836\n552 837\n553 838\n554 839\n555 840\n556 841\n557 842\n558 843\n559 844\n560 845\n561 846\n562 847\n563 848\n564 849\n565 850\n566 851\n567 852\n568 853\n569 854\n570 855\n571 856\n572 857\n573 858\n574 859\n575 860\n576 861\n577 862\n578 863\n579 864\n580 865\n581 866\n582 867\n583 868\n584 869\n585 870\n586 871\n587 872\n588 873\n589 874\n590 875\n591 876\n592 877\n593 878\n594 879\n595 880\n596 881\n597 882\n598 883\n599 884\n600 885\n601 886\n602 887\n603 888\n604 889\n605 890\n606 891\n607 892\n608 893\n609 894\n610 895\n611 896\n612 897\n613 898\n614 899\n615 900\n616 901\n617 902\n618 903\n619 904\n620 905\n621 906\n622 907\n623 908\n624 909\n625 910\n626 911\n627 912\n628 913\n629 914\n630 915\n631 916\n632 917\n633 918\n634 919\n635 920\n636 921\n637 922\n638 923\n639 924\n640 925\n641 926\n642 927\n643 928\n644 929\n645 930\n646 931\n647 932\n648 933\n649 934\n650 935\n651 936\n652 937\n653 938\n654 939\n655 940\n656 941\n657 942\n658 943\n659 944\n660 945\n661 946\n662 947\n663 948\n664 949\n665 950\n666 951\n667 952\n668 953\n669 954\n670 955\n671 956\n672 957\n673 958\n674 959\n675 960\n676 961\n677 962\n678 963\n679 964\n680 965\n681 966\n682 967\n683 968\n684 969\n685 970\n686 971\n687 972\n688 973\n689 974\n690 975\n691 976\n692 977\n693 978\n694 979\n695 980\n696 981\n697 982\n698 983\n699 984\n700 985\n701 986\n702 987\n703 988\n704 989\n705 990\n706 991\n707 992\n708 993\n709 994\n710 995\n711 996\n712 997\n713 998\n714 999\n715 1000\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n2 510\n3 511\n4 512\n5 513\n6 514\n7 515\n8 516\n9 517\n10 518\n11 519\n12 520\n13 521\n14 522\n15 523\n16 524\n17 525\n18 526\n19 527\n20 528\n21 529\n22 530\n23 531\n24 532\n25 533\n26 534\n27 535\n28 536\n29 537\n30 538\n31 539\n32 540\n33 541\n34 542\n35 543\n36 544\n37 545\n38 546\n39 547\n40 548\n41 549\n42 550\n43 551\n44 552\n45 553\n46 554\n47 555\n48 556\n49 557\n50 558\n51 559\n52 560\n53 561\n54 562\n55 563\n56 564\n57 565\n58 566\n59 567\n60 568\n61 569\n62 570\n63 571\n64 572\n65 573\n66 574\n67 575\n68 576\n69 577\n70 578\n71 579\n72 580\n73 581\n74 582\n75 583\n76 584\n77 585\n78 586\n79 587\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n2 509\n3 510\n4 511\n5 512\n6 513\n7 514\n8 515\n9 516\n10 517\n11 518\n12 519\n13 520\n14 521\n15 522\n16 523\n17 524\n18 525\n19 526\n20 527\n21 528\n22 529\n23 530\n24 531\n25 532\n26 533\n27 534\n28 535\n29 536\n30 537\n31 538\n32 539\n33 540\n34 541\n35 542\n36 543\n37 544\n38 545\n39 546\n40 547\n41 548\n42 549\n43 550\n44 551\n45 552\n46 553\n47 554\n48 555\n49 556\n50 557\n51 558\n52 559\n53 560\n54 561\n55 562\n56 563\n57 564\n58 565\n59 566\n60 567\n61 568\n62 569\n63 570\n64 571\n65 572\n66 573\n67 574\n68 575\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n2 68\n3 69\n4 70\n5 71\n6 72\n7 73\n8 74\n9 75\n10 76\n11 77\n12 78\n13 79\n14 80\n15 81\n16 82\n17 83\n18 84\n19 85\n20 86\n21 87\n22 88\n23 89\n24 90\n25 91\n26 92\n27 93\n28 94\n29 95\n30 96\n31 97\n32 98\n33 99\n34 100\n",
"6\n1 2\n1 3\n1 4\n2 5\n3 6\n4 7\n5 8\n6 9\n7 10\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n1 581\n1 582\n1 583\n1 584\n1 585\n1 586\n1 587\n1 588\n1 589\n1 590\n1 591\n1 592\n1 593\n1 594\n1 595\n1 596\n1 597\n1 598\n1 599\n1 600\n1 601\n1 602\n1 603\n1 604\n1 605\n1 606\n1 607\n1 608\n1 609\n1 610\n1 611\n1 612\n1 613\n1 614\n1 615\n1 616\n1 617\n1 618\n1 619\n1 620\n1 621\n1 622\n1 623\n1 624\n1 625\n1 626\n1 627\n1 628\n1 629\n1 630\n1 631\n1 632\n1 633\n1 634\n1 635\n1 636\n1 637\n1 638\n1 639\n1 640\n1 641\n1 642\n1 643\n1 644\n1 645\n1 646\n1 647\n1 648\n1 649\n1 650\n1 651\n1 652\n1 653\n1 654\n1 655\n1 656\n1 657\n1 658\n1 659\n1 660\n1 661\n1 662\n1 663\n1 664\n1 665\n1 666\n1 667\n1 668\n1 669\n1 670\n1 671\n1 672\n1 673\n1 674\n1 675\n1 676\n1 677\n1 678\n1 679\n1 680\n1 681\n1 682\n1 683\n1 684\n1 685\n1 686\n1 687\n1 688\n1 689\n1 690\n1 691\n1 692\n1 693\n1 694\n1 695\n1 696\n1 697\n1 698\n1 699\n1 700\n1 701\n1 702\n1 703\n1 704\n1 705\n1 706\n1 707\n1 708\n1 709\n1 710\n1 711\n1 712\n1 713\n1 714\n1 715\n1 716\n1 717\n1 718\n1 719\n1 720\n1 721\n1 722\n1 723\n1 724\n1 725\n1 726\n1 727\n1 728\n1 729\n1 730\n1 731\n1 732\n1 733\n1 734\n1 735\n1 736\n1 737\n1 738\n1 739\n1 740\n1 741\n1 742\n1 743\n1 744\n1 745\n1 746\n1 747\n1 748\n1 749\n1 750\n1 751\n1 752\n1 753\n1 754\n1 755\n1 756\n1 757\n1 758\n1 759\n1 760\n1 761\n1 762\n1 763\n1 764\n1 765\n1 766\n1 767\n1 768\n1 769\n1 770\n1 771\n1 772\n1 773\n1 774\n1 775\n1 776\n1 777\n1 778\n1 779\n1 780\n1 781\n1 782\n1 783\n1 784\n1 785\n1 786\n1 787\n1 788\n1 789\n1 790\n1 791\n1 792\n1 793\n1 794\n1 795\n1 796\n1 797\n1 798\n1 799\n1 800\n1 801\n1 802\n1 803\n1 804\n1 805\n1 806\n1 807\n1 808\n1 809\n1 810\n1 811\n1 812\n1 813\n1 814\n1 815\n1 816\n1 817\n1 818\n1 819\n1 820\n1 821\n1 822\n1 823\n1 824\n1 825\n1 826\n1 827\n1 828\n1 829\n1 830\n1 831\n1 832\n1 833\n1 834\n1 835\n1 836\n1 837\n1 838\n1 839\n1 840\n1 841\n1 842\n1 843\n1 844\n1 845\n1 846\n1 847\n1 848\n1 849\n1 850\n1 851\n1 852\n1 853\n1 854\n1 855\n1 856\n1 857\n1 858\n1 859\n1 860\n1 861\n1 862\n1 863\n1 864\n1 865\n1 866\n1 867\n1 868\n1 869\n1 870\n1 871\n1 872\n1 873\n1 874\n1 875\n1 876\n1 877\n1 878\n1 879\n1 880\n1 881\n1 882\n1 883\n1 884\n1 885\n1 886\n1 887\n1 888\n1 889\n1 890\n1 891\n1 892\n1 893\n1 894\n1 895\n1 896\n1 897\n1 898\n1 899\n1 900\n1 901\n1 902\n1 903\n1 904\n1 905\n1 906\n1 907\n1 908\n1 909\n1 910\n1 911\n1 912\n1 913\n1 914\n1 915\n1 916\n1 917\n1 918\n1 919\n1 920\n1 921\n1 922\n1 923\n1 924\n1 925\n1 926\n1 927\n1 928\n1 929\n1 930\n1 931\n1 932\n1 933\n1 934\n1 935\n1 936\n1 937\n1 938\n1 939\n1 940\n1 941\n1 942\n1 943\n1 944\n1 945\n1 946\n1 947\n1 948\n1 949\n1 950\n1 951\n1 952\n1 953\n1 954\n1 955\n1 956\n1 957\n1 958\n1 959\n1 960\n1 961\n1 962\n1 963\n1 964\n1 965\n1 966\n1 967\n1 968\n1 969\n1 970\n1 971\n1 972\n1 973\n1 974\n1 975\n1 976\n1 977\n1 978\n1 979\n1 980\n1 981\n1 982\n1 983\n1 984\n1 985\n1 986\n1 987\n1 988\n1 989\n1 990\n1 991\n1 992\n1 993\n1 994\n1 995\n1 996\n1 997\n1 998\n1 999\n1 1000\n1 1001\n1 1002\n1 1003\n1 1004\n1 1005\n1 1006\n1 1007\n1 1008\n1 1009\n1 1010\n1 1011\n1 1012\n1 1013\n2 1014\n3 1015\n4 1016\n5 1017\n6 1018\n7 1019\n8 1020\n9 1021\n10 1022\n11 1023\n12 1024\n13 1025\n14 1026\n15 1027\n16 1028\n17 1029\n18 1030\n19 1031\n20 1032\n21 1033\n22 1034\n23 1035\n24 1036\n25 1037\n26 1038\n27 1039\n28 1040\n29 1041\n30 1042\n31 1043\n32 1044\n33 1045\n34 1046\n35 1047\n36 1048\n37 1049\n38 1050\n39 1051\n40 1052\n41 1053\n42 1054\n43 1055\n44 1056\n45 1057\n46 1058\n47 1059\n48 1060\n49 1061\n50 1062\n51 1063\n52 1064\n53 1065\n54 1066\n55 1067\n56 1068\n57 1069\n58 1070\n59 1071\n60 1072\n61 1073\n62 1074\n63 1075\n64 1076\n65 1077\n66 1078\n67 1079\n68 1080\n69 1081\n70 1082\n71 1083\n72 1084\n73 1085\n74 1086\n75 1087\n76 1088\n77 1089\n78 1090\n79 1091\n80 1092\n81 1093\n82 1094\n83 1095\n84 1096\n85 1097\n86 1098\n87 1099\n88 1100\n89 1101\n90 1102\n91 1103\n92 1104\n93 1105\n94 1106\n95 1107\n96 1108\n97 1109\n98 1110\n99 1111\n100 1112\n101 1113\n102 1114\n103 1115\n104 1116\n105 1117\n106 1118\n107 1119\n108 1120\n109 1121\n110 1122\n111 1123\n112 1124\n113 1125\n114 1126\n115 1127\n116 1128\n117 1129\n118 1130\n119 1131\n120 1132\n121 1133\n122 1134\n123 1135\n124 1136\n125 1137\n126 1138\n127 1139\n128 1140\n129 1141\n130 1142\n131 1143\n132 1144\n133 1145\n134 1146\n135 1147\n136 1148\n137 1149\n138 1150\n139 1151\n140 1152\n141 1153\n142 1154\n143 1155\n144 1156\n145 1157\n146 1158\n147 1159\n148 1160\n149 1161\n150 1162\n151 1163\n152 1164\n153 1165\n154 1166\n155 1167\n156 1168\n157 1169\n158 1170\n159 1171\n160 1172\n161 1173\n162 1174\n163 1175\n164 1176\n165 1177\n166 1178\n167 1179\n168 1180\n169 1181\n170 1182\n171 1183\n172 1184\n173 1185\n174 1186\n175 1187\n176 1188\n177 1189\n178 1190\n179 1191\n180 1192\n181 1193\n182 1194\n183 1195\n184 1196\n185 1197\n186 1198\n187 1199\n188 1200\n189 1201\n190 1202\n191 1203\n192 1204\n193 1205\n194 1206\n195 1207\n196 1208\n197 1209\n198 1210\n199 1211\n200 1212\n201 1213\n202 1214\n203 1215\n204 1216\n205 1217\n206 1218\n207 1219\n208 1220\n209 1221\n210 1222\n211 1223\n212 1224\n213 1225\n214 1226\n215 1227\n216 1228\n217 1229\n218 1230\n219 1231\n220 1232\n221 1233\n222 1234\n",
"44\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n6 11\n7 12\n8 13\n9 14\n10 15\n11 16\n12 17\n13 18\n14 19\n15 20\n16 21\n17 22\n18 23\n19 24\n20 25\n21 26\n22 27\n23 28\n24 29\n25 30\n26 31\n27 32\n28 33\n29 34\n30 35\n31 36\n32 37\n33 38\n34 39\n35 40\n36 41\n37 42\n38 43\n39 44\n40 45\n41 46\n42 47\n43 48\n44 49\n45 50\n46 51\n47 52\n48 53\n49 54\n50 55\n51 56\n52 57\n53 58\n54 59\n55 60\n56 61\n57 62\n58 63\n59 64\n60 65\n61 66\n62 67\n63 68\n64 69\n65 70\n66 71\n67 72\n68 73\n69 74\n70 75\n71 76\n72 77\n73 78\n74 79\n75 80\n76 81\n77 82\n78 83\n79 84\n80 85\n81 86\n82 87\n83 88\n84 89\n85 90\n86 91\n87 92\n88 93\n89 94\n90 95\n91 96\n92 97\n93 98\n94 99\n95 100\n96 101\n97 102\n98 103\n99 104\n100 105\n101 106\n102 107\n103 108\n104 109\n105 110\n",
"10\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n2 247\n3 248\n4 249\n5 250\n6 251\n7 252\n8 253\n9 254\n10 255\n11 256\n12 257\n13 258\n14 259\n15 260\n16 261\n17 262\n18 263\n19 264\n20 265\n21 266\n22 267\n23 268\n24 269\n25 270\n26 271\n27 272\n28 273\n29 274\n30 275\n31 276\n32 277\n33 278\n34 279\n35 280\n36 281\n37 282\n38 283\n39 284\n40 285\n41 286\n42 287\n43 288\n44 289\n45 290\n46 291\n47 292\n48 293\n49 294\n50 295\n51 296\n52 297\n53 298\n54 299\n55 300\n56 301\n57 302\n58 303\n59 304\n60 305\n61 306\n62 307\n63 308\n64 309\n65 310\n66 311\n67 312\n68 313\n69 314\n70 315\n71 316\n72 317\n73 318\n74 319\n75 320\n76 321\n77 322\n78 323\n79 324\n80 325\n81 326\n82 327\n83 328\n84 329\n85 330\n86 331\n87 332\n88 333\n89 334\n90 335\n91 336\n92 337\n93 338\n94 339\n95 340\n96 341\n97 342\n98 343\n99 344\n100 345\n101 346\n102 347\n103 348\n104 349\n105 350\n106 351\n107 352\n108 353\n109 354\n110 355\n111 356\n112 357\n113 358\n114 359\n115 360\n116 361\n117 362\n118 363\n119 364\n120 365\n121 366\n122 367\n123 368\n124 369\n125 370\n126 371\n127 372\n128 373\n129 374\n130 375\n131 376\n132 377\n133 378\n134 379\n135 380\n136 381\n137 382\n138 383\n139 384\n140 385\n141 386\n142 387\n143 388\n144 389\n145 390\n146 391\n147 392\n148 393\n149 394\n150 395\n151 396\n152 397\n153 398\n154 399\n155 400\n156 401\n157 402\n158 403\n159 404\n160 405\n161 406\n162 407\n163 408\n164 409\n165 410\n166 411\n167 412\n168 413\n169 414\n170 415\n171 416\n172 417\n173 418\n174 419\n175 420\n176 421\n177 422\n178 423\n179 424\n180 425\n181 426\n182 427\n183 428\n184 429\n185 430\n186 431\n187 432\n188 433\n189 434\n190 435\n191 436\n192 437\n193 438\n194 439\n195 440\n196 441\n197 442\n198 443\n199 444\n200 445\n201 446\n202 447\n203 448\n204 449\n205 450\n206 451\n207 452\n208 453\n209 454\n210 455\n211 456\n212 457\n213 458\n214 459\n215 460\n216 461\n217 462\n218 463\n219 464\n220 465\n221 466\n222 467\n223 468\n224 469\n225 470\n226 471\n227 472\n228 473\n229 474\n230 475\n231 476\n232 477\n233 478\n234 479\n235 480\n236 481\n237 482\n238 483\n239 484\n240 485\n241 486\n242 487\n243 488\n244 489\n245 490\n246 491\n247 492\n248 493\n249 494\n250 495\n251 496\n252 497\n253 498\n254 499\n255 500\n256 501\n257 502\n258 503\n259 504\n260 505\n261 506\n262 507\n263 508\n264 509\n265 510\n266 511\n267 512\n268 513\n269 514\n270 515\n271 516\n272 517\n273 518\n274 519\n275 520\n276 521\n277 522\n278 523\n279 524\n280 525\n281 526\n282 527\n283 528\n284 529\n285 530\n286 531\n287 532\n288 533\n289 534\n290 535\n291 536\n292 537\n293 538\n294 539\n295 540\n296 541\n297 542\n298 543\n299 544\n300 545\n301 546\n302 547\n303 548\n304 549\n305 550\n306 551\n307 552\n308 553\n309 554\n310 555\n311 556\n312 557\n313 558\n314 559\n315 560\n316 561\n317 562\n318 563\n319 564\n320 565\n321 566\n322 567\n323 568\n324 569\n325 570\n326 571\n327 572\n328 573\n329 574\n330 575\n331 576\n332 577\n333 578\n334 579\n335 580\n336 581\n337 582\n338 583\n339 584\n340 585\n341 586\n342 587\n343 588\n344 589\n345 590\n346 591\n347 592\n348 593\n349 594\n350 595\n351 596\n352 597\n353 598\n354 599\n355 600\n356 601\n357 602\n358 603\n359 604\n360 605\n361 606\n362 607\n363 608\n364 609\n365 610\n366 611\n367 612\n368 613\n369 614\n370 615\n371 616\n372 617\n373 618\n374 619\n375 620\n376 621\n377 622\n378 623\n379 624\n380 625\n381 626\n382 627\n383 628\n384 629\n385 630\n386 631\n387 632\n388 633\n389 634\n390 635\n391 636\n392 637\n393 638\n394 639\n395 640\n396 641\n397 642\n398 643\n399 644\n400 645\n401 646\n402 647\n403 648\n404 649\n405 650\n406 651\n407 652\n408 653\n409 654\n410 655\n411 656\n412 657\n413 658\n414 659\n415 660\n416 661\n417 662\n418 663\n419 664\n420 665\n421 666\n422 667\n423 668\n424 669\n425 670\n426 671\n427 672\n428 673\n429 674\n430 675\n431 676\n432 677\n433 678\n434 679\n435 680\n436 681\n437 682\n438 683\n439 684\n440 685\n441 686\n442 687\n443 688\n444 689\n445 690\n446 691\n447 692\n448 693\n449 694\n450 695\n451 696\n452 697\n453 698\n454 699\n455 700\n456 701\n457 702\n458 703\n459 704\n460 705\n461 706\n462 707\n463 708\n464 709\n465 710\n466 711\n467 712\n468 713\n469 714\n470 715\n471 716\n472 717\n473 718\n474 719\n475 720\n476 721\n477 722\n478 723\n479 724\n480 725\n481 726\n482 727\n483 728\n484 729\n485 730\n486 731\n487 732\n488 733\n489 734\n490 735\n491 736\n492 737\n493 738\n494 739\n495 740\n496 741\n497 742\n498 743\n499 744\n500 745\n501 746\n502 747\n503 748\n504 749\n505 750\n506 751\n507 752\n508 753\n509 754\n510 755\n511 756\n512 757\n513 758\n514 759\n515 760\n516 761\n517 762\n518 763\n519 764\n520 765\n521 766\n522 767\n523 768\n524 769\n525 770\n526 771\n527 772\n528 773\n529 774\n530 775\n531 776\n532 777\n533 778\n534 779\n535 780\n536 781\n537 782\n538 783\n539 784\n540 785\n541 786\n542 787\n543 788\n544 789\n545 790\n546 791\n547 792\n548 793\n549 794\n550 795\n551 796\n552 797\n553 798\n554 799\n555 800\n556 801\n557 802\n558 803\n559 804\n560 805\n561 806\n562 807\n563 808\n564 809\n565 810\n566 811\n567 812\n568 813\n569 814\n570 815\n571 816\n572 817\n573 818\n574 819\n575 820\n576 821\n577 822\n578 823\n579 824\n580 825\n581 826\n582 827\n583 828\n584 829\n585 830\n586 831\n587 832\n588 833\n589 834\n590 835\n591 836\n592 837\n593 838\n594 839\n595 840\n596 841\n597 842\n598 843\n599 844\n600 845\n601 846\n602 847\n603 848\n604 849\n605 850\n606 851\n607 852\n608 853\n609 854\n610 855\n611 856\n612 857\n613 858\n614 859\n615 860\n616 861\n617 862\n618 863\n619 864\n620 865\n621 866\n622 867\n623 868\n624 869\n625 870\n626 871\n627 872\n628 873\n629 874\n630 875\n631 876\n632 877\n633 878\n634 879\n635 880\n636 881\n637 882\n638 883\n639 884\n640 885\n641 886\n642 887\n643 888\n644 889\n645 890\n646 891\n647 892\n648 893\n649 894\n650 895\n651 896\n652 897\n653 898\n654 899\n655 900\n656 901\n657 902\n658 903\n659 904\n660 905\n661 906\n662 907\n663 908\n664 909\n665 910\n666 911\n667 912\n668 913\n669 914\n670 915\n671 916\n672 917\n673 918\n674 919\n675 920\n676 921\n677 922\n678 923\n679 924\n680 925\n681 926\n682 927\n683 928\n684 929\n685 930\n686 931\n687 932\n688 933\n689 934\n690 935\n691 936\n692 937\n693 938\n694 939\n695 940\n696 941\n697 942\n698 943\n699 944\n700 945\n701 946\n702 947\n703 948\n704 949\n705 950\n706 951\n707 952\n708 953\n709 954\n710 955\n711 956\n712 957\n713 958\n714 959\n715 960\n716 961\n717 962\n718 963\n719 964\n720 965\n721 966\n722 967\n723 968\n724 969\n725 970\n726 971\n727 972\n728 973\n729 974\n730 975\n731 976\n732 977\n733 978\n734 979\n735 980\n736 981\n737 982\n738 983\n739 984\n740 985\n741 986\n742 987\n743 988\n744 989\n745 990\n746 991\n747 992\n748 993\n749 994\n750 995\n751 996\n752 997\n753 998\n754 999\n755 1000\n756 1001\n757 1002\n758 1003\n759 1004\n760 1005\n761 1006\n762 1007\n763 1008\n764 1009\n765 1010\n766 1011\n767 1012\n768 1013\n769 1014\n770 1015\n771 1016\n772 1017\n773 1018\n774 1019\n775 1020\n776 1021\n777 1022\n778 1023\n779 1024\n780 1025\n781 1026\n782 1027\n783 1028\n784 1029\n785 1030\n786 1031\n787 1032\n788 1033\n789 1034\n790 1035\n791 1036\n792 1037\n793 1038\n794 1039\n795 1040\n796 1041\n797 1042\n798 1043\n799 1044\n800 1045\n801 1046\n802 1047\n803 1048\n804 1049\n805 1050\n806 1051\n807 1052\n808 1053\n809 1054\n810 1055\n811 1056\n812 1057\n813 1058\n814 1059\n815 1060\n816 1061\n817 1062\n818 1063\n819 1064\n820 1065\n821 1066\n822 1067\n823 1068\n824 1069\n825 1070\n826 1071\n827 1072\n828 1073\n829 1074\n830 1075\n831 1076\n832 1077\n833 1078\n834 1079\n835 1080\n836 1081\n837 1082\n838 1083\n839 1084\n840 1085\n841 1086\n842 1087\n843 1088\n844 1089\n845 1090\n846 1091\n847 1092\n848 1093\n849 1094\n850 1095\n851 1096\n852 1097\n853 1098\n854 1099\n855 1100\n",
"1130\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n554 556\n555 557\n556 558\n557 559\n558 560\n559 561\n560 562\n561 563\n562 564\n563 565\n564 566\n565 567\n566 568\n567 569\n568 570\n569 571\n570 572\n571 573\n572 574\n573 575\n574 576\n575 577\n576 578\n577 579\n578 580\n579 581\n580 582\n581 583\n582 584\n583 585\n584 586\n585 587\n586 588\n587 589\n588 590\n589 591\n590 592\n591 593\n592 594\n593 595\n594 596\n595 597\n596 598\n597 599\n598 600\n599 601\n600 602\n601 603\n602 604\n603 605\n604 606\n605 607\n606 608\n607 609\n608 610\n609 611\n610 612\n611 613\n612 614\n613 615\n614 616\n615 617\n616 618\n617 619\n618 620\n619 621\n620 622\n621 623\n622 624\n623 625\n624 626\n625 627\n626 628\n627 629\n628 630\n629 631\n630 632\n631 633\n632 634\n633 635\n634 636\n635 637\n636 638\n637 639\n638 640\n639 641\n640 642\n641 643\n642 644\n643 645\n644 646\n645 647\n646 648\n647 649\n648 650\n649 651\n650 652\n651 653\n652 654\n653 655\n654 656\n655 657\n656 658\n657 659\n658 660\n659 661\n660 662\n661 663\n662 664\n663 665\n664 666\n665 667\n666 668\n667 669\n668 670\n669 671\n670 672\n671 673\n672 674\n673 675\n674 676\n675 677\n676 678\n677 679\n678 680\n679 681\n680 682\n681 683\n682 684\n683 685\n684 686\n685 687\n686 688\n687 689\n688 690\n689 691\n690 692\n691 693\n692 694\n693 695\n694 696\n695 697\n696 698\n697 699\n698 700\n699 701\n700 702\n701 703\n702 704\n703 705\n704 706\n705 707\n706 708\n707 709\n708 710\n709 711\n710 712\n711 713\n712 714\n713 715\n714 716\n715 717\n716 718\n717 719\n718 720\n719 721\n720 722\n721 723\n722 724\n723 725\n724 726\n725 727\n726 728\n727 729\n728 730\n729 731\n730 732\n731 733\n732 734\n733 735\n734 736\n735 737\n736 738\n737 739\n738 740\n739 741\n740 742\n741 743\n742 744\n743 745\n744 746\n745 747\n746 748\n747 749\n748 750\n749 751\n750 752\n751 753\n752 754\n753 755\n754 756\n755 757\n756 758\n757 759\n758 760\n759 761\n760 762\n761 763\n762 764\n763 765\n764 766\n765 767\n766 768\n767 769\n768 770\n769 771\n770 772\n771 773\n772 774\n773 775\n774 776\n775 777\n776 778\n777 779\n778 780\n779 781\n780 782\n781 783\n782 784\n783 785\n784 786\n785 787\n786 788\n787 789\n788 790\n789 791\n790 792\n791 793\n792 794\n793 795\n794 796\n795 797\n796 798\n797 799\n798 800\n799 801\n800 802\n801 803\n802 804\n803 805\n804 806\n805 807\n806 808\n807 809\n808 810\n809 811\n810 812\n811 813\n812 814\n813 815\n814 816\n815 817\n816 818\n817 819\n818 820\n819 821\n820 822\n821 823\n822 824\n823 825\n824 826\n825 827\n826 828\n827 829\n828 830\n829 831\n830 832\n831 833\n832 834\n833 835\n834 836\n835 837\n836 838\n837 839\n838 840\n839 841\n840 842\n841 843\n842 844\n843 845\n844 846\n845 847\n846 848\n847 849\n848 850\n849 851\n850 852\n851 853\n852 854\n853 855\n854 856\n855 857\n856 858\n857 859\n858 860\n859 861\n860 862\n861 863\n862 864\n863 865\n864 866\n865 867\n866 868\n867 869\n868 870\n869 871\n870 872\n871 873\n872 874\n873 875\n874 876\n875 877\n876 878\n877 879\n878 880\n879 881\n880 882\n881 883\n882 884\n883 885\n884 886\n885 887\n886 888\n887 889\n888 890\n889 891\n890 892\n891 893\n892 894\n893 895\n894 896\n895 897\n896 898\n897 899\n898 900\n899 901\n900 902\n901 903\n902 904\n903 905\n904 906\n905 907\n906 908\n907 909\n908 910\n909 911\n910 912\n911 913\n912 914\n913 915\n914 916\n915 917\n916 918\n917 919\n918 920\n919 921\n920 922\n921 923\n922 924\n923 925\n924 926\n925 927\n926 928\n927 929\n928 930\n929 931\n930 932\n931 933\n932 934\n933 935\n934 936\n935 937\n936 938\n937 939\n938 940\n939 941\n940 942\n941 943\n942 944\n943 945\n944 946\n945 947\n946 948\n947 949\n948 950\n949 951\n950 952\n951 953\n952 954\n953 955\n954 956\n955 957\n956 958\n957 959\n958 960\n959 961\n960 962\n961 963\n962 964\n963 965\n964 966\n965 967\n966 968\n967 969\n968 970\n969 971\n970 972\n971 973\n972 974\n973 975\n974 976\n975 977\n976 978\n977 979\n978 980\n979 981\n980 982\n981 983\n982 984\n983 985\n984 986\n985 987\n986 988\n987 989\n988 990\n989 991\n990 992\n991 993\n992 994\n993 995\n994 996\n995 997\n996 998\n997 999\n998 1000\n999 1001\n1000 1002\n1001 1003\n1002 1004\n1003 1005\n1004 1006\n1005 1007\n1006 1008\n1007 1009\n1008 1010\n1009 1011\n1010 1012\n1011 1013\n1012 1014\n1013 1015\n1014 1016\n1015 1017\n1016 1018\n1017 1019\n1018 1020\n1019 1021\n1020 1022\n1021 1023\n1022 1024\n1023 1025\n1024 1026\n1025 1027\n1026 1028\n1027 1029\n1028 1030\n1029 1031\n1030 1032\n1031 1033\n1032 1034\n1033 1035\n1034 1036\n1035 1037\n1036 1038\n1037 1039\n1038 1040\n1039 1041\n1040 1042\n1041 1043\n1042 1044\n1043 1045\n1044 1046\n1045 1047\n1046 1048\n1047 1049\n1048 1050\n1049 1051\n1050 1052\n1051 1053\n1052 1054\n1053 1055\n1054 1056\n1055 1057\n1056 1058\n1057 1059\n1058 1060\n1059 1061\n1060 1062\n1061 1063\n1062 1064\n1063 1065\n1064 1066\n1065 1067\n1066 1068\n1067 1069\n1068 1070\n1069 1071\n1070 1072\n1071 1073\n1072 1074\n1073 1075\n1074 1076\n1075 1077\n1076 1078\n1077 1079\n1078 1080\n1079 1081\n1080 1082\n1081 1083\n1082 1084\n1083 1085\n1084 1086\n1085 1087\n1086 1088\n1087 1089\n1088 1090\n1089 1091\n1090 1092\n1091 1093\n1092 1094\n1093 1095\n1094 1096\n1095 1097\n1096 1098\n1097 1099\n1098 1100\n1099 1101\n1100 1102\n1101 1103\n1102 1104\n1103 1105\n1104 1106\n1105 1107\n1106 1108\n1107 1109\n1108 1110\n1109 1111\n1110 1112\n1111 1113\n1112 1114\n1113 1115\n1114 1116\n1115 1117\n1116 1118\n1117 1119\n1118 1120\n1119 1121\n1120 1122\n1121 1123\n1122 1124\n1123 1125\n1124 1126\n1125 1127\n1126 1128\n1127 1129\n1128 1130\n1129 1131\n",
"100\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n",
"5\n1 2\n1 3\n1 4\n2 5\n3 6\n4 7\n5 8\n",
"597\n1 2\n1 3\n2 4\n3 5\n4 6\n5 7\n6 8\n7 9\n8 10\n9 11\n10 12\n11 13\n12 14\n13 15\n14 16\n15 17\n16 18\n17 19\n18 20\n19 21\n20 22\n21 23\n22 24\n23 25\n24 26\n25 27\n26 28\n27 29\n28 30\n29 31\n30 32\n31 33\n32 34\n33 35\n34 36\n35 37\n36 38\n37 39\n38 40\n39 41\n40 42\n41 43\n42 44\n43 45\n44 46\n45 47\n46 48\n47 49\n48 50\n49 51\n50 52\n51 53\n52 54\n53 55\n54 56\n55 57\n56 58\n57 59\n58 60\n59 61\n60 62\n61 63\n62 64\n63 65\n64 66\n65 67\n66 68\n67 69\n68 70\n69 71\n70 72\n71 73\n72 74\n73 75\n74 76\n75 77\n76 78\n77 79\n78 80\n79 81\n80 82\n81 83\n82 84\n83 85\n84 86\n85 87\n86 88\n87 89\n88 90\n89 91\n90 92\n91 93\n92 94\n93 95\n94 96\n95 97\n96 98\n97 99\n98 100\n99 101\n100 102\n101 103\n102 104\n103 105\n104 106\n105 107\n106 108\n107 109\n108 110\n109 111\n110 112\n111 113\n112 114\n113 115\n114 116\n115 117\n116 118\n117 119\n118 120\n119 121\n120 122\n121 123\n122 124\n123 125\n124 126\n125 127\n126 128\n127 129\n128 130\n129 131\n130 132\n131 133\n132 134\n133 135\n134 136\n135 137\n136 138\n137 139\n138 140\n139 141\n140 142\n141 143\n142 144\n143 145\n144 146\n145 147\n146 148\n147 149\n148 150\n149 151\n150 152\n151 153\n152 154\n153 155\n154 156\n155 157\n156 158\n157 159\n158 160\n159 161\n160 162\n161 163\n162 164\n163 165\n164 166\n165 167\n166 168\n167 169\n168 170\n169 171\n170 172\n171 173\n172 174\n173 175\n174 176\n175 177\n176 178\n177 179\n178 180\n179 181\n180 182\n181 183\n182 184\n183 185\n184 186\n185 187\n186 188\n187 189\n188 190\n189 191\n190 192\n191 193\n192 194\n193 195\n194 196\n195 197\n196 198\n197 199\n198 200\n199 201\n200 202\n201 203\n202 204\n203 205\n204 206\n205 207\n206 208\n207 209\n208 210\n209 211\n210 212\n211 213\n212 214\n213 215\n214 216\n215 217\n216 218\n217 219\n218 220\n219 221\n220 222\n221 223\n222 224\n223 225\n224 226\n225 227\n226 228\n227 229\n228 230\n229 231\n230 232\n231 233\n232 234\n233 235\n234 236\n235 237\n236 238\n237 239\n238 240\n239 241\n240 242\n241 243\n242 244\n243 245\n244 246\n245 247\n246 248\n247 249\n248 250\n249 251\n250 252\n251 253\n252 254\n253 255\n254 256\n255 257\n256 258\n257 259\n258 260\n259 261\n260 262\n261 263\n262 264\n263 265\n264 266\n265 267\n266 268\n267 269\n268 270\n269 271\n270 272\n271 273\n272 274\n273 275\n274 276\n275 277\n276 278\n277 279\n278 280\n279 281\n280 282\n281 283\n282 284\n283 285\n284 286\n285 287\n286 288\n287 289\n288 290\n289 291\n290 292\n291 293\n292 294\n293 295\n294 296\n295 297\n296 298\n297 299\n298 300\n299 301\n300 302\n301 303\n302 304\n303 305\n304 306\n305 307\n306 308\n307 309\n308 310\n309 311\n310 312\n311 313\n312 314\n313 315\n314 316\n315 317\n316 318\n317 319\n318 320\n319 321\n320 322\n321 323\n322 324\n323 325\n324 326\n325 327\n326 328\n327 329\n328 330\n329 331\n330 332\n331 333\n332 334\n333 335\n334 336\n335 337\n336 338\n337 339\n338 340\n339 341\n340 342\n341 343\n342 344\n343 345\n344 346\n345 347\n346 348\n347 349\n348 350\n349 351\n350 352\n351 353\n352 354\n353 355\n354 356\n355 357\n356 358\n357 359\n358 360\n359 361\n360 362\n361 363\n362 364\n363 365\n364 366\n365 367\n366 368\n367 369\n368 370\n369 371\n370 372\n371 373\n372 374\n373 375\n374 376\n375 377\n376 378\n377 379\n378 380\n379 381\n380 382\n381 383\n382 384\n383 385\n384 386\n385 387\n386 388\n387 389\n388 390\n389 391\n390 392\n391 393\n392 394\n393 395\n394 396\n395 397\n396 398\n397 399\n398 400\n399 401\n400 402\n401 403\n402 404\n403 405\n404 406\n405 407\n406 408\n407 409\n408 410\n409 411\n410 412\n411 413\n412 414\n413 415\n414 416\n415 417\n416 418\n417 419\n418 420\n419 421\n420 422\n421 423\n422 424\n423 425\n424 426\n425 427\n426 428\n427 429\n428 430\n429 431\n430 432\n431 433\n432 434\n433 435\n434 436\n435 437\n436 438\n437 439\n438 440\n439 441\n440 442\n441 443\n442 444\n443 445\n444 446\n445 447\n446 448\n447 449\n448 450\n449 451\n450 452\n451 453\n452 454\n453 455\n454 456\n455 457\n456 458\n457 459\n458 460\n459 461\n460 462\n461 463\n462 464\n463 465\n464 466\n465 467\n466 468\n467 469\n468 470\n469 471\n470 472\n471 473\n472 474\n473 475\n474 476\n475 477\n476 478\n477 479\n478 480\n479 481\n480 482\n481 483\n482 484\n483 485\n484 486\n485 487\n486 488\n487 489\n488 490\n489 491\n490 492\n491 493\n492 494\n493 495\n494 496\n495 497\n496 498\n497 499\n498 500\n499 501\n500 502\n501 503\n502 504\n503 505\n504 506\n505 507\n506 508\n507 509\n508 510\n509 511\n510 512\n511 513\n512 514\n513 515\n514 516\n515 517\n516 518\n517 519\n518 520\n519 521\n520 522\n521 523\n522 524\n523 525\n524 526\n525 527\n526 528\n527 529\n528 530\n529 531\n530 532\n531 533\n532 534\n533 535\n534 536\n535 537\n536 538\n537 539\n538 540\n539 541\n540 542\n541 543\n542 544\n543 545\n544 546\n545 547\n546 548\n547 549\n548 550\n549 551\n550 552\n551 553\n552 554\n553 555\n554 556\n555 557\n556 558\n557 559\n558 560\n559 561\n560 562\n561 563\n562 564\n563 565\n564 566\n565 567\n566 568\n567 569\n568 570\n569 571\n570 572\n571 573\n572 574\n573 575\n574 576\n575 577\n576 578\n577 579\n578 580\n579 581\n580 582\n581 583\n582 584\n583 585\n584 586\n585 587\n586 588\n587 589\n588 590\n589 591\n590 592\n591 593\n592 594\n593 595\n594 596\n595 597\n596 598\n",
"182\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n2 13\n3 14\n4 15\n5 16\n6 17\n7 18\n8 19\n9 20\n10 21\n11 22\n12 23\n13 24\n14 25\n15 26\n16 27\n17 28\n18 29\n19 30\n20 31\n21 32\n22 33\n23 34\n24 35\n25 36\n26 37\n27 38\n28 39\n29 40\n30 41\n31 42\n32 43\n33 44\n34 45\n35 46\n36 47\n37 48\n38 49\n39 50\n40 51\n41 52\n42 53\n43 54\n44 55\n45 56\n46 57\n47 58\n48 59\n49 60\n50 61\n51 62\n52 63\n53 64\n54 65\n55 66\n56 67\n57 68\n58 69\n59 70\n60 71\n61 72\n62 73\n63 74\n64 75\n65 76\n66 77\n67 78\n68 79\n69 80\n70 81\n71 82\n72 83\n73 84\n74 85\n75 86\n76 87\n77 88\n78 89\n79 90\n80 91\n81 92\n82 93\n83 94\n84 95\n85 96\n86 97\n87 98\n88 99\n89 100\n90 101\n91 102\n92 103\n93 104\n94 105\n95 106\n96 107\n97 108\n98 109\n99 110\n100 111\n101 112\n102 113\n103 114\n104 115\n105 116\n106 117\n107 118\n108 119\n109 120\n110 121\n111 122\n112 123\n113 124\n114 125\n115 126\n116 127\n117 128\n118 129\n119 130\n120 131\n121 132\n122 133\n123 134\n124 135\n125 136\n126 137\n127 138\n128 139\n129 140\n130 141\n131 142\n132 143\n133 144\n134 145\n135 146\n136 147\n137 148\n138 149\n139 150\n140 151\n141 152\n142 153\n143 154\n144 155\n145 156\n146 157\n147 158\n148 159\n149 160\n150 161\n151 162\n152 163\n153 164\n154 165\n155 166\n156 167\n157 168\n158 169\n159 170\n160 171\n161 172\n162 173\n163 174\n164 175\n165 176\n166 177\n167 178\n168 179\n169 180\n170 181\n171 182\n172 183\n173 184\n174 185\n175 186\n176 187\n177 188\n178 189\n179 190\n180 191\n181 192\n182 193\n183 194\n184 195\n185 196\n186 197\n187 198\n188 199\n189 200\n190 201\n191 202\n192 203\n193 204\n194 205\n195 206\n196 207\n197 208\n198 209\n199 210\n200 211\n201 212\n202 213\n203 214\n204 215\n205 216\n206 217\n207 218\n208 219\n209 220\n210 221\n211 222\n212 223\n213 224\n214 225\n215 226\n216 227\n217 228\n218 229\n219 230\n220 231\n221 232\n222 233\n223 234\n224 235\n225 236\n226 237\n227 238\n228 239\n229 240\n230 241\n231 242\n232 243\n233 244\n234 245\n235 246\n236 247\n237 248\n238 249\n239 250\n240 251\n241 252\n242 253\n243 254\n244 255\n245 256\n246 257\n247 258\n248 259\n249 260\n250 261\n251 262\n252 263\n253 264\n254 265\n255 266\n256 267\n257 268\n258 269\n259 270\n260 271\n261 272\n262 273\n263 274\n264 275\n265 276\n266 277\n267 278\n268 279\n269 280\n270 281\n271 282\n272 283\n273 284\n274 285\n275 286\n276 287\n277 288\n278 289\n279 290\n280 291\n281 292\n282 293\n283 294\n284 295\n285 296\n286 297\n287 298\n288 299\n289 300\n290 301\n291 302\n292 303\n293 304\n294 305\n295 306\n296 307\n297 308\n298 309\n299 310\n300 311\n301 312\n302 313\n303 314\n304 315\n305 316\n306 317\n307 318\n308 319\n309 320\n310 321\n311 322\n312 323\n313 324\n314 325\n315 326\n316 327\n317 328\n318 329\n319 330\n320 331\n321 332\n322 333\n323 334\n324 335\n325 336\n326 337\n327 338\n328 339\n329 340\n330 341\n331 342\n332 343\n333 344\n334 345\n335 346\n336 347\n337 348\n338 349\n339 350\n340 351\n341 352\n342 353\n343 354\n344 355\n345 356\n346 357\n347 358\n348 359\n349 360\n350 361\n351 362\n352 363\n353 364\n354 365\n355 366\n356 367\n357 368\n358 369\n359 370\n360 371\n361 372\n362 373\n363 374\n364 375\n365 376\n366 377\n367 378\n368 379\n369 380\n370 381\n371 382\n372 383\n373 384\n374 385\n375 386\n376 387\n377 388\n378 389\n379 390\n380 391\n381 392\n382 393\n383 394\n384 395\n385 396\n386 397\n387 398\n388 399\n389 400\n390 401\n391 402\n392 403\n393 404\n394 405\n395 406\n396 407\n397 408\n398 409\n399 410\n400 411\n401 412\n402 413\n403 414\n404 415\n405 416\n406 417\n407 418\n408 419\n409 420\n410 421\n411 422\n412 423\n413 424\n414 425\n415 426\n416 427\n417 428\n418 429\n419 430\n420 431\n421 432\n422 433\n423 434\n424 435\n425 436\n426 437\n427 438\n428 439\n429 440\n430 441\n431 442\n432 443\n433 444\n434 445\n435 446\n436 447\n437 448\n438 449\n439 450\n440 451\n441 452\n442 453\n443 454\n444 455\n445 456\n446 457\n447 458\n448 459\n449 460\n450 461\n451 462\n452 463\n453 464\n454 465\n455 466\n456 467\n457 468\n458 469\n459 470\n460 471\n461 472\n462 473\n463 474\n464 475\n465 476\n466 477\n467 478\n468 479\n469 480\n470 481\n471 482\n472 483\n473 484\n474 485\n475 486\n476 487\n477 488\n478 489\n479 490\n480 491\n481 492\n482 493\n483 494\n484 495\n485 496\n486 497\n487 498\n488 499\n489 500\n490 501\n491 502\n492 503\n493 504\n494 505\n495 506\n496 507\n497 508\n498 509\n499 510\n500 511\n501 512\n502 513\n503 514\n504 515\n505 516\n506 517\n507 518\n508 519\n509 520\n510 521\n511 522\n512 523\n513 524\n514 525\n515 526\n516 527\n517 528\n518 529\n519 530\n520 531\n521 532\n522 533\n523 534\n524 535\n525 536\n526 537\n527 538\n528 539\n529 540\n530 541\n531 542\n532 543\n533 544\n534 545\n535 546\n536 547\n537 548\n538 549\n539 550\n540 551\n541 552\n542 553\n543 554\n544 555\n545 556\n546 557\n547 558\n548 559\n549 560\n550 561\n551 562\n552 563\n553 564\n554 565\n555 566\n556 567\n557 568\n558 569\n559 570\n560 571\n561 572\n562 573\n563 574\n564 575\n565 576\n566 577\n567 578\n568 579\n569 580\n570 581\n571 582\n572 583\n573 584\n574 585\n575 586\n576 587\n577 588\n578 589\n579 590\n580 591\n581 592\n582 593\n583 594\n584 595\n585 596\n586 597\n587 598\n588 599\n589 600\n590 601\n591 602\n592 603\n593 604\n594 605\n595 606\n596 607\n597 608\n598 609\n599 610\n600 611\n601 612\n602 613\n603 614\n604 615\n605 616\n606 617\n607 618\n608 619\n609 620\n610 621\n611 622\n612 623\n613 624\n614 625\n615 626\n616 627\n617 628\n618 629\n619 630\n620 631\n621 632\n622 633\n623 634\n624 635\n625 636\n626 637\n627 638\n628 639\n629 640\n630 641\n631 642\n632 643\n633 644\n634 645\n635 646\n636 647\n637 648\n638 649\n639 650\n640 651\n641 652\n642 653\n643 654\n644 655\n645 656\n646 657\n647 658\n648 659\n649 660\n650 661\n651 662\n652 663\n653 664\n654 665\n655 666\n656 667\n657 668\n658 669\n659 670\n660 671\n661 672\n662 673\n663 674\n664 675\n665 676\n666 677\n667 678\n668 679\n669 680\n670 681\n671 682\n672 683\n673 684\n674 685\n675 686\n676 687\n677 688\n678 689\n679 690\n680 691\n681 692\n682 693\n683 694\n684 695\n685 696\n686 697\n687 698\n688 699\n689 700\n690 701\n691 702\n692 703\n693 704\n694 705\n695 706\n696 707\n697 708\n698 709\n699 710\n700 711\n701 712\n702 713\n703 714\n704 715\n705 716\n706 717\n707 718\n708 719\n709 720\n710 721\n711 722\n712 723\n713 724\n714 725\n715 726\n716 727\n717 728\n718 729\n719 730\n720 731\n721 732\n722 733\n723 734\n724 735\n725 736\n726 737\n727 738\n728 739\n729 740\n730 741\n731 742\n732 743\n733 744\n734 745\n735 746\n736 747\n737 748\n738 749\n739 750\n740 751\n741 752\n742 753\n743 754\n744 755\n745 756\n746 757\n747 758\n748 759\n749 760\n750 761\n751 762\n752 763\n753 764\n754 765\n755 766\n756 767\n757 768\n758 769\n759 770\n760 771\n761 772\n762 773\n763 774\n764 775\n765 776\n766 777\n767 778\n768 779\n769 780\n770 781\n771 782\n772 783\n773 784\n774 785\n775 786\n776 787\n777 788\n778 789\n779 790\n780 791\n781 792\n782 793\n783 794\n784 795\n785 796\n786 797\n787 798\n788 799\n789 800\n790 801\n791 802\n792 803\n793 804\n794 805\n795 806\n796 807\n797 808\n798 809\n799 810\n800 811\n801 812\n802 813\n803 814\n804 815\n805 816\n806 817\n807 818\n808 819\n809 820\n810 821\n811 822\n812 823\n813 824\n814 825\n815 826\n816 827\n817 828\n818 829\n819 830\n820 831\n821 832\n822 833\n823 834\n824 835\n825 836\n826 837\n827 838\n828 839\n829 840\n830 841\n831 842\n832 843\n833 844\n834 845\n835 846\n836 847\n837 848\n838 849\n839 850\n840 851\n841 852\n842 853\n843 854\n844 855\n845 856\n846 857\n847 858\n848 859\n849 860\n850 861\n851 862\n852 863\n853 864\n854 865\n855 866\n856 867\n857 868\n858 869\n859 870\n860 871\n861 872\n862 873\n863 874\n864 875\n865 876\n866 877\n867 878\n868 879\n869 880\n870 881\n871 882\n872 883\n873 884\n874 885\n875 886\n876 887\n877 888\n878 889\n879 890\n880 891\n881 892\n882 893\n883 894\n884 895\n885 896\n886 897\n887 898\n888 899\n889 900\n890 901\n891 902\n892 903\n893 904\n894 905\n895 906\n896 907\n897 908\n898 909\n899 910\n900 911\n901 912\n902 913\n903 914\n904 915\n905 916\n906 917\n907 918\n908 919\n909 920\n910 921\n911 922\n912 923\n913 924\n914 925\n915 926\n916 927\n917 928\n918 929\n919 930\n920 931\n921 932\n922 933\n923 934\n924 935\n925 936\n926 937\n927 938\n928 939\n929 940\n930 941\n931 942\n932 943\n933 944\n934 945\n935 946\n936 947\n937 948\n938 949\n939 950\n940 951\n941 952\n942 953\n943 954\n944 955\n945 956\n946 957\n947 958\n948 959\n949 960\n950 961\n951 962\n952 963\n953 964\n954 965\n955 966\n956 967\n957 968\n958 969\n959 970\n960 971\n961 972\n962 973\n963 974\n964 975\n965 976\n966 977\n967 978\n968 979\n969 980\n970 981\n971 982\n972 983\n973 984\n974 985\n975 986\n976 987\n977 988\n978 989\n979 990\n980 991\n981 992\n982 993\n983 994\n984 995\n985 996\n986 997\n987 998\n988 999\n989 1000\n",
"6\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n2 448\n3 449\n4 450\n5 451\n6 452\n7 453\n8 454\n9 455\n10 456\n11 457\n12 458\n13 459\n14 460\n15 461\n16 462\n17 463\n18 464\n19 465\n20 466\n21 467\n22 468\n23 469\n24 470\n25 471\n26 472\n27 473\n28 474\n29 475\n30 476\n31 477\n32 478\n33 479\n34 480\n35 481\n36 482\n37 483\n38 484\n39 485\n40 486\n41 487\n42 488\n43 489\n44 490\n45 491\n46 492\n47 493\n48 494\n49 495\n50 496\n51 497\n52 498\n53 499\n54 500\n55 501\n56 502\n57 503\n58 504\n59 505\n60 506\n61 507\n62 508\n63 509\n64 510\n65 511\n66 512\n67 513\n68 514\n69 515\n70 516\n71 517\n72 518\n73 519\n74 520\n75 521\n76 522\n77 523\n78 524\n79 525\n80 526\n81 527\n82 528\n83 529\n84 530\n85 531\n86 532\n87 533\n88 534\n89 535\n90 536\n91 537\n92 538\n93 539\n94 540\n95 541\n96 542\n97 543\n98 544\n99 545\n100 546\n101 547\n102 548\n103 549\n104 550\n105 551\n106 552\n107 553\n108 554\n109 555\n110 556\n111 557\n112 558\n113 559\n114 560\n115 561\n116 562\n117 563\n118 564\n119 565\n120 566\n121 567\n122 568\n123 569\n124 570\n125 571\n126 572\n127 573\n128 574\n129 575\n130 576\n131 577\n132 578\n133 579\n134 580\n135 581\n136 582\n137 583\n138 584\n139 585\n140 586\n141 587\n142 588\n143 589\n144 590\n145 591\n146 592\n147 593\n148 594\n149 595\n150 596\n151 597\n152 598\n153 599\n154 600\n155 601\n156 602\n157 603\n158 604\n159 605\n160 606\n161 607\n162 608\n163 609\n164 610\n165 611\n166 612\n167 613\n168 614\n169 615\n170 616\n171 617\n172 618\n173 619\n174 620\n175 621\n176 622\n177 623\n178 624\n179 625\n180 626\n181 627\n182 628\n183 629\n184 630\n185 631\n186 632\n187 633\n188 634\n189 635\n190 636\n191 637\n192 638\n193 639\n194 640\n195 641\n196 642\n197 643\n198 644\n199 645\n200 646\n201 647\n202 648\n203 649\n204 650\n205 651\n206 652\n207 653\n208 654\n209 655\n210 656\n211 657\n212 658\n213 659\n214 660\n215 661\n216 662\n217 663\n218 664\n219 665\n220 666\n221 667\n222 668\n223 669\n224 670\n225 671\n226 672\n227 673\n228 674\n229 675\n230 676\n231 677\n232 678\n233 679\n234 680\n235 681\n236 682\n237 683\n238 684\n239 685\n240 686\n241 687\n242 688\n243 689\n244 690\n245 691\n246 692\n247 693\n248 694\n249 695\n250 696\n251 697\n252 698\n253 699\n254 700\n255 701\n256 702\n257 703\n258 704\n259 705\n260 706\n261 707\n262 708\n263 709\n264 710\n265 711\n266 712\n267 713\n268 714\n269 715\n270 716\n271 717\n272 718\n273 719\n274 720\n275 721\n276 722\n277 723\n278 724\n279 725\n280 726\n281 727\n282 728\n283 729\n284 730\n285 731\n286 732\n287 733\n288 734\n289 735\n290 736\n291 737\n292 738\n293 739\n294 740\n295 741\n296 742\n297 743\n298 744\n299 745\n300 746\n301 747\n302 748\n303 749\n304 750\n305 751\n306 752\n307 753\n308 754\n309 755\n310 756\n311 757\n312 758\n313 759\n314 760\n315 761\n316 762\n317 763\n318 764\n319 765\n320 766\n321 767\n322 768\n323 769\n324 770\n325 771\n326 772\n327 773\n328 774\n329 775\n330 776\n331 777\n332 778\n333 779\n334 780\n335 781\n336 782\n337 783\n338 784\n339 785\n340 786\n341 787\n342 788\n343 789\n344 790\n345 791\n346 792\n347 793\n348 794\n349 795\n350 796\n351 797\n352 798\n353 799\n354 800\n355 801\n356 802\n357 803\n358 804\n359 805\n360 806\n361 807\n362 808\n363 809\n364 810\n365 811\n366 812\n367 813\n368 814\n369 815\n370 816\n371 817\n372 818\n373 819\n374 820\n375 821\n376 822\n377 823\n378 824\n379 825\n380 826\n381 827\n382 828\n383 829\n384 830\n385 831\n386 832\n387 833\n388 834\n389 835\n390 836\n391 837\n392 838\n393 839\n394 840\n395 841\n396 842\n397 843\n398 844\n399 845\n400 846\n401 847\n402 848\n403 849\n404 850\n405 851\n406 852\n407 853\n408 854\n409 855\n410 856\n411 857\n412 858\n413 859\n414 860\n415 861\n416 862\n417 863\n418 864\n419 865\n420 866\n421 867\n422 868\n423 869\n424 870\n425 871\n426 872\n427 873\n428 874\n429 875\n430 876\n431 877\n432 878\n433 879\n434 880\n435 881\n436 882\n437 883\n438 884\n439 885\n440 886\n441 887\n442 888\n443 889\n444 890\n445 891\n446 892\n447 893\n448 894\n449 895\n450 896\n451 897\n452 898\n453 899\n454 900\n455 901\n456 902\n457 903\n458 904\n459 905\n460 906\n461 907\n462 908\n463 909\n464 910\n465 911\n466 912\n467 913\n468 914\n469 915\n470 916\n471 917\n472 918\n473 919\n474 920\n475 921\n476 922\n477 923\n478 924\n479 925\n480 926\n481 927\n482 928\n483 929\n484 930\n485 931\n486 932\n487 933\n488 934\n489 935\n490 936\n491 937\n492 938\n493 939\n494 940\n495 941\n496 942\n497 943\n498 944\n499 945\n500 946\n501 947\n502 948\n503 949\n504 950\n505 951\n506 952\n507 953\n508 954\n509 955\n510 956\n511 957\n512 958\n513 959\n514 960\n515 961\n516 962\n517 963\n518 964\n519 965\n520 966\n521 967\n522 968\n523 969\n524 970\n525 971\n526 972\n527 973\n528 974\n529 975\n530 976\n531 977\n532 978\n533 979\n534 980\n535 981\n536 982\n537 983\n538 984\n539 985\n540 986\n541 987\n542 988\n543 989\n544 990\n545 991\n546 992\n547 993\n548 994\n549 995\n550 996\n551 997\n552 998\n553 999\n554 1000\n555 1001\n556 1002\n557 1003\n558 1004\n559 1005\n560 1006\n561 1007\n562 1008\n563 1009\n564 1010\n565 1011\n566 1012\n567 1013\n568 1014\n569 1015\n570 1016\n571 1017\n572 1018\n573 1019\n574 1020\n575 1021\n576 1022\n577 1023\n578 1024\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n2 581\n3 582\n4 583\n5 584\n6 585\n7 586\n8 587\n9 588\n10 589\n11 590\n12 591\n13 592\n14 593\n15 594\n16 595\n17 596\n18 597\n19 598\n20 599\n21 600\n22 601\n23 602\n24 603\n25 604\n26 605\n27 606\n28 607\n29 608\n30 609\n31 610\n32 611\n33 612\n34 613\n35 614\n36 615\n37 616\n38 617\n39 618\n40 619\n41 620\n42 621\n43 622\n44 623\n45 624\n46 625\n47 626\n48 627\n49 628\n50 629\n51 630\n52 631\n53 632\n54 633\n55 634\n56 635\n57 636\n58 637\n59 638\n60 639\n61 640\n62 641\n63 642\n64 643\n65 644\n66 645\n67 646\n68 647\n69 648\n70 649\n71 650\n72 651\n73 652\n74 653\n75 654\n76 655\n77 656\n78 657\n79 658\n80 659\n81 660\n82 661\n83 662\n84 663\n85 664\n86 665\n87 666\n88 667\n89 668\n90 669\n91 670\n92 671\n93 672\n94 673\n95 674\n96 675\n97 676\n98 677\n99 678\n100 679\n101 680\n102 681\n103 682\n104 683\n105 684\n106 685\n107 686\n108 687\n109 688\n110 689\n111 690\n112 691\n113 692\n114 693\n115 694\n116 695\n117 696\n118 697\n119 698\n120 699\n121 700\n122 701\n123 702\n124 703\n125 704\n126 705\n127 706\n128 707\n129 708\n130 709\n131 710\n132 711\n133 712\n134 713\n135 714\n136 715\n137 716\n138 717\n139 718\n140 719\n141 720\n142 721\n143 722\n144 723\n145 724\n146 725\n147 726\n148 727\n149 728\n150 729\n151 730\n152 731\n153 732\n154 733\n155 734\n156 735\n157 736\n158 737\n159 738\n160 739\n161 740\n162 741\n163 742\n164 743\n165 744\n166 745\n167 746\n168 747\n169 748\n170 749\n171 750\n172 751\n173 752\n174 753\n175 754\n176 755\n177 756\n178 757\n179 758\n180 759\n181 760\n182 761\n183 762\n184 763\n185 764\n186 765\n187 766\n188 767\n189 768\n190 769\n191 770\n192 771\n193 772\n194 773\n195 774\n196 775\n197 776\n198 777\n199 778\n200 779\n201 780\n202 781\n203 782\n204 783\n205 784\n206 785\n207 786\n208 787\n209 788\n210 789\n211 790\n212 791\n213 792\n214 793\n215 794\n216 795\n217 796\n218 797\n219 798\n220 799\n221 800\n222 801\n223 802\n224 803\n225 804\n226 805\n227 806\n228 807\n229 808\n230 809\n231 810\n232 811\n233 812\n234 813\n235 814\n236 815\n237 816\n238 817\n239 818\n240 819\n241 820\n242 821\n243 822\n244 823\n245 824\n246 825\n247 826\n248 827\n249 828\n250 829\n251 830\n252 831\n253 832\n254 833\n255 834\n256 835\n257 836\n258 837\n259 838\n260 839\n261 840\n262 841\n263 842\n264 843\n265 844\n266 845\n267 846\n268 847\n269 848\n270 849\n271 850\n272 851\n273 852\n274 853\n275 854\n276 855\n277 856\n278 857\n279 858\n280 859\n281 860\n282 861\n283 862\n284 863\n285 864\n286 865\n287 866\n288 867\n289 868\n290 869\n291 870\n292 871\n293 872\n294 873\n295 874\n296 875\n297 876\n298 877\n299 878\n300 879\n301 880\n302 881\n303 882\n304 883\n305 884\n306 885\n307 886\n308 887\n309 888\n310 889\n311 890\n312 891\n313 892\n314 893\n315 894\n316 895\n317 896\n318 897\n319 898\n320 899\n321 900\n322 901\n323 902\n324 903\n325 904\n326 905\n327 906\n328 907\n329 908\n330 909\n331 910\n332 911\n333 912\n334 913\n335 914\n336 915\n337 916\n338 917\n339 918\n340 919\n341 920\n342 921\n343 922\n344 923\n345 924\n346 925\n347 926\n348 927\n349 928\n350 929\n351 930\n352 931\n353 932\n354 933\n355 934\n356 935\n357 936\n358 937\n359 938\n360 939\n361 940\n362 941\n363 942\n364 943\n365 944\n366 945\n367 946\n368 947\n369 948\n370 949\n371 950\n372 951\n373 952\n374 953\n375 954\n376 955\n377 956\n378 957\n379 958\n380 959\n381 960\n382 961\n383 962\n384 963\n385 964\n386 965\n387 966\n388 967\n389 968\n390 969\n391 970\n392 971\n393 972\n394 973\n395 974\n396 975\n397 976\n398 977\n399 978\n400 979\n401 980\n402 981\n403 982\n404 983\n405 984\n406 985\n407 986\n408 987\n409 988\n410 989\n411 990\n412 991\n413 992\n414 993\n415 994\n416 995\n417 996\n418 997\n419 998\n420 999\n421 1000\n422 1001\n423 1002\n424 1003\n425 1004\n426 1005\n427 1006\n428 1007\n429 1008\n430 1009\n431 1010\n432 1011\n433 1012\n434 1013\n435 1014\n436 1015\n437 1016\n438 1017\n439 1018\n440 1019\n441 1020\n442 1021\n443 1022\n444 1023\n445 1024\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n",
"192\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n2 22\n3 23\n4 24\n5 25\n6 26\n7 27\n8 28\n9 29\n10 30\n11 31\n12 32\n13 33\n14 34\n15 35\n16 36\n17 37\n18 38\n19 39\n20 40\n21 41\n22 42\n23 43\n24 44\n25 45\n26 46\n27 47\n28 48\n29 49\n30 50\n31 51\n32 52\n33 53\n34 54\n35 55\n36 56\n37 57\n38 58\n39 59\n40 60\n41 61\n42 62\n43 63\n44 64\n45 65\n46 66\n47 67\n48 68\n49 69\n50 70\n51 71\n52 72\n53 73\n54 74\n55 75\n56 76\n57 77\n58 78\n59 79\n60 80\n61 81\n62 82\n63 83\n64 84\n65 85\n66 86\n67 87\n68 88\n69 89\n70 90\n71 91\n72 92\n73 93\n74 94\n75 95\n76 96\n77 97\n78 98\n79 99\n80 100\n81 101\n82 102\n83 103\n84 104\n85 105\n86 106\n87 107\n88 108\n89 109\n90 110\n91 111\n92 112\n93 113\n94 114\n95 115\n96 116\n97 117\n98 118\n99 119\n100 120\n101 121\n102 122\n103 123\n104 124\n105 125\n106 126\n107 127\n108 128\n109 129\n110 130\n111 131\n112 132\n113 133\n114 134\n115 135\n116 136\n117 137\n118 138\n119 139\n120 140\n121 141\n122 142\n123 143\n124 144\n125 145\n126 146\n127 147\n128 148\n129 149\n130 150\n131 151\n132 152\n133 153\n134 154\n135 155\n136 156\n137 157\n138 158\n139 159\n140 160\n141 161\n142 162\n143 163\n144 164\n145 165\n146 166\n147 167\n148 168\n149 169\n150 170\n151 171\n152 172\n153 173\n154 174\n155 175\n156 176\n157 177\n158 178\n159 179\n160 180\n161 181\n162 182\n163 183\n164 184\n165 185\n166 186\n167 187\n168 188\n169 189\n170 190\n171 191\n172 192\n173 193\n174 194\n175 195\n176 196\n177 197\n178 198\n179 199\n180 200\n181 201\n182 202\n183 203\n184 204\n185 205\n186 206\n187 207\n188 208\n189 209\n190 210\n191 211\n192 212\n193 213\n194 214\n195 215\n196 216\n197 217\n198 218\n199 219\n200 220\n201 221\n202 222\n203 223\n204 224\n205 225\n206 226\n207 227\n208 228\n209 229\n210 230\n211 231\n212 232\n213 233\n214 234\n215 235\n216 236\n217 237\n218 238\n219 239\n220 240\n221 241\n222 242\n223 243\n224 244\n225 245\n226 246\n227 247\n228 248\n229 249\n230 250\n231 251\n232 252\n233 253\n234 254\n235 255\n236 256\n237 257\n238 258\n239 259\n240 260\n241 261\n242 262\n243 263\n244 264\n245 265\n246 266\n247 267\n248 268\n249 269\n250 270\n251 271\n252 272\n253 273\n254 274\n255 275\n256 276\n257 277\n258 278\n259 279\n260 280\n261 281\n262 282\n263 283\n264 284\n265 285\n266 286\n267 287\n268 288\n269 289\n270 290\n271 291\n272 292\n273 293\n274 294\n275 295\n276 296\n277 297\n278 298\n279 299\n280 300\n281 301\n282 302\n283 303\n284 304\n285 305\n286 306\n287 307\n288 308\n289 309\n290 310\n291 311\n292 312\n293 313\n294 314\n295 315\n296 316\n297 317\n298 318\n299 319\n300 320\n301 321\n302 322\n303 323\n304 324\n305 325\n306 326\n307 327\n308 328\n309 329\n310 330\n311 331\n312 332\n313 333\n314 334\n315 335\n316 336\n317 337\n318 338\n319 339\n320 340\n321 341\n322 342\n323 343\n324 344\n325 345\n326 346\n327 347\n328 348\n329 349\n330 350\n331 351\n332 352\n333 353\n334 354\n335 355\n336 356\n337 357\n338 358\n339 359\n340 360\n341 361\n342 362\n343 363\n344 364\n345 365\n346 366\n347 367\n348 368\n349 369\n350 370\n351 371\n352 372\n353 373\n354 374\n355 375\n356 376\n357 377\n358 378\n359 379\n360 380\n361 381\n362 382\n363 383\n364 384\n365 385\n366 386\n367 387\n368 388\n369 389\n370 390\n371 391\n372 392\n373 393\n374 394\n375 395\n376 396\n377 397\n378 398\n379 399\n380 400\n381 401\n382 402\n383 403\n384 404\n385 405\n386 406\n387 407\n388 408\n389 409\n390 410\n391 411\n392 412\n393 413\n394 414\n395 415\n396 416\n397 417\n398 418\n399 419\n400 420\n401 421\n402 422\n403 423\n404 424\n405 425\n406 426\n407 427\n408 428\n409 429\n410 430\n411 431\n412 432\n413 433\n414 434\n415 435\n416 436\n417 437\n418 438\n419 439\n420 440\n421 441\n422 442\n423 443\n424 444\n425 445\n426 446\n427 447\n428 448\n429 449\n430 450\n431 451\n432 452\n433 453\n434 454\n435 455\n436 456\n437 457\n438 458\n439 459\n440 460\n441 461\n442 462\n443 463\n444 464\n445 465\n446 466\n447 467\n448 468\n449 469\n450 470\n451 471\n452 472\n453 473\n454 474\n455 475\n456 476\n457 477\n458 478\n459 479\n460 480\n461 481\n462 482\n463 483\n464 484\n465 485\n466 486\n467 487\n468 488\n469 489\n470 490\n471 491\n472 492\n473 493\n474 494\n475 495\n476 496\n477 497\n478 498\n479 499\n480 500\n481 501\n482 502\n483 503\n484 504\n485 505\n486 506\n487 507\n488 508\n489 509\n490 510\n491 511\n492 512\n493 513\n494 514\n495 515\n496 516\n497 517\n498 518\n499 519\n500 520\n501 521\n502 522\n503 523\n504 524\n505 525\n506 526\n507 527\n508 528\n509 529\n510 530\n511 531\n512 532\n513 533\n514 534\n515 535\n516 536\n517 537\n518 538\n519 539\n520 540\n521 541\n522 542\n523 543\n524 544\n525 545\n526 546\n527 547\n528 548\n529 549\n530 550\n531 551\n532 552\n533 553\n534 554\n535 555\n536 556\n537 557\n538 558\n539 559\n540 560\n541 561\n542 562\n543 563\n544 564\n545 565\n546 566\n547 567\n548 568\n549 569\n550 570\n551 571\n552 572\n553 573\n554 574\n555 575\n556 576\n557 577\n558 578\n559 579\n560 580\n561 581\n562 582\n563 583\n564 584\n565 585\n566 586\n567 587\n568 588\n569 589\n570 590\n571 591\n572 592\n573 593\n574 594\n575 595\n576 596\n577 597\n578 598\n579 599\n580 600\n581 601\n582 602\n583 603\n584 604\n585 605\n586 606\n587 607\n588 608\n589 609\n590 610\n591 611\n592 612\n593 613\n594 614\n595 615\n596 616\n597 617\n598 618\n599 619\n600 620\n601 621\n602 622\n603 623\n604 624\n605 625\n606 626\n607 627\n608 628\n609 629\n610 630\n611 631\n612 632\n613 633\n614 634\n615 635\n616 636\n617 637\n618 638\n619 639\n620 640\n621 641\n622 642\n623 643\n624 644\n625 645\n626 646\n627 647\n628 648\n629 649\n630 650\n631 651\n632 652\n633 653\n634 654\n635 655\n636 656\n637 657\n638 658\n639 659\n640 660\n641 661\n642 662\n643 663\n644 664\n645 665\n646 666\n647 667\n648 668\n649 669\n650 670\n651 671\n652 672\n653 673\n654 674\n655 675\n656 676\n657 677\n658 678\n659 679\n660 680\n661 681\n662 682\n663 683\n664 684\n665 685\n666 686\n667 687\n668 688\n669 689\n670 690\n671 691\n672 692\n673 693\n674 694\n675 695\n676 696\n677 697\n678 698\n679 699\n680 700\n681 701\n682 702\n683 703\n684 704\n685 705\n686 706\n687 707\n688 708\n689 709\n690 710\n691 711\n692 712\n693 713\n694 714\n695 715\n696 716\n697 717\n698 718\n699 719\n700 720\n701 721\n702 722\n703 723\n704 724\n705 725\n706 726\n707 727\n708 728\n709 729\n710 730\n711 731\n712 732\n713 733\n714 734\n715 735\n716 736\n717 737\n718 738\n719 739\n720 740\n721 741\n722 742\n723 743\n724 744\n725 745\n726 746\n727 747\n728 748\n729 749\n730 750\n731 751\n732 752\n733 753\n734 754\n735 755\n736 756\n737 757\n738 758\n739 759\n740 760\n741 761\n742 762\n743 763\n744 764\n745 765\n746 766\n747 767\n748 768\n749 769\n750 770\n751 771\n752 772\n753 773\n754 774\n755 775\n756 776\n757 777\n758 778\n759 779\n760 780\n761 781\n762 782\n763 783\n764 784\n765 785\n766 786\n767 787\n768 788\n769 789\n770 790\n771 791\n772 792\n773 793\n774 794\n775 795\n776 796\n777 797\n778 798\n779 799\n780 800\n781 801\n782 802\n783 803\n784 804\n785 805\n786 806\n787 807\n788 808\n789 809\n790 810\n791 811\n792 812\n793 813\n794 814\n795 815\n796 816\n797 817\n798 818\n799 819\n800 820\n801 821\n802 822\n803 823\n804 824\n805 825\n806 826\n807 827\n808 828\n809 829\n810 830\n811 831\n812 832\n813 833\n814 834\n815 835\n816 836\n817 837\n818 838\n819 839\n820 840\n821 841\n822 842\n823 843\n824 844\n825 845\n826 846\n827 847\n828 848\n829 849\n830 850\n831 851\n832 852\n833 853\n834 854\n835 855\n836 856\n837 857\n838 858\n839 859\n840 860\n841 861\n842 862\n843 863\n844 864\n845 865\n846 866\n847 867\n848 868\n849 869\n850 870\n851 871\n852 872\n853 873\n854 874\n855 875\n856 876\n857 877\n858 878\n859 879\n860 880\n861 881\n862 882\n863 883\n864 884\n865 885\n866 886\n867 887\n868 888\n869 889\n870 890\n871 891\n872 892\n873 893\n874 894\n875 895\n876 896\n877 897\n878 898\n879 899\n880 900\n881 901\n882 902\n883 903\n884 904\n885 905\n886 906\n887 907\n888 908\n889 909\n890 910\n891 911\n892 912\n893 913\n894 914\n895 915\n896 916\n897 917\n898 918\n899 919\n900 920\n901 921\n902 922\n903 923\n904 924\n905 925\n906 926\n907 927\n908 928\n909 929\n910 930\n911 931\n912 932\n913 933\n914 934\n915 935\n916 936\n917 937\n918 938\n919 939\n920 940\n921 941\n922 942\n923 943\n924 944\n925 945\n926 946\n927 947\n928 948\n929 949\n930 950\n931 951\n932 952\n933 953\n934 954\n935 955\n936 956\n937 957\n938 958\n939 959\n940 960\n941 961\n942 962\n943 963\n944 964\n945 965\n946 966\n947 967\n948 968\n949 969\n950 970\n951 971\n952 972\n953 973\n954 974\n955 975\n956 976\n957 977\n958 978\n959 979\n960 980\n961 981\n962 982\n963 983\n964 984\n965 985\n966 986\n967 987\n968 988\n969 989\n970 990\n971 991\n972 992\n973 993\n974 994\n975 995\n976 996\n977 997\n978 998\n979 999\n980 1000\n981 1001\n982 1002\n983 1003\n984 1004\n985 1005\n986 1006\n987 1007\n988 1008\n989 1009\n990 1010\n991 1011\n992 1012\n993 1013\n994 1014\n995 1015\n996 1016\n997 1017\n998 1018\n999 1019\n1000 1020\n1001 1021\n1002 1022\n1003 1023\n1004 1024\n1005 1025\n1006 1026\n1007 1027\n1008 1028\n1009 1029\n1010 1030\n1011 1031\n1012 1032\n1013 1033\n1014 1034\n1015 1035\n1016 1036\n1017 1037\n1018 1038\n1019 1039\n1020 1040\n1021 1041\n1022 1042\n1023 1043\n1024 1044\n1025 1045\n1026 1046\n1027 1047\n1028 1048\n1029 1049\n1030 1050\n1031 1051\n1032 1052\n1033 1053\n1034 1054\n1035 1055\n1036 1056\n1037 1057\n1038 1058\n1039 1059\n1040 1060\n1041 1061\n1042 1062\n1043 1063\n1044 1064\n1045 1065\n1046 1066\n1047 1067\n1048 1068\n1049 1069\n1050 1070\n1051 1071\n1052 1072\n1053 1073\n1054 1074\n1055 1075\n1056 1076\n1057 1077\n1058 1078\n1059 1079\n1060 1080\n1061 1081\n1062 1082\n1063 1083\n1064 1084\n1065 1085\n1066 1086\n1067 1087\n1068 1088\n1069 1089\n1070 1090\n1071 1091\n1072 1092\n1073 1093\n1074 1094\n1075 1095\n1076 1096\n1077 1097\n1078 1098\n1079 1099\n1080 1100\n1081 1101\n1082 1102\n1083 1103\n1084 1104\n1085 1105\n1086 1106\n1087 1107\n1088 1108\n1089 1109\n1090 1110\n1091 1111\n1092 1112\n1093 1113\n1094 1114\n1095 1115\n1096 1116\n1097 1117\n1098 1118\n1099 1119\n1100 1120\n1101 1121\n1102 1122\n1103 1123\n1104 1124\n1105 1125\n1106 1126\n1107 1127\n1108 1128\n1109 1129\n1110 1130\n1111 1131\n1112 1132\n1113 1133\n1114 1134\n1115 1135\n1116 1136\n1117 1137\n1118 1138\n1119 1139\n1120 1140\n1121 1141\n1122 1142\n1123 1143\n1124 1144\n1125 1145\n1126 1146\n1127 1147\n1128 1148\n1129 1149\n1130 1150\n1131 1151\n1132 1152\n1133 1153\n1134 1154\n1135 1155\n1136 1156\n1137 1157\n1138 1158\n1139 1159\n1140 1160\n1141 1161\n1142 1162\n1143 1163\n1144 1164\n1145 1165\n1146 1166\n1147 1167\n1148 1168\n1149 1169\n1150 1170\n1151 1171\n1152 1172\n1153 1173\n1154 1174\n1155 1175\n1156 1176\n1157 1177\n1158 1178\n1159 1179\n1160 1180\n1161 1181\n1162 1182\n1163 1183\n1164 1184\n1165 1185\n1166 1186\n1167 1187\n1168 1188\n1169 1189\n1170 1190\n1171 1191\n1172 1192\n1173 1193\n1174 1194\n1175 1195\n1176 1196\n1177 1197\n1178 1198\n1179 1199\n1180 1200\n1181 1201\n1182 1202\n1183 1203\n1184 1204\n1185 1205\n1186 1206\n1187 1207\n1188 1208\n1189 1209\n1190 1210\n1191 1211\n1192 1212\n1193 1213\n1194 1214\n1195 1215\n1196 1216\n1197 1217\n1198 1218\n1199 1219\n1200 1220\n1201 1221\n1202 1222\n1203 1223\n1204 1224\n1205 1225\n1206 1226\n1207 1227\n1208 1228\n1209 1229\n1210 1230\n1211 1231\n1212 1232\n1213 1233\n1214 1234\n1215 1235\n1216 1236\n1217 1237\n1218 1238\n1219 1239\n1220 1240\n1221 1241\n1222 1242\n1223 1243\n1224 1244\n1225 1245\n1226 1246\n1227 1247\n1228 1248\n1229 1249\n1230 1250\n1231 1251\n1232 1252\n1233 1253\n1234 1254\n1235 1255\n1236 1256\n1237 1257\n1238 1258\n1239 1259\n1240 1260\n1241 1261\n1242 1262\n1243 1263\n1244 1264\n1245 1265\n1246 1266\n1247 1267\n1248 1268\n1249 1269\n1250 1270\n1251 1271\n1252 1272\n1253 1273\n1254 1274\n1255 1275\n1256 1276\n1257 1277\n1258 1278\n1259 1279\n1260 1280\n1261 1281\n1262 1282\n1263 1283\n1264 1284\n1265 1285\n1266 1286\n1267 1287\n1268 1288\n1269 1289\n1270 1290\n1271 1291\n1272 1292\n1273 1293\n1274 1294\n1275 1295\n1276 1296\n1277 1297\n1278 1298\n1279 1299\n1280 1300\n1281 1301\n1282 1302\n1283 1303\n1284 1304\n1285 1305\n1286 1306\n1287 1307\n1288 1308\n1289 1309\n1290 1310\n1291 1311\n1292 1312\n1293 1313\n1294 1314\n1295 1315\n1296 1316\n1297 1317\n1298 1318\n1299 1319\n1300 1320\n1301 1321\n1302 1322\n1303 1323\n1304 1324\n1305 1325\n1306 1326\n1307 1327\n1308 1328\n1309 1329\n1310 1330\n1311 1331\n1312 1332\n1313 1333\n1314 1334\n1315 1335\n1316 1336\n1317 1337\n1318 1338\n1319 1339\n1320 1340\n1321 1341\n1322 1342\n1323 1343\n1324 1344\n1325 1345\n1326 1346\n1327 1347\n1328 1348\n1329 1349\n1330 1350\n1331 1351\n1332 1352\n1333 1353\n1334 1354\n1335 1355\n1336 1356\n1337 1357\n1338 1358\n1339 1359\n1340 1360\n1341 1361\n1342 1362\n1343 1363\n1344 1364\n1345 1365\n1346 1366\n1347 1367\n1348 1368\n1349 1369\n1350 1370\n1351 1371\n1352 1372\n1353 1373\n1354 1374\n1355 1375\n1356 1376\n1357 1377\n1358 1378\n1359 1379\n1360 1380\n1361 1381\n1362 1382\n1363 1383\n1364 1384\n1365 1385\n1366 1386\n1367 1387\n1368 1388\n1369 1389\n1370 1390\n1371 1391\n1372 1392\n1373 1393\n1374 1394\n1375 1395\n1376 1396\n1377 1397\n1378 1398\n1379 1399\n1380 1400\n1381 1401\n1382 1402\n1383 1403\n1384 1404\n1385 1405\n1386 1406\n1387 1407\n1388 1408\n1389 1409\n1390 1410\n1391 1411\n1392 1412\n1393 1413\n1394 1414\n1395 1415\n1396 1416\n1397 1417\n1398 1418\n1399 1419\n1400 1420\n1401 1421\n1402 1422\n1403 1423\n1404 1424\n1405 1425\n1406 1426\n1407 1427\n1408 1428\n1409 1429\n1410 1430\n1411 1431\n1412 1432\n1413 1433\n1414 1434\n1415 1435\n1416 1436\n1417 1437\n1418 1438\n1419 1439\n1420 1440\n1421 1441\n1422 1442\n1423 1443\n1424 1444\n1425 1445\n1426 1446\n1427 1447\n1428 1448\n1429 1449\n1430 1450\n1431 1451\n1432 1452\n1433 1453\n1434 1454\n1435 1455\n1436 1456\n1437 1457\n1438 1458\n1439 1459\n1440 1460\n1441 1461\n1442 1462\n1443 1463\n1444 1464\n1445 1465\n1446 1466\n1447 1467\n1448 1468\n1449 1469\n1450 1470\n1451 1471\n1452 1472\n1453 1473\n1454 1474\n1455 1475\n1456 1476\n1457 1477\n1458 1478\n1459 1479\n1460 1480\n1461 1481\n1462 1482\n1463 1483\n1464 1484\n1465 1485\n1466 1486\n1467 1487\n1468 1488\n1469 1489\n1470 1490\n1471 1491\n1472 1492\n1473 1493\n1474 1494\n1475 1495\n1476 1496\n1477 1497\n1478 1498\n1479 1499\n1480 1500\n1481 1501\n1482 1502\n1483 1503\n1484 1504\n1485 1505\n1486 1506\n1487 1507\n1488 1508\n1489 1509\n1490 1510\n1491 1511\n1492 1512\n1493 1513\n1494 1514\n1495 1515\n1496 1516\n1497 1517\n1498 1518\n1499 1519\n1500 1520\n1501 1521\n1502 1522\n1503 1523\n1504 1524\n1505 1525\n1506 1526\n1507 1527\n1508 1528\n1509 1529\n1510 1530\n1511 1531\n1512 1532\n1513 1533\n1514 1534\n1515 1535\n1516 1536\n1517 1537\n1518 1538\n1519 1539\n1520 1540\n1521 1541\n1522 1542\n1523 1543\n1524 1544\n1525 1545\n1526 1546\n1527 1547\n1528 1548\n1529 1549\n1530 1550\n1531 1551\n1532 1552\n1533 1553\n1534 1554\n1535 1555\n1536 1556\n1537 1557\n1538 1558\n1539 1559\n1540 1560\n1541 1561\n1542 1562\n1543 1563\n1544 1564\n1545 1565\n1546 1566\n1547 1567\n1548 1568\n1549 1569\n1550 1570\n1551 1571\n1552 1572\n1553 1573\n1554 1574\n1555 1575\n1556 1576\n1557 1577\n1558 1578\n1559 1579\n1560 1580\n1561 1581\n1562 1582\n1563 1583\n1564 1584\n1565 1585\n1566 1586\n1567 1587\n1568 1588\n1569 1589\n1570 1590\n1571 1591\n1572 1592\n1573 1593\n1574 1594\n1575 1595\n1576 1596\n1577 1597\n1578 1598\n1579 1599\n1580 1600\n1581 1601\n1582 1602\n1583 1603\n1584 1604\n1585 1605\n1586 1606\n1587 1607\n1588 1608\n1589 1609\n1590 1610\n1591 1611\n1592 1612\n1593 1613\n1594 1614\n1595 1615\n1596 1616\n1597 1617\n1598 1618\n1599 1619\n1600 1620\n1601 1621\n1602 1622\n1603 1623\n1604 1624\n1605 1625\n1606 1626\n1607 1627\n1608 1628\n1609 1629\n1610 1630\n1611 1631\n1612 1632\n1613 1633\n1614 1634\n1615 1635\n1616 1636\n1617 1637\n1618 1638\n1619 1639\n1620 1640\n1621 1641\n1622 1642\n1623 1643\n1624 1644\n1625 1645\n1626 1646\n1627 1647\n1628 1648\n1629 1649\n1630 1650\n1631 1651\n1632 1652\n1633 1653\n1634 1654\n1635 1655\n1636 1656\n1637 1657\n1638 1658\n1639 1659\n1640 1660\n1641 1661\n1642 1662\n1643 1663\n1644 1664\n1645 1665\n1646 1666\n1647 1667\n1648 1668\n1649 1669\n1650 1670\n1651 1671\n1652 1672\n1653 1673\n1654 1674\n1655 1675\n1656 1676\n1657 1677\n1658 1678\n1659 1679\n1660 1680\n1661 1681\n1662 1682\n1663 1683\n1664 1684\n1665 1685\n1666 1686\n1667 1687\n1668 1688\n1669 1689\n1670 1690\n1671 1691\n1672 1692\n1673 1693\n1674 1694\n1675 1695\n1676 1696\n1677 1697\n1678 1698\n1679 1699\n1680 1700\n1681 1701\n1682 1702\n1683 1703\n1684 1704\n1685 1705\n1686 1706\n1687 1707\n1688 1708\n1689 1709\n1690 1710\n1691 1711\n1692 1712\n1693 1713\n1694 1714\n1695 1715\n1696 1716\n1697 1717\n1698 1718\n1699 1719\n1700 1720\n1701 1721\n1702 1722\n1703 1723\n1704 1724\n1705 1725\n1706 1726\n1707 1727\n1708 1728\n1709 1729\n1710 1730\n1711 1731\n1712 1732\n1713 1733\n1714 1734\n1715 1735\n1716 1736\n1717 1737\n1718 1738\n1719 1739\n1720 1740\n1721 1741\n1722 1742\n1723 1743\n1724 1744\n1725 1745\n1726 1746\n1727 1747\n1728 1748\n1729 1749\n1730 1750\n1731 1751\n1732 1752\n1733 1753\n1734 1754\n1735 1755\n1736 1756\n1737 1757\n1738 1758\n1739 1759\n1740 1760\n1741 1761\n1742 1762\n1743 1763\n1744 1764\n1745 1765\n1746 1766\n1747 1767\n1748 1768\n1749 1769\n1750 1770\n1751 1771\n1752 1772\n1753 1773\n1754 1774\n1755 1775\n1756 1776\n1757 1777\n1758 1778\n1759 1779\n1760 1780\n1761 1781\n1762 1782\n1763 1783\n1764 1784\n1765 1785\n1766 1786\n1767 1787\n1768 1788\n1769 1789\n1770 1790\n1771 1791\n1772 1792\n1773 1793\n1774 1794\n1775 1795\n1776 1796\n1777 1797\n1778 1798\n1779 1799\n1780 1800\n1781 1801\n1782 1802\n1783 1803\n1784 1804\n1785 1805\n1786 1806\n1787 1807\n1788 1808\n1789 1809\n1790 1810\n1791 1811\n1792 1812\n1793 1813\n1794 1814\n1795 1815\n1796 1816\n1797 1817\n1798 1818\n1799 1819\n1800 1820\n1801 1821\n1802 1822\n1803 1823\n1804 1824\n1805 1825\n1806 1826\n1807 1827\n1808 1828\n1809 1829\n1810 1830\n1811 1831\n1812 1832\n1813 1833\n1814 1834\n1815 1835\n1816 1836\n1817 1837\n1818 1838\n1819 1839\n1820 1840\n1821 1841\n1822 1842\n1823 1843\n1824 1844\n1825 1845\n1826 1846\n1827 1847\n1828 1848\n1829 1849\n1830 1850\n1831 1851\n1832 1852\n1833 1853\n1834 1854\n1835 1855\n1836 1856\n1837 1857\n1838 1858\n1839 1859\n1840 1860\n1841 1861\n1842 1862\n1843 1863\n1844 1864\n1845 1865\n1846 1866\n1847 1867\n1848 1868\n1849 1869\n1850 1870\n1851 1871\n1852 1872\n1853 1873\n1854 1874\n1855 1875\n1856 1876\n1857 1877\n1858 1878\n1859 1879\n1860 1880\n1861 1881\n1862 1882\n1863 1883\n1864 1884\n1865 1885\n1866 1886\n1867 1887\n1868 1888\n1869 1889\n1870 1890\n1871 1891\n1872 1892\n1873 1893\n1874 1894\n1875 1895\n1876 1896\n1877 1897\n1878 1898\n1879 1899\n1880 1900\n1881 1901\n1882 1902\n1883 1903\n1884 1904\n1885 1905\n1886 1906\n1887 1907\n1888 1908\n1889 1909\n1890 1910\n1891 1911\n1892 1912\n",
"12\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n2 179\n3 180\n4 181\n5 182\n6 183\n7 184\n8 185\n9 186\n10 187\n11 188\n12 189\n13 190\n14 191\n15 192\n16 193\n17 194\n18 195\n19 196\n20 197\n21 198\n22 199\n23 200\n24 201\n25 202\n26 203\n27 204\n28 205\n29 206\n30 207\n31 208\n32 209\n33 210\n34 211\n35 212\n36 213\n37 214\n38 215\n39 216\n40 217\n41 218\n42 219\n43 220\n44 221\n45 222\n46 223\n47 224\n48 225\n49 226\n50 227\n51 228\n52 229\n53 230\n54 231\n55 232\n56 233\n57 234\n58 235\n59 236\n60 237\n61 238\n62 239\n63 240\n64 241\n65 242\n66 243\n67 244\n68 245\n69 246\n70 247\n71 248\n72 249\n73 250\n74 251\n75 252\n76 253\n77 254\n78 255\n79 256\n80 257\n81 258\n82 259\n83 260\n84 261\n85 262\n86 263\n87 264\n88 265\n89 266\n90 267\n91 268\n92 269\n93 270\n94 271\n95 272\n96 273\n97 274\n98 275\n99 276\n100 277\n101 278\n102 279\n103 280\n104 281\n105 282\n106 283\n107 284\n108 285\n109 286\n110 287\n111 288\n112 289\n113 290\n114 291\n115 292\n116 293\n117 294\n118 295\n119 296\n120 297\n121 298\n122 299\n123 300\n124 301\n125 302\n126 303\n127 304\n128 305\n129 306\n130 307\n131 308\n132 309\n133 310\n134 311\n135 312\n136 313\n137 314\n138 315\n139 316\n140 317\n141 318\n142 319\n143 320\n144 321\n145 322\n146 323\n147 324\n148 325\n149 326\n150 327\n151 328\n152 329\n153 330\n154 331\n155 332\n156 333\n157 334\n158 335\n159 336\n160 337\n161 338\n162 339\n163 340\n164 341\n165 342\n166 343\n167 344\n168 345\n169 346\n170 347\n171 348\n172 349\n173 350\n174 351\n175 352\n176 353\n177 354\n178 355\n179 356\n180 357\n181 358\n182 359\n183 360\n184 361\n185 362\n186 363\n187 364\n188 365\n189 366\n190 367\n191 368\n192 369\n193 370\n194 371\n195 372\n196 373\n197 374\n198 375\n199 376\n200 377\n201 378\n202 379\n203 380\n204 381\n205 382\n206 383\n207 384\n208 385\n209 386\n210 387\n211 388\n212 389\n213 390\n214 391\n215 392\n216 393\n217 394\n218 395\n219 396\n220 397\n221 398\n222 399\n223 400\n224 401\n225 402\n226 403\n227 404\n228 405\n229 406\n230 407\n231 408\n232 409\n233 410\n234 411\n235 412\n236 413\n237 414\n238 415\n239 416\n240 417\n241 418\n242 419\n243 420\n244 421\n245 422\n246 423\n247 424\n248 425\n249 426\n250 427\n251 428\n252 429\n253 430\n254 431\n255 432\n256 433\n257 434\n258 435\n259 436\n260 437\n261 438\n262 439\n263 440\n264 441\n265 442\n266 443\n267 444\n268 445\n269 446\n270 447\n271 448\n272 449\n273 450\n274 451\n275 452\n276 453\n277 454\n278 455\n279 456\n280 457\n281 458\n282 459\n283 460\n284 461\n285 462\n286 463\n287 464\n288 465\n289 466\n290 467\n291 468\n292 469\n293 470\n294 471\n295 472\n296 473\n297 474\n298 475\n299 476\n300 477\n301 478\n302 479\n303 480\n304 481\n305 482\n306 483\n307 484\n308 485\n309 486\n310 487\n311 488\n312 489\n313 490\n314 491\n315 492\n316 493\n317 494\n318 495\n319 496\n320 497\n321 498\n322 499\n323 500\n324 501\n325 502\n326 503\n327 504\n328 505\n329 506\n330 507\n331 508\n332 509\n333 510\n334 511\n335 512\n336 513\n337 514\n338 515\n339 516\n340 517\n341 518\n342 519\n343 520\n344 521\n345 522\n346 523\n347 524\n348 525\n349 526\n350 527\n351 528\n352 529\n353 530\n354 531\n355 532\n356 533\n357 534\n358 535\n359 536\n360 537\n361 538\n362 539\n363 540\n364 541\n365 542\n366 543\n367 544\n368 545\n369 546\n370 547\n371 548\n372 549\n373 550\n374 551\n375 552\n376 553\n377 554\n378 555\n379 556\n380 557\n381 558\n382 559\n383 560\n384 561\n385 562\n386 563\n387 564\n388 565\n389 566\n390 567\n391 568\n392 569\n393 570\n394 571\n395 572\n396 573\n397 574\n398 575\n399 576\n400 577\n401 578\n402 579\n403 580\n404 581\n405 582\n406 583\n407 584\n408 585\n409 586\n410 587\n411 588\n412 589\n413 590\n414 591\n415 592\n416 593\n417 594\n418 595\n419 596\n420 597\n421 598\n422 599\n423 600\n424 601\n425 602\n426 603\n427 604\n428 605\n429 606\n430 607\n431 608\n432 609\n433 610\n434 611\n435 612\n436 613\n437 614\n438 615\n439 616\n440 617\n441 618\n442 619\n443 620\n444 621\n445 622\n446 623\n447 624\n448 625\n449 626\n450 627\n451 628\n452 629\n453 630\n454 631\n455 632\n456 633\n457 634\n458 635\n459 636\n460 637\n461 638\n462 639\n463 640\n464 641\n465 642\n466 643\n467 644\n468 645\n469 646\n470 647\n471 648\n472 649\n473 650\n474 651\n475 652\n476 653\n477 654\n478 655\n479 656\n480 657\n481 658\n482 659\n483 660\n484 661\n485 662\n486 663\n487 664\n488 665\n489 666\n490 667\n491 668\n492 669\n493 670\n494 671\n495 672\n496 673\n497 674\n498 675\n499 676\n500 677\n501 678\n502 679\n503 680\n504 681\n505 682\n506 683\n507 684\n508 685\n509 686\n510 687\n511 688\n512 689\n513 690\n514 691\n515 692\n516 693\n517 694\n518 695\n519 696\n520 697\n521 698\n522 699\n523 700\n524 701\n525 702\n526 703\n527 704\n528 705\n529 706\n530 707\n531 708\n532 709\n533 710\n534 711\n535 712\n536 713\n537 714\n538 715\n539 716\n540 717\n541 718\n542 719\n543 720\n544 721\n545 722\n546 723\n547 724\n548 725\n549 726\n550 727\n551 728\n552 729\n553 730\n554 731\n555 732\n556 733\n557 734\n558 735\n559 736\n560 737\n561 738\n562 739\n563 740\n564 741\n565 742\n566 743\n567 744\n568 745\n569 746\n570 747\n571 748\n572 749\n573 750\n574 751\n575 752\n576 753\n577 754\n578 755\n579 756\n580 757\n581 758\n582 759\n583 760\n584 761\n585 762\n586 763\n587 764\n588 765\n589 766\n590 767\n591 768\n592 769\n593 770\n594 771\n595 772\n596 773\n597 774\n598 775\n599 776\n600 777\n601 778\n602 779\n603 780\n604 781\n605 782\n606 783\n607 784\n608 785\n609 786\n610 787\n611 788\n612 789\n613 790\n614 791\n615 792\n616 793\n617 794\n618 795\n619 796\n620 797\n621 798\n622 799\n623 800\n624 801\n625 802\n626 803\n627 804\n628 805\n629 806\n630 807\n631 808\n632 809\n633 810\n634 811\n635 812\n636 813\n637 814\n638 815\n639 816\n640 817\n641 818\n642 819\n643 820\n644 821\n645 822\n646 823\n647 824\n648 825\n649 826\n650 827\n651 828\n652 829\n653 830\n654 831\n655 832\n656 833\n657 834\n658 835\n659 836\n660 837\n661 838\n662 839\n663 840\n664 841\n665 842\n666 843\n667 844\n668 845\n669 846\n670 847\n671 848\n672 849\n673 850\n674 851\n675 852\n676 853\n677 854\n678 855\n679 856\n680 857\n681 858\n682 859\n683 860\n684 861\n685 862\n686 863\n687 864\n688 865\n689 866\n690 867\n691 868\n692 869\n693 870\n694 871\n695 872\n696 873\n697 874\n698 875\n699 876\n700 877\n701 878\n702 879\n703 880\n704 881\n705 882\n706 883\n707 884\n708 885\n709 886\n710 887\n711 888\n712 889\n713 890\n714 891\n715 892\n716 893\n717 894\n718 895\n719 896\n720 897\n721 898\n722 899\n723 900\n724 901\n725 902\n726 903\n727 904\n728 905\n729 906\n730 907\n731 908\n732 909\n733 910\n734 911\n735 912\n736 913\n737 914\n738 915\n739 916\n740 917\n741 918\n742 919\n743 920\n744 921\n745 922\n746 923\n747 924\n748 925\n749 926\n750 927\n751 928\n752 929\n753 930\n754 931\n755 932\n756 933\n757 934\n758 935\n759 936\n760 937\n761 938\n762 939\n763 940\n764 941\n765 942\n766 943\n767 944\n768 945\n769 946\n770 947\n771 948\n772 949\n773 950\n774 951\n775 952\n776 953\n777 954\n778 955\n779 956\n780 957\n781 958\n782 959\n783 960\n784 961\n785 962\n786 963\n787 964\n788 965\n789 966\n790 967\n791 968\n792 969\n793 970\n794 971\n795 972\n796 973\n797 974\n798 975\n799 976\n800 977\n801 978\n802 979\n803 980\n804 981\n805 982\n806 983\n807 984\n808 985\n809 986\n810 987\n811 988\n812 989\n813 990\n814 991\n815 992\n816 993\n817 994\n818 995\n819 996\n",
"180\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n2 16\n3 17\n4 18\n5 19\n6 20\n7 21\n8 22\n9 23\n10 24\n11 25\n12 26\n13 27\n14 28\n15 29\n16 30\n17 31\n18 32\n19 33\n20 34\n21 35\n22 36\n23 37\n24 38\n25 39\n26 40\n27 41\n28 42\n29 43\n30 44\n31 45\n32 46\n33 47\n34 48\n35 49\n36 50\n37 51\n38 52\n39 53\n40 54\n41 55\n42 56\n43 57\n44 58\n45 59\n46 60\n47 61\n48 62\n49 63\n50 64\n51 65\n52 66\n53 67\n54 68\n55 69\n56 70\n57 71\n58 72\n59 73\n60 74\n61 75\n62 76\n63 77\n64 78\n65 79\n66 80\n67 81\n68 82\n69 83\n70 84\n71 85\n72 86\n73 87\n74 88\n75 89\n76 90\n77 91\n78 92\n79 93\n80 94\n81 95\n82 96\n83 97\n84 98\n85 99\n86 100\n87 101\n88 102\n89 103\n90 104\n91 105\n92 106\n93 107\n94 108\n95 109\n96 110\n97 111\n98 112\n99 113\n100 114\n101 115\n102 116\n103 117\n104 118\n105 119\n106 120\n107 121\n108 122\n109 123\n110 124\n111 125\n112 126\n113 127\n114 128\n115 129\n116 130\n117 131\n118 132\n119 133\n120 134\n121 135\n122 136\n123 137\n124 138\n125 139\n126 140\n127 141\n128 142\n129 143\n130 144\n131 145\n132 146\n133 147\n134 148\n135 149\n136 150\n137 151\n138 152\n139 153\n140 154\n141 155\n142 156\n143 157\n144 158\n145 159\n146 160\n147 161\n148 162\n149 163\n150 164\n151 165\n152 166\n153 167\n154 168\n155 169\n156 170\n157 171\n158 172\n159 173\n160 174\n161 175\n162 176\n163 177\n164 178\n165 179\n166 180\n167 181\n168 182\n169 183\n170 184\n171 185\n172 186\n173 187\n174 188\n175 189\n176 190\n177 191\n178 192\n179 193\n180 194\n181 195\n182 196\n183 197\n184 198\n185 199\n186 200\n187 201\n188 202\n189 203\n190 204\n191 205\n192 206\n193 207\n194 208\n195 209\n196 210\n197 211\n198 212\n199 213\n200 214\n201 215\n202 216\n203 217\n204 218\n205 219\n206 220\n207 221\n208 222\n209 223\n210 224\n211 225\n212 226\n213 227\n214 228\n215 229\n216 230\n217 231\n218 232\n219 233\n220 234\n221 235\n222 236\n223 237\n224 238\n225 239\n226 240\n227 241\n228 242\n229 243\n230 244\n231 245\n232 246\n233 247\n234 248\n235 249\n236 250\n237 251\n238 252\n239 253\n240 254\n241 255\n242 256\n243 257\n244 258\n245 259\n246 260\n247 261\n248 262\n249 263\n250 264\n251 265\n252 266\n253 267\n254 268\n255 269\n256 270\n257 271\n258 272\n259 273\n260 274\n261 275\n262 276\n263 277\n264 278\n265 279\n266 280\n267 281\n268 282\n269 283\n270 284\n271 285\n272 286\n273 287\n274 288\n275 289\n276 290\n277 291\n278 292\n279 293\n280 294\n281 295\n282 296\n283 297\n284 298\n285 299\n286 300\n287 301\n288 302\n289 303\n290 304\n291 305\n292 306\n293 307\n294 308\n295 309\n296 310\n297 311\n298 312\n299 313\n300 314\n301 315\n302 316\n303 317\n304 318\n305 319\n306 320\n307 321\n308 322\n309 323\n310 324\n311 325\n312 326\n313 327\n314 328\n315 329\n316 330\n317 331\n318 332\n319 333\n320 334\n321 335\n322 336\n323 337\n324 338\n325 339\n326 340\n327 341\n328 342\n329 343\n330 344\n331 345\n332 346\n333 347\n334 348\n335 349\n336 350\n337 351\n338 352\n339 353\n340 354\n341 355\n342 356\n343 357\n344 358\n345 359\n346 360\n347 361\n348 362\n349 363\n350 364\n351 365\n352 366\n353 367\n354 368\n355 369\n356 370\n357 371\n358 372\n359 373\n360 374\n361 375\n362 376\n363 377\n364 378\n365 379\n366 380\n367 381\n368 382\n369 383\n370 384\n371 385\n372 386\n373 387\n374 388\n375 389\n376 390\n377 391\n378 392\n379 393\n380 394\n381 395\n382 396\n383 397\n384 398\n385 399\n386 400\n387 401\n388 402\n389 403\n390 404\n391 405\n392 406\n393 407\n394 408\n395 409\n396 410\n397 411\n398 412\n399 413\n400 414\n401 415\n402 416\n403 417\n404 418\n405 419\n406 420\n407 421\n408 422\n409 423\n410 424\n411 425\n412 426\n413 427\n414 428\n415 429\n416 430\n417 431\n418 432\n419 433\n420 434\n421 435\n422 436\n423 437\n424 438\n425 439\n426 440\n427 441\n428 442\n429 443\n430 444\n431 445\n432 446\n433 447\n434 448\n435 449\n436 450\n437 451\n438 452\n439 453\n440 454\n441 455\n442 456\n443 457\n444 458\n445 459\n446 460\n447 461\n448 462\n449 463\n450 464\n451 465\n452 466\n453 467\n454 468\n455 469\n456 470\n457 471\n458 472\n459 473\n460 474\n461 475\n462 476\n463 477\n464 478\n465 479\n466 480\n467 481\n468 482\n469 483\n470 484\n471 485\n472 486\n473 487\n474 488\n475 489\n476 490\n477 491\n478 492\n479 493\n480 494\n481 495\n482 496\n483 497\n484 498\n485 499\n486 500\n487 501\n488 502\n489 503\n490 504\n491 505\n492 506\n493 507\n494 508\n495 509\n496 510\n497 511\n498 512\n499 513\n500 514\n501 515\n502 516\n503 517\n504 518\n505 519\n506 520\n507 521\n508 522\n509 523\n510 524\n511 525\n512 526\n513 527\n514 528\n515 529\n516 530\n517 531\n518 532\n519 533\n520 534\n521 535\n522 536\n523 537\n524 538\n525 539\n526 540\n527 541\n528 542\n529 543\n530 544\n531 545\n532 546\n533 547\n534 548\n535 549\n536 550\n537 551\n538 552\n539 553\n540 554\n541 555\n542 556\n543 557\n544 558\n545 559\n546 560\n547 561\n548 562\n549 563\n550 564\n551 565\n552 566\n553 567\n554 568\n555 569\n556 570\n557 571\n558 572\n559 573\n560 574\n561 575\n562 576\n563 577\n564 578\n565 579\n566 580\n567 581\n568 582\n569 583\n570 584\n571 585\n572 586\n573 587\n574 588\n575 589\n576 590\n577 591\n578 592\n579 593\n580 594\n581 595\n582 596\n583 597\n584 598\n585 599\n586 600\n587 601\n588 602\n589 603\n590 604\n591 605\n592 606\n593 607\n594 608\n595 609\n596 610\n597 611\n598 612\n599 613\n600 614\n601 615\n602 616\n603 617\n604 618\n605 619\n606 620\n607 621\n608 622\n609 623\n610 624\n611 625\n612 626\n613 627\n614 628\n615 629\n616 630\n617 631\n618 632\n619 633\n620 634\n621 635\n622 636\n623 637\n624 638\n625 639\n626 640\n627 641\n628 642\n629 643\n630 644\n631 645\n632 646\n633 647\n634 648\n635 649\n636 650\n637 651\n638 652\n639 653\n640 654\n641 655\n642 656\n643 657\n644 658\n645 659\n646 660\n647 661\n648 662\n649 663\n650 664\n651 665\n652 666\n653 667\n654 668\n655 669\n656 670\n657 671\n658 672\n659 673\n660 674\n661 675\n662 676\n663 677\n664 678\n665 679\n666 680\n667 681\n668 682\n669 683\n670 684\n671 685\n672 686\n673 687\n674 688\n675 689\n676 690\n677 691\n678 692\n679 693\n680 694\n681 695\n682 696\n683 697\n684 698\n685 699\n686 700\n687 701\n688 702\n689 703\n690 704\n691 705\n692 706\n693 707\n694 708\n695 709\n696 710\n697 711\n698 712\n699 713\n700 714\n701 715\n702 716\n703 717\n704 718\n705 719\n706 720\n707 721\n708 722\n709 723\n710 724\n711 725\n712 726\n713 727\n714 728\n715 729\n716 730\n717 731\n718 732\n719 733\n720 734\n721 735\n722 736\n723 737\n724 738\n725 739\n726 740\n727 741\n728 742\n729 743\n730 744\n731 745\n732 746\n733 747\n734 748\n735 749\n736 750\n737 751\n738 752\n739 753\n740 754\n741 755\n742 756\n743 757\n744 758\n745 759\n746 760\n747 761\n748 762\n749 763\n750 764\n751 765\n752 766\n753 767\n754 768\n755 769\n756 770\n757 771\n758 772\n759 773\n760 774\n761 775\n762 776\n763 777\n764 778\n765 779\n766 780\n767 781\n768 782\n769 783\n770 784\n771 785\n772 786\n773 787\n774 788\n775 789\n776 790\n777 791\n778 792\n779 793\n780 794\n781 795\n782 796\n783 797\n784 798\n785 799\n786 800\n787 801\n788 802\n789 803\n790 804\n791 805\n792 806\n793 807\n794 808\n795 809\n796 810\n797 811\n798 812\n799 813\n800 814\n801 815\n802 816\n803 817\n804 818\n805 819\n806 820\n807 821\n808 822\n809 823\n810 824\n811 825\n812 826\n813 827\n814 828\n815 829\n816 830\n817 831\n818 832\n819 833\n820 834\n821 835\n822 836\n823 837\n824 838\n825 839\n826 840\n827 841\n828 842\n829 843\n830 844\n831 845\n832 846\n833 847\n834 848\n835 849\n836 850\n837 851\n838 852\n839 853\n840 854\n841 855\n842 856\n843 857\n844 858\n845 859\n846 860\n847 861\n848 862\n849 863\n850 864\n851 865\n852 866\n853 867\n854 868\n855 869\n856 870\n857 871\n858 872\n859 873\n860 874\n861 875\n862 876\n863 877\n864 878\n865 879\n866 880\n867 881\n868 882\n869 883\n870 884\n871 885\n872 886\n873 887\n874 888\n875 889\n876 890\n877 891\n878 892\n879 893\n880 894\n881 895\n882 896\n883 897\n884 898\n885 899\n886 900\n887 901\n888 902\n889 903\n890 904\n891 905\n892 906\n893 907\n894 908\n895 909\n896 910\n897 911\n898 912\n899 913\n900 914\n901 915\n902 916\n903 917\n904 918\n905 919\n906 920\n907 921\n908 922\n909 923\n910 924\n911 925\n912 926\n913 927\n914 928\n915 929\n916 930\n917 931\n918 932\n919 933\n920 934\n921 935\n922 936\n923 937\n924 938\n925 939\n926 940\n927 941\n928 942\n929 943\n930 944\n931 945\n932 946\n933 947\n934 948\n935 949\n936 950\n937 951\n938 952\n939 953\n940 954\n941 955\n942 956\n943 957\n944 958\n945 959\n946 960\n947 961\n948 962\n949 963\n950 964\n951 965\n952 966\n953 967\n954 968\n955 969\n956 970\n957 971\n958 972\n959 973\n960 974\n961 975\n962 976\n963 977\n964 978\n965 979\n966 980\n967 981\n968 982\n969 983\n970 984\n971 985\n972 986\n973 987\n974 988\n975 989\n976 990\n977 991\n978 992\n979 993\n980 994\n981 995\n982 996\n983 997\n984 998\n985 999\n986 1000\n987 1001\n988 1002\n989 1003\n990 1004\n991 1005\n992 1006\n993 1007\n994 1008\n995 1009\n996 1010\n997 1011\n998 1012\n999 1013\n1000 1014\n1001 1015\n1002 1016\n1003 1017\n1004 1018\n1005 1019\n1006 1020\n1007 1021\n1008 1022\n1009 1023\n1010 1024\n1011 1025\n1012 1026\n1013 1027\n1014 1028\n1015 1029\n1016 1030\n1017 1031\n1018 1032\n1019 1033\n1020 1034\n1021 1035\n1022 1036\n1023 1037\n1024 1038\n1025 1039\n1026 1040\n1027 1041\n1028 1042\n1029 1043\n1030 1044\n1031 1045\n1032 1046\n1033 1047\n1034 1048\n1035 1049\n1036 1050\n1037 1051\n1038 1052\n1039 1053\n1040 1054\n1041 1055\n1042 1056\n1043 1057\n1044 1058\n1045 1059\n1046 1060\n1047 1061\n1048 1062\n1049 1063\n1050 1064\n1051 1065\n1052 1066\n1053 1067\n1054 1068\n1055 1069\n1056 1070\n1057 1071\n1058 1072\n1059 1073\n1060 1074\n1061 1075\n1062 1076\n1063 1077\n1064 1078\n1065 1079\n1066 1080\n1067 1081\n1068 1082\n1069 1083\n1070 1084\n1071 1085\n1072 1086\n1073 1087\n1074 1088\n1075 1089\n1076 1090\n1077 1091\n1078 1092\n1079 1093\n1080 1094\n1081 1095\n1082 1096\n1083 1097\n1084 1098\n1085 1099\n1086 1100\n1087 1101\n1088 1102\n1089 1103\n1090 1104\n1091 1105\n1092 1106\n1093 1107\n1094 1108\n1095 1109\n1096 1110\n1097 1111\n1098 1112\n1099 1113\n1100 1114\n1101 1115\n1102 1116\n1103 1117\n1104 1118\n1105 1119\n1106 1120\n1107 1121\n1108 1122\n1109 1123\n1110 1124\n1111 1125\n1112 1126\n1113 1127\n1114 1128\n1115 1129\n1116 1130\n1117 1131\n1118 1132\n1119 1133\n1120 1134\n1121 1135\n1122 1136\n1123 1137\n1124 1138\n1125 1139\n1126 1140\n1127 1141\n1128 1142\n1129 1143\n1130 1144\n1131 1145\n1132 1146\n1133 1147\n1134 1148\n1135 1149\n1136 1150\n1137 1151\n1138 1152\n1139 1153\n1140 1154\n1141 1155\n1142 1156\n1143 1157\n1144 1158\n1145 1159\n1146 1160\n1147 1161\n1148 1162\n1149 1163\n1150 1164\n1151 1165\n1152 1166\n1153 1167\n1154 1168\n1155 1169\n1156 1170\n1157 1171\n1158 1172\n1159 1173\n1160 1174\n1161 1175\n1162 1176\n1163 1177\n1164 1178\n1165 1179\n1166 1180\n1167 1181\n1168 1182\n1169 1183\n1170 1184\n1171 1185\n1172 1186\n1173 1187\n1174 1188\n1175 1189\n1176 1190\n1177 1191\n1178 1192\n1179 1193\n1180 1194\n1181 1195\n1182 1196\n1183 1197\n1184 1198\n1185 1199\n1186 1200\n1187 1201\n1188 1202\n1189 1203\n1190 1204\n1191 1205\n1192 1206\n1193 1207\n1194 1208\n1195 1209\n1196 1210\n1197 1211\n1198 1212\n1199 1213\n1200 1214\n1201 1215\n1202 1216\n1203 1217\n1204 1218\n1205 1219\n1206 1220\n1207 1221\n1208 1222\n1209 1223\n1210 1224\n1211 1225\n1212 1226\n1213 1227\n1214 1228\n1215 1229\n1216 1230\n1217 1231\n1218 1232\n1219 1233\n1220 1234\n1221 1235\n1222 1236\n1223 1237\n1224 1238\n1225 1239\n1226 1240\n1227 1241\n1228 1242\n1229 1243\n1230 1244\n1231 1245\n1232 1246\n1233 1247\n1234 1248\n1235 1249\n1236 1250\n1237 1251\n1238 1252\n1239 1253\n1240 1254\n1241 1255\n1242 1256\n1243 1257\n1244 1258\n1245 1259\n1246 1260\n1247 1261\n",
"10\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n2 34\n3 35\n4 36\n5 37\n6 38\n7 39\n8 40\n9 41\n10 42\n11 43\n12 44\n13 45\n14 46\n15 47\n16 48\n17 49\n18 50\n19 51\n20 52\n21 53\n22 54\n23 55\n24 56\n25 57\n26 58\n27 59\n28 60\n29 61\n30 62\n31 63\n32 64\n33 65\n34 66\n35 67\n36 68\n37 69\n38 70\n39 71\n40 72\n41 73\n42 74\n43 75\n44 76\n45 77\n46 78\n47 79\n48 80\n49 81\n50 82\n51 83\n52 84\n53 85\n54 86\n55 87\n56 88\n57 89\n58 90\n59 91\n60 92\n61 93\n62 94\n63 95\n64 96\n65 97\n66 98\n67 99\n68 100\n69 101\n70 102\n71 103\n72 104\n73 105\n74 106\n75 107\n76 108\n77 109\n78 110\n79 111\n80 112\n81 113\n82 114\n83 115\n84 116\n85 117\n86 118\n87 119\n88 120\n89 121\n90 122\n91 123\n92 124\n93 125\n94 126\n95 127\n96 128\n97 129\n98 130\n99 131\n100 132\n101 133\n102 134\n103 135\n104 136\n105 137\n106 138\n107 139\n108 140\n",
"128\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n2 25\n3 26\n4 27\n5 28\n6 29\n7 30\n8 31\n9 32\n10 33\n11 34\n12 35\n13 36\n14 37\n15 38\n16 39\n17 40\n18 41\n19 42\n20 43\n21 44\n22 45\n23 46\n24 47\n25 48\n26 49\n27 50\n28 51\n29 52\n30 53\n31 54\n32 55\n33 56\n34 57\n35 58\n36 59\n37 60\n38 61\n39 62\n40 63\n41 64\n42 65\n43 66\n44 67\n45 68\n46 69\n47 70\n48 71\n49 72\n50 73\n51 74\n52 75\n53 76\n54 77\n55 78\n56 79\n57 80\n58 81\n59 82\n60 83\n61 84\n62 85\n63 86\n64 87\n65 88\n66 89\n67 90\n68 91\n69 92\n70 93\n71 94\n72 95\n73 96\n74 97\n75 98\n76 99\n77 100\n78 101\n79 102\n80 103\n81 104\n82 105\n83 106\n84 107\n85 108\n86 109\n87 110\n88 111\n89 112\n90 113\n91 114\n92 115\n93 116\n94 117\n95 118\n96 119\n97 120\n98 121\n99 122\n100 123\n101 124\n102 125\n103 126\n104 127\n105 128\n106 129\n107 130\n108 131\n109 132\n110 133\n111 134\n112 135\n113 136\n114 137\n115 138\n116 139\n117 140\n118 141\n119 142\n120 143\n121 144\n122 145\n123 146\n124 147\n125 148\n126 149\n127 150\n128 151\n129 152\n130 153\n131 154\n132 155\n133 156\n134 157\n135 158\n136 159\n137 160\n138 161\n139 162\n140 163\n141 164\n142 165\n143 166\n144 167\n145 168\n146 169\n147 170\n148 171\n149 172\n150 173\n151 174\n152 175\n153 176\n154 177\n155 178\n156 179\n157 180\n158 181\n159 182\n160 183\n161 184\n162 185\n163 186\n164 187\n165 188\n166 189\n167 190\n168 191\n169 192\n170 193\n171 194\n172 195\n173 196\n174 197\n175 198\n176 199\n177 200\n178 201\n179 202\n180 203\n181 204\n182 205\n183 206\n184 207\n185 208\n186 209\n187 210\n188 211\n189 212\n190 213\n191 214\n192 215\n193 216\n194 217\n195 218\n196 219\n197 220\n198 221\n199 222\n200 223\n201 224\n202 225\n203 226\n204 227\n205 228\n206 229\n207 230\n208 231\n209 232\n210 233\n211 234\n212 235\n213 236\n214 237\n215 238\n216 239\n217 240\n218 241\n219 242\n220 243\n221 244\n222 245\n223 246\n224 247\n225 248\n226 249\n227 250\n228 251\n229 252\n230 253\n231 254\n232 255\n233 256\n234 257\n235 258\n236 259\n237 260\n238 261\n239 262\n240 263\n241 264\n242 265\n243 266\n244 267\n245 268\n246 269\n247 270\n248 271\n249 272\n250 273\n251 274\n252 275\n253 276\n254 277\n255 278\n256 279\n257 280\n258 281\n259 282\n260 283\n261 284\n262 285\n263 286\n264 287\n265 288\n266 289\n267 290\n268 291\n269 292\n270 293\n271 294\n272 295\n273 296\n274 297\n275 298\n276 299\n277 300\n278 301\n279 302\n280 303\n281 304\n282 305\n283 306\n284 307\n285 308\n286 309\n287 310\n288 311\n289 312\n290 313\n291 314\n292 315\n293 316\n294 317\n295 318\n296 319\n297 320\n298 321\n299 322\n300 323\n301 324\n302 325\n303 326\n304 327\n305 328\n306 329\n307 330\n308 331\n309 332\n310 333\n311 334\n312 335\n313 336\n314 337\n315 338\n316 339\n317 340\n318 341\n319 342\n320 343\n321 344\n322 345\n323 346\n324 347\n325 348\n326 349\n327 350\n328 351\n329 352\n330 353\n331 354\n332 355\n333 356\n334 357\n335 358\n336 359\n337 360\n338 361\n339 362\n340 363\n341 364\n342 365\n343 366\n344 367\n345 368\n346 369\n347 370\n348 371\n349 372\n350 373\n351 374\n352 375\n353 376\n354 377\n355 378\n356 379\n357 380\n358 381\n359 382\n360 383\n361 384\n362 385\n363 386\n364 387\n365 388\n366 389\n367 390\n368 391\n369 392\n370 393\n371 394\n372 395\n373 396\n374 397\n375 398\n376 399\n377 400\n378 401\n379 402\n380 403\n381 404\n382 405\n383 406\n384 407\n385 408\n386 409\n387 410\n388 411\n389 412\n390 413\n391 414\n392 415\n393 416\n394 417\n395 418\n396 419\n397 420\n398 421\n399 422\n400 423\n401 424\n402 425\n403 426\n404 427\n405 428\n406 429\n407 430\n408 431\n409 432\n410 433\n411 434\n412 435\n413 436\n414 437\n415 438\n416 439\n417 440\n418 441\n419 442\n420 443\n421 444\n422 445\n423 446\n424 447\n425 448\n426 449\n427 450\n428 451\n429 452\n430 453\n431 454\n432 455\n433 456\n434 457\n435 458\n436 459\n437 460\n438 461\n439 462\n440 463\n441 464\n442 465\n443 466\n444 467\n445 468\n446 469\n447 470\n448 471\n449 472\n450 473\n451 474\n452 475\n453 476\n454 477\n455 478\n456 479\n457 480\n458 481\n459 482\n460 483\n461 484\n462 485\n463 486\n464 487\n465 488\n466 489\n467 490\n468 491\n469 492\n470 493\n471 494\n472 495\n473 496\n474 497\n475 498\n476 499\n477 500\n478 501\n479 502\n480 503\n481 504\n482 505\n483 506\n484 507\n485 508\n486 509\n487 510\n488 511\n489 512\n490 513\n491 514\n492 515\n493 516\n494 517\n495 518\n496 519\n497 520\n498 521\n499 522\n500 523\n501 524\n502 525\n503 526\n504 527\n505 528\n506 529\n507 530\n508 531\n509 532\n510 533\n511 534\n512 535\n513 536\n514 537\n515 538\n516 539\n517 540\n518 541\n519 542\n520 543\n521 544\n522 545\n523 546\n524 547\n525 548\n526 549\n527 550\n528 551\n529 552\n530 553\n531 554\n532 555\n533 556\n534 557\n535 558\n536 559\n537 560\n538 561\n539 562\n540 563\n541 564\n542 565\n543 566\n544 567\n545 568\n546 569\n547 570\n548 571\n549 572\n550 573\n551 574\n552 575\n553 576\n554 577\n555 578\n556 579\n557 580\n558 581\n559 582\n560 583\n561 584\n562 585\n563 586\n564 587\n565 588\n566 589\n567 590\n568 591\n569 592\n570 593\n571 594\n572 595\n573 596\n574 597\n575 598\n576 599\n577 600\n578 601\n579 602\n580 603\n581 604\n582 605\n583 606\n584 607\n585 608\n586 609\n587 610\n588 611\n589 612\n590 613\n591 614\n592 615\n593 616\n594 617\n595 618\n596 619\n597 620\n598 621\n599 622\n600 623\n601 624\n602 625\n603 626\n604 627\n605 628\n606 629\n607 630\n608 631\n609 632\n610 633\n611 634\n612 635\n613 636\n614 637\n615 638\n616 639\n617 640\n618 641\n619 642\n620 643\n621 644\n622 645\n623 646\n624 647\n625 648\n626 649\n627 650\n628 651\n629 652\n630 653\n631 654\n632 655\n633 656\n634 657\n635 658\n636 659\n637 660\n638 661\n639 662\n640 663\n641 664\n642 665\n643 666\n644 667\n645 668\n646 669\n647 670\n648 671\n649 672\n650 673\n651 674\n652 675\n653 676\n654 677\n655 678\n656 679\n657 680\n658 681\n659 682\n660 683\n661 684\n662 685\n663 686\n664 687\n665 688\n666 689\n667 690\n668 691\n669 692\n670 693\n671 694\n672 695\n673 696\n674 697\n675 698\n676 699\n677 700\n678 701\n679 702\n680 703\n681 704\n682 705\n683 706\n684 707\n685 708\n686 709\n687 710\n688 711\n689 712\n690 713\n691 714\n692 715\n693 716\n694 717\n695 718\n696 719\n697 720\n698 721\n699 722\n700 723\n701 724\n702 725\n703 726\n704 727\n705 728\n706 729\n707 730\n708 731\n709 732\n710 733\n711 734\n712 735\n713 736\n714 737\n715 738\n716 739\n717 740\n718 741\n719 742\n720 743\n721 744\n722 745\n723 746\n724 747\n725 748\n726 749\n727 750\n728 751\n729 752\n730 753\n731 754\n732 755\n733 756\n734 757\n735 758\n736 759\n737 760\n738 761\n739 762\n740 763\n741 764\n742 765\n743 766\n744 767\n745 768\n746 769\n747 770\n748 771\n749 772\n750 773\n751 774\n752 775\n753 776\n754 777\n755 778\n756 779\n757 780\n758 781\n759 782\n760 783\n761 784\n762 785\n763 786\n764 787\n765 788\n766 789\n767 790\n768 791\n769 792\n770 793\n771 794\n772 795\n773 796\n774 797\n775 798\n776 799\n777 800\n778 801\n779 802\n780 803\n781 804\n782 805\n783 806\n784 807\n785 808\n786 809\n787 810\n788 811\n789 812\n790 813\n791 814\n792 815\n793 816\n794 817\n795 818\n796 819\n797 820\n798 821\n799 822\n800 823\n801 824\n802 825\n803 826\n804 827\n805 828\n806 829\n807 830\n808 831\n809 832\n810 833\n811 834\n812 835\n813 836\n814 837\n815 838\n816 839\n817 840\n818 841\n819 842\n820 843\n821 844\n822 845\n823 846\n824 847\n825 848\n826 849\n827 850\n828 851\n829 852\n830 853\n831 854\n832 855\n833 856\n834 857\n835 858\n836 859\n837 860\n838 861\n839 862\n840 863\n841 864\n842 865\n843 866\n844 867\n845 868\n846 869\n847 870\n848 871\n849 872\n850 873\n851 874\n852 875\n853 876\n854 877\n855 878\n856 879\n857 880\n858 881\n859 882\n860 883\n861 884\n862 885\n863 886\n864 887\n865 888\n866 889\n867 890\n868 891\n869 892\n870 893\n871 894\n872 895\n873 896\n874 897\n875 898\n876 899\n877 900\n878 901\n879 902\n880 903\n881 904\n882 905\n883 906\n884 907\n885 908\n886 909\n887 910\n888 911\n889 912\n890 913\n891 914\n892 915\n893 916\n894 917\n895 918\n896 919\n897 920\n898 921\n899 922\n900 923\n901 924\n902 925\n903 926\n904 927\n905 928\n906 929\n907 930\n908 931\n909 932\n910 933\n911 934\n912 935\n913 936\n914 937\n915 938\n916 939\n917 940\n918 941\n919 942\n920 943\n921 944\n922 945\n923 946\n924 947\n925 948\n926 949\n927 950\n928 951\n929 952\n930 953\n931 954\n932 955\n933 956\n934 957\n935 958\n936 959\n937 960\n938 961\n939 962\n940 963\n941 964\n942 965\n943 966\n944 967\n945 968\n946 969\n947 970\n948 971\n949 972\n950 973\n951 974\n952 975\n953 976\n954 977\n955 978\n956 979\n957 980\n958 981\n959 982\n960 983\n961 984\n962 985\n963 986\n964 987\n965 988\n966 989\n967 990\n968 991\n969 992\n970 993\n971 994\n972 995\n973 996\n974 997\n975 998\n976 999\n977 1000\n978 1001\n979 1002\n980 1003\n981 1004\n982 1005\n983 1006\n984 1007\n985 1008\n986 1009\n987 1010\n988 1011\n989 1012\n990 1013\n991 1014\n992 1015\n993 1016\n994 1017\n995 1018\n996 1019\n997 1020\n998 1021\n999 1022\n1000 1023\n1001 1024\n1002 1025\n1003 1026\n1004 1027\n1005 1028\n1006 1029\n1007 1030\n1008 1031\n1009 1032\n1010 1033\n1011 1034\n1012 1035\n1013 1036\n1014 1037\n1015 1038\n1016 1039\n1017 1040\n1018 1041\n1019 1042\n1020 1043\n1021 1044\n1022 1045\n1023 1046\n1024 1047\n1025 1048\n1026 1049\n1027 1050\n1028 1051\n1029 1052\n1030 1053\n1031 1054\n1032 1055\n1033 1056\n1034 1057\n1035 1058\n1036 1059\n1037 1060\n1038 1061\n1039 1062\n1040 1063\n1041 1064\n1042 1065\n1043 1066\n1044 1067\n1045 1068\n1046 1069\n1047 1070\n1048 1071\n1049 1072\n1050 1073\n1051 1074\n1052 1075\n1053 1076\n1054 1077\n1055 1078\n1056 1079\n1057 1080\n1058 1081\n1059 1082\n1060 1083\n1061 1084\n1062 1085\n1063 1086\n1064 1087\n1065 1088\n1066 1089\n1067 1090\n1068 1091\n1069 1092\n1070 1093\n1071 1094\n1072 1095\n1073 1096\n1074 1097\n1075 1098\n1076 1099\n1077 1100\n1078 1101\n1079 1102\n1080 1103\n1081 1104\n1082 1105\n1083 1106\n1084 1107\n1085 1108\n1086 1109\n1087 1110\n1088 1111\n1089 1112\n1090 1113\n1091 1114\n1092 1115\n1093 1116\n1094 1117\n1095 1118\n1096 1119\n1097 1120\n1098 1121\n1099 1122\n1100 1123\n1101 1124\n1102 1125\n1103 1126\n1104 1127\n1105 1128\n1106 1129\n1107 1130\n1108 1131\n1109 1132\n1110 1133\n1111 1134\n1112 1135\n1113 1136\n1114 1137\n1115 1138\n1116 1139\n1117 1140\n1118 1141\n1119 1142\n1120 1143\n1121 1144\n1122 1145\n1123 1146\n1124 1147\n1125 1148\n1126 1149\n1127 1150\n1128 1151\n1129 1152\n1130 1153\n1131 1154\n1132 1155\n1133 1156\n1134 1157\n1135 1158\n1136 1159\n1137 1160\n1138 1161\n1139 1162\n1140 1163\n1141 1164\n1142 1165\n1143 1166\n1144 1167\n1145 1168\n1146 1169\n1147 1170\n1148 1171\n1149 1172\n1150 1173\n1151 1174\n1152 1175\n1153 1176\n1154 1177\n1155 1178\n1156 1179\n1157 1180\n1158 1181\n1159 1182\n1160 1183\n1161 1184\n1162 1185\n1163 1186\n1164 1187\n1165 1188\n1166 1189\n1167 1190\n1168 1191\n1169 1192\n1170 1193\n1171 1194\n1172 1195\n1173 1196\n1174 1197\n1175 1198\n1176 1199\n1177 1200\n1178 1201\n1179 1202\n1180 1203\n1181 1204\n1182 1205\n1183 1206\n1184 1207\n1185 1208\n1186 1209\n1187 1210\n1188 1211\n1189 1212\n1190 1213\n1191 1214\n1192 1215\n1193 1216\n1194 1217\n1195 1218\n1196 1219\n1197 1220\n1198 1221\n1199 1222\n1200 1223\n1201 1224\n1202 1225\n1203 1226\n1204 1227\n1205 1228\n1206 1229\n1207 1230\n1208 1231\n1209 1232\n1210 1233\n1211 1234\n1212 1235\n1213 1236\n1214 1237\n1215 1238\n1216 1239\n1217 1240\n1218 1241\n1219 1242\n1220 1243\n1221 1244\n1222 1245\n1223 1246\n1224 1247\n1225 1248\n1226 1249\n1227 1250\n1228 1251\n1229 1252\n1230 1253\n1231 1254\n1232 1255\n1233 1256\n1234 1257\n1235 1258\n1236 1259\n1237 1260\n1238 1261\n1239 1262\n1240 1263\n1241 1264\n1242 1265\n1243 1266\n1244 1267\n1245 1268\n1246 1269\n1247 1270\n1248 1271\n1249 1272\n1250 1273\n1251 1274\n1252 1275\n1253 1276\n1254 1277\n1255 1278\n1256 1279\n1257 1280\n1258 1281\n1259 1282\n1260 1283\n1261 1284\n1262 1285\n1263 1286\n1264 1287\n1265 1288\n1266 1289\n1267 1290\n1268 1291\n1269 1292\n1270 1293\n1271 1294\n1272 1295\n1273 1296\n1274 1297\n1275 1298\n1276 1299\n1277 1300\n1278 1301\n1279 1302\n1280 1303\n1281 1304\n1282 1305\n1283 1306\n1284 1307\n1285 1308\n1286 1309\n1287 1310\n1288 1311\n1289 1312\n1290 1313\n1291 1314\n1292 1315\n1293 1316\n1294 1317\n1295 1318\n1296 1319\n1297 1320\n1298 1321\n1299 1322\n1300 1323\n1301 1324\n1302 1325\n1303 1326\n1304 1327\n1305 1328\n1306 1329\n1307 1330\n1308 1331\n1309 1332\n1310 1333\n1311 1334\n1312 1335\n1313 1336\n1314 1337\n1315 1338\n1316 1339\n1317 1340\n1318 1341\n1319 1342\n1320 1343\n1321 1344\n1322 1345\n1323 1346\n1324 1347\n1325 1348\n1326 1349\n1327 1350\n1328 1351\n1329 1352\n1330 1353\n1331 1354\n1332 1355\n1333 1356\n1334 1357\n1335 1358\n1336 1359\n1337 1360\n1338 1361\n1339 1362\n1340 1363\n1341 1364\n1342 1365\n1343 1366\n1344 1367\n1345 1368\n1346 1369\n1347 1370\n1348 1371\n1349 1372\n1350 1373\n1351 1374\n1352 1375\n1353 1376\n1354 1377\n1355 1378\n1356 1379\n1357 1380\n1358 1381\n1359 1382\n1360 1383\n1361 1384\n1362 1385\n1363 1386\n1364 1387\n1365 1388\n1366 1389\n1367 1390\n1368 1391\n1369 1392\n1370 1393\n1371 1394\n1372 1395\n1373 1396\n1374 1397\n1375 1398\n1376 1399\n1377 1400\n1378 1401\n1379 1402\n1380 1403\n1381 1404\n1382 1405\n1383 1406\n1384 1407\n1385 1408\n1386 1409\n1387 1410\n1388 1411\n1389 1412\n1390 1413\n1391 1414\n1392 1415\n1393 1416\n1394 1417\n1395 1418\n1396 1419\n1397 1420\n1398 1421\n1399 1422\n1400 1423\n1401 1424\n1402 1425\n1403 1426\n1404 1427\n1405 1428\n1406 1429\n1407 1430\n1408 1431\n1409 1432\n1410 1433\n1411 1434\n1412 1435\n1413 1436\n1414 1437\n1415 1438\n1416 1439\n1417 1440\n1418 1441\n1419 1442\n1420 1443\n1421 1444\n1422 1445\n1423 1446\n1424 1447\n1425 1448\n1426 1449\n1427 1450\n1428 1451\n1429 1452\n1430 1453\n1431 1454\n1432 1455\n1433 1456\n1434 1457\n",
"8\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n2 271\n3 272\n4 273\n5 274\n6 275\n7 276\n8 277\n9 278\n10 279\n11 280\n12 281\n13 282\n14 283\n15 284\n16 285\n17 286\n18 287\n19 288\n20 289\n21 290\n22 291\n23 292\n24 293\n25 294\n26 295\n27 296\n28 297\n29 298\n30 299\n31 300\n32 301\n33 302\n34 303\n35 304\n36 305\n37 306\n38 307\n39 308\n40 309\n41 310\n42 311\n43 312\n44 313\n45 314\n46 315\n47 316\n48 317\n49 318\n50 319\n51 320\n52 321\n53 322\n54 323\n55 324\n56 325\n57 326\n58 327\n59 328\n60 329\n61 330\n62 331\n63 332\n64 333\n65 334\n66 335\n67 336\n68 337\n69 338\n70 339\n71 340\n72 341\n73 342\n74 343\n75 344\n76 345\n77 346\n78 347\n79 348\n80 349\n81 350\n82 351\n83 352\n84 353\n85 354\n86 355\n87 356\n88 357\n89 358\n90 359\n91 360\n92 361\n93 362\n94 363\n95 364\n96 365\n97 366\n98 367\n99 368\n100 369\n101 370\n102 371\n103 372\n104 373\n105 374\n106 375\n107 376\n108 377\n109 378\n110 379\n111 380\n112 381\n113 382\n114 383\n115 384\n116 385\n117 386\n118 387\n119 388\n120 389\n121 390\n122 391\n123 392\n124 393\n125 394\n126 395\n127 396\n128 397\n129 398\n130 399\n131 400\n132 401\n133 402\n134 403\n135 404\n136 405\n137 406\n138 407\n139 408\n140 409\n141 410\n142 411\n143 412\n144 413\n145 414\n146 415\n147 416\n148 417\n149 418\n150 419\n151 420\n152 421\n153 422\n154 423\n155 424\n156 425\n157 426\n158 427\n159 428\n160 429\n161 430\n162 431\n163 432\n164 433\n165 434\n166 435\n167 436\n168 437\n169 438\n170 439\n171 440\n172 441\n173 442\n174 443\n175 444\n176 445\n177 446\n178 447\n179 448\n180 449\n181 450\n182 451\n183 452\n184 453\n185 454\n186 455\n187 456\n188 457\n189 458\n190 459\n191 460\n192 461\n193 462\n194 463\n195 464\n196 465\n197 466\n198 467\n199 468\n200 469\n201 470\n202 471\n203 472\n204 473\n205 474\n206 475\n207 476\n208 477\n209 478\n210 479\n211 480\n212 481\n213 482\n214 483\n215 484\n216 485\n217 486\n218 487\n219 488\n220 489\n221 490\n222 491\n223 492\n224 493\n225 494\n226 495\n227 496\n228 497\n229 498\n230 499\n231 500\n232 501\n233 502\n234 503\n235 504\n236 505\n237 506\n238 507\n239 508\n240 509\n241 510\n242 511\n243 512\n244 513\n245 514\n246 515\n247 516\n248 517\n249 518\n250 519\n251 520\n252 521\n253 522\n254 523\n255 524\n256 525\n257 526\n258 527\n259 528\n260 529\n261 530\n262 531\n263 532\n264 533\n265 534\n266 535\n267 536\n268 537\n269 538\n270 539\n271 540\n272 541\n273 542\n274 543\n275 544\n276 545\n277 546\n278 547\n279 548\n280 549\n281 550\n282 551\n283 552\n284 553\n285 554\n286 555\n287 556\n288 557\n289 558\n290 559\n291 560\n292 561\n293 562\n294 563\n295 564\n296 565\n297 566\n298 567\n299 568\n300 569\n301 570\n302 571\n303 572\n304 573\n305 574\n306 575\n307 576\n308 577\n309 578\n310 579\n311 580\n312 581\n313 582\n314 583\n315 584\n316 585\n317 586\n318 587\n319 588\n320 589\n321 590\n322 591\n323 592\n324 593\n325 594\n326 595\n327 596\n328 597\n329 598\n330 599\n331 600\n332 601\n333 602\n334 603\n335 604\n336 605\n337 606\n338 607\n339 608\n340 609\n341 610\n342 611\n343 612\n344 613\n345 614\n346 615\n347 616\n348 617\n349 618\n350 619\n351 620\n352 621\n353 622\n354 623\n355 624\n356 625\n357 626\n358 627\n359 628\n360 629\n361 630\n362 631\n363 632\n364 633\n365 634\n366 635\n367 636\n368 637\n369 638\n370 639\n371 640\n372 641\n373 642\n374 643\n375 644\n376 645\n377 646\n378 647\n379 648\n380 649\n381 650\n382 651\n383 652\n384 653\n385 654\n386 655\n387 656\n388 657\n389 658\n390 659\n391 660\n392 661\n393 662\n394 663\n395 664\n396 665\n397 666\n398 667\n399 668\n400 669\n401 670\n402 671\n403 672\n404 673\n405 674\n406 675\n407 676\n408 677\n409 678\n410 679\n411 680\n412 681\n413 682\n414 683\n415 684\n416 685\n417 686\n418 687\n419 688\n420 689\n421 690\n422 691\n423 692\n424 693\n425 694\n426 695\n427 696\n428 697\n429 698\n430 699\n431 700\n432 701\n433 702\n434 703\n435 704\n436 705\n437 706\n438 707\n439 708\n440 709\n441 710\n442 711\n443 712\n444 713\n445 714\n446 715\n447 716\n448 717\n449 718\n450 719\n451 720\n452 721\n453 722\n454 723\n455 724\n456 725\n457 726\n458 727\n459 728\n460 729\n461 730\n462 731\n463 732\n464 733\n465 734\n466 735\n467 736\n468 737\n469 738\n470 739\n471 740\n472 741\n473 742\n474 743\n475 744\n476 745\n477 746\n478 747\n479 748\n480 749\n481 750\n482 751\n483 752\n484 753\n485 754\n486 755\n487 756\n488 757\n489 758\n490 759\n491 760\n492 761\n493 762\n494 763\n495 764\n496 765\n497 766\n498 767\n499 768\n500 769\n501 770\n502 771\n503 772\n504 773\n505 774\n506 775\n507 776\n508 777\n509 778\n510 779\n511 780\n512 781\n513 782\n514 783\n515 784\n516 785\n517 786\n518 787\n519 788\n520 789\n521 790\n522 791\n523 792\n524 793\n525 794\n526 795\n527 796\n528 797\n529 798\n530 799\n531 800\n532 801\n533 802\n534 803\n535 804\n536 805\n537 806\n538 807\n539 808\n540 809\n541 810\n542 811\n543 812\n544 813\n545 814\n546 815\n547 816\n548 817\n549 818\n550 819\n551 820\n552 821\n553 822\n554 823\n555 824\n556 825\n557 826\n558 827\n559 828\n560 829\n561 830\n562 831\n563 832\n564 833\n565 834\n566 835\n567 836\n568 837\n569 838\n570 839\n571 840\n572 841\n573 842\n574 843\n575 844\n576 845\n577 846\n578 847\n579 848\n580 849\n581 850\n582 851\n583 852\n584 853\n585 854\n586 855\n587 856\n588 857\n589 858\n590 859\n591 860\n592 861\n593 862\n594 863\n595 864\n596 865\n597 866\n598 867\n599 868\n600 869\n601 870\n602 871\n603 872\n604 873\n605 874\n606 875\n607 876\n608 877\n609 878\n610 879\n611 880\n612 881\n613 882\n614 883\n615 884\n616 885\n617 886\n618 887\n619 888\n620 889\n621 890\n622 891\n623 892\n624 893\n625 894\n626 895\n627 896\n628 897\n629 898\n630 899\n631 900\n632 901\n633 902\n634 903\n635 904\n636 905\n637 906\n638 907\n639 908\n640 909\n641 910\n642 911\n643 912\n644 913\n645 914\n646 915\n647 916\n648 917\n649 918\n650 919\n651 920\n652 921\n653 922\n654 923\n655 924\n656 925\n657 926\n658 927\n659 928\n660 929\n661 930\n662 931\n663 932\n664 933\n665 934\n666 935\n667 936\n668 937\n669 938\n670 939\n671 940\n672 941\n673 942\n674 943\n675 944\n676 945\n677 946\n678 947\n679 948\n680 949\n681 950\n682 951\n683 952\n684 953\n685 954\n686 955\n687 956\n688 957\n689 958\n690 959\n691 960\n692 961\n693 962\n694 963\n695 964\n696 965\n697 966\n698 967\n699 968\n700 969\n701 970\n702 971\n703 972\n704 973\n705 974\n706 975\n707 976\n708 977\n709 978\n710 979\n711 980\n712 981\n713 982\n714 983\n715 984\n716 985\n717 986\n718 987\n719 988\n720 989\n721 990\n722 991\n723 992\n724 993\n725 994\n726 995\n727 996\n728 997\n729 998\n730 999\n731 1000\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n2 490\n3 491\n4 492\n5 493\n6 494\n7 495\n8 496\n9 497\n10 498\n11 499\n12 500\n13 501\n14 502\n15 503\n16 504\n17 505\n18 506\n19 507\n20 508\n21 509\n22 510\n23 511\n24 512\n25 513\n26 514\n27 515\n28 516\n29 517\n30 518\n31 519\n32 520\n33 521\n34 522\n35 523\n36 524\n37 525\n38 526\n39 527\n40 528\n41 529\n42 530\n43 531\n44 532\n45 533\n46 534\n47 535\n48 536\n49 537\n50 538\n51 539\n52 540\n53 541\n54 542\n55 543\n56 544\n57 545\n58 546\n59 547\n60 548\n61 549\n62 550\n63 551\n64 552\n65 553\n66 554\n67 555\n68 556\n69 557\n70 558\n71 559\n72 560\n73 561\n74 562\n75 563\n76 564\n77 565\n78 566\n79 567\n80 568\n81 569\n82 570\n83 571\n84 572\n85 573\n86 574\n87 575\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n2 68\n3 69\n4 70\n5 71\n6 72\n7 73\n8 74\n9 75\n10 76\n11 77\n12 78\n13 79\n14 80\n15 81\n16 82\n17 83\n18 84\n19 85\n20 86\n21 87\n22 88\n23 89\n24 90\n25 91\n26 92\n27 93\n28 94\n29 95\n30 96\n31 97\n32 98\n33 99\n34 100\n35 101\n",
"6\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n2 370\n3 371\n4 372\n5 373\n6 374\n7 375\n8 376\n9 377\n10 378\n11 379\n12 380\n13 381\n14 382\n15 383\n16 384\n17 385\n18 386\n19 387\n20 388\n21 389\n22 390\n23 391\n24 392\n25 393\n26 394\n27 395\n28 396\n29 397\n30 398\n31 399\n32 400\n33 401\n34 402\n35 403\n36 404\n37 405\n38 406\n39 407\n40 408\n41 409\n42 410\n43 411\n44 412\n45 413\n46 414\n47 415\n48 416\n49 417\n50 418\n51 419\n52 420\n53 421\n54 422\n55 423\n56 424\n57 425\n58 426\n59 427\n60 428\n61 429\n62 430\n63 431\n64 432\n65 433\n66 434\n67 435\n68 436\n69 437\n70 438\n71 439\n72 440\n73 441\n74 442\n75 443\n76 444\n77 445\n78 446\n79 447\n80 448\n81 449\n82 450\n83 451\n84 452\n85 453\n86 454\n87 455\n88 456\n89 457\n90 458\n91 459\n92 460\n93 461\n94 462\n95 463\n96 464\n97 465\n98 466\n99 467\n100 468\n101 469\n102 470\n103 471\n104 472\n105 473\n106 474\n107 475\n108 476\n109 477\n110 478\n111 479\n112 480\n113 481\n114 482\n115 483\n116 484\n117 485\n118 486\n119 487\n120 488\n121 489\n122 490\n123 491\n124 492\n125 493\n126 494\n127 495\n128 496\n129 497\n130 498\n131 499\n132 500\n133 501\n134 502\n135 503\n136 504\n137 505\n138 506\n139 507\n140 508\n141 509\n142 510\n143 511\n144 512\n145 513\n146 514\n147 515\n148 516\n149 517\n150 518\n151 519\n152 520\n153 521\n154 522\n155 523\n156 524\n157 525\n158 526\n159 527\n160 528\n161 529\n162 530\n163 531\n164 532\n165 533\n166 534\n167 535\n168 536\n169 537\n170 538\n171 539\n172 540\n173 541\n174 542\n175 543\n176 544\n177 545\n178 546\n179 547\n180 548\n181 549\n182 550\n183 551\n184 552\n185 553\n186 554\n187 555\n188 556\n189 557\n190 558\n191 559\n192 560\n193 561\n194 562\n195 563\n196 564\n197 565\n198 566\n199 567\n200 568\n201 569\n202 570\n203 571\n204 572\n205 573\n206 574\n207 575\n208 576\n209 577\n210 578\n211 579\n212 580\n213 581\n214 582\n215 583\n216 584\n217 585\n218 586\n219 587\n220 588\n221 589\n222 590\n223 591\n224 592\n225 593\n226 594\n227 595\n228 596\n229 597\n230 598\n231 599\n232 600\n233 601\n234 602\n235 603\n236 604\n237 605\n238 606\n239 607\n240 608\n241 609\n242 610\n243 611\n244 612\n245 613\n246 614\n247 615\n248 616\n249 617\n250 618\n251 619\n252 620\n253 621\n254 622\n255 623\n256 624\n257 625\n258 626\n259 627\n260 628\n261 629\n262 630\n263 631\n264 632\n265 633\n266 634\n267 635\n268 636\n269 637\n270 638\n271 639\n272 640\n273 641\n274 642\n275 643\n276 644\n277 645\n278 646\n279 647\n280 648\n281 649\n282 650\n283 651\n284 652\n285 653\n286 654\n287 655\n288 656\n289 657\n290 658\n291 659\n292 660\n293 661\n294 662\n295 663\n296 664\n297 665\n298 666\n299 667\n300 668\n301 669\n302 670\n303 671\n304 672\n305 673\n306 674\n307 675\n308 676\n309 677\n310 678\n311 679\n312 680\n313 681\n314 682\n315 683\n316 684\n317 685\n318 686\n319 687\n320 688\n321 689\n322 690\n323 691\n324 692\n325 693\n326 694\n327 695\n328 696\n329 697\n330 698\n331 699\n332 700\n333 701\n334 702\n335 703\n336 704\n337 705\n338 706\n339 707\n340 708\n341 709\n342 710\n343 711\n344 712\n345 713\n346 714\n347 715\n348 716\n349 717\n350 718\n351 719\n352 720\n353 721\n354 722\n355 723\n356 724\n357 725\n358 726\n359 727\n360 728\n361 729\n362 730\n363 731\n364 732\n365 733\n366 734\n367 735\n368 736\n369 737\n370 738\n371 739\n372 740\n373 741\n374 742\n375 743\n376 744\n377 745\n378 746\n379 747\n380 748\n381 749\n382 750\n383 751\n384 752\n385 753\n386 754\n387 755\n388 756\n389 757\n390 758\n391 759\n392 760\n393 761\n394 762\n395 763\n396 764\n397 765\n398 766\n399 767\n400 768\n401 769\n402 770\n403 771\n404 772\n405 773\n406 774\n407 775\n408 776\n409 777\n410 778\n411 779\n412 780\n413 781\n414 782\n415 783\n416 784\n417 785\n418 786\n419 787\n420 788\n421 789\n422 790\n423 791\n424 792\n425 793\n426 794\n427 795\n428 796\n429 797\n430 798\n431 799\n432 800\n433 801\n434 802\n435 803\n436 804\n437 805\n438 806\n439 807\n440 808\n441 809\n442 810\n443 811\n444 812\n445 813\n446 814\n447 815\n448 816\n449 817\n450 818\n451 819\n452 820\n453 821\n454 822\n455 823\n456 824\n457 825\n458 826\n459 827\n460 828\n461 829\n462 830\n463 831\n464 832\n465 833\n466 834\n467 835\n468 836\n469 837\n470 838\n471 839\n472 840\n473 841\n474 842\n475 843\n476 844\n477 845\n478 846\n479 847\n480 848\n481 849\n482 850\n483 851\n484 852\n485 853\n486 854\n487 855\n488 856\n489 857\n490 858\n491 859\n492 860\n493 861\n494 862\n495 863\n496 864\n497 865\n498 866\n499 867\n500 868\n501 869\n502 870\n503 871\n504 872\n505 873\n506 874\n507 875\n508 876\n509 877\n510 878\n511 879\n512 880\n513 881\n514 882\n515 883\n516 884\n517 885\n518 886\n519 887\n520 888\n521 889\n522 890\n523 891\n524 892\n525 893\n526 894\n527 895\n528 896\n529 897\n530 898\n531 899\n532 900\n533 901\n534 902\n535 903\n536 904\n537 905\n538 906\n539 907\n540 908\n541 909\n542 910\n543 911\n544 912\n545 913\n546 914\n547 915\n548 916\n549 917\n550 918\n551 919\n552 920\n553 921\n554 922\n555 923\n556 924\n557 925\n558 926\n559 927\n560 928\n561 929\n562 930\n563 931\n564 932\n565 933\n566 934\n567 935\n568 936\n569 937\n570 938\n571 939\n572 940\n573 941\n574 942\n575 943\n576 944\n577 945\n578 946\n579 947\n580 948\n581 949\n582 950\n583 951\n584 952\n585 953\n586 954\n587 955\n588 956\n589 957\n590 958\n591 959\n592 960\n593 961\n594 962\n595 963\n596 964\n597 965\n598 966\n599 967\n600 968\n601 969\n602 970\n603 971\n604 972\n605 973\n606 974\n607 975\n608 976\n609 977\n610 978\n611 979\n612 980\n613 981\n614 982\n615 983\n616 984\n617 985\n618 986\n619 987\n620 988\n621 989\n622 990\n623 991\n624 992\n625 993\n626 994\n627 995\n628 996\n629 997\n630 998\n631 999\n632 1000\n633 1001\n634 1002\n635 1003\n636 1004\n637 1005\n638 1006\n639 1007\n640 1008\n641 1009\n642 1010\n643 1011\n644 1012\n645 1013\n646 1014\n647 1015\n648 1016\n649 1017\n650 1018\n651 1019\n652 1020\n653 1021\n654 1022\n655 1023\n656 1024\n657 1025\n658 1026\n659 1027\n660 1028\n661 1029\n662 1030\n663 1031\n664 1032\n665 1033\n666 1034\n667 1035\n668 1036\n669 1037\n670 1038\n671 1039\n672 1040\n673 1041\n674 1042\n675 1043\n676 1044\n677 1045\n678 1046\n679 1047\n680 1048\n681 1049\n682 1050\n683 1051\n684 1052\n685 1053\n686 1054\n687 1055\n688 1056\n689 1057\n690 1058\n691 1059\n692 1060\n693 1061\n694 1062\n695 1063\n696 1064\n697 1065\n698 1066\n699 1067\n700 1068\n701 1069\n702 1070\n703 1071\n704 1072\n705 1073\n706 1074\n707 1075\n708 1076\n709 1077\n710 1078\n711 1079\n712 1080\n713 1081\n714 1082\n715 1083\n716 1084\n717 1085\n718 1086\n719 1087\n720 1088\n721 1089\n722 1090\n723 1091\n724 1092\n725 1093\n726 1094\n727 1095\n728 1096\n729 1097\n730 1098\n731 1099\n732 1100\n",
"8\n1 2\n1 3\n1 4\n2 5\n3 6\n4 7\n5 8\n6 9\n7 10\n8 11\n9 12\n",
"250\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n2 10\n3 11\n4 12\n5 13\n6 14\n7 15\n8 16\n9 17\n10 18\n11 19\n12 20\n13 21\n14 22\n15 23\n16 24\n17 25\n18 26\n19 27\n20 28\n21 29\n22 30\n23 31\n24 32\n25 33\n26 34\n27 35\n28 36\n29 37\n30 38\n31 39\n32 40\n33 41\n34 42\n35 43\n36 44\n37 45\n38 46\n39 47\n40 48\n41 49\n42 50\n43 51\n44 52\n45 53\n46 54\n47 55\n48 56\n49 57\n50 58\n51 59\n52 60\n53 61\n54 62\n55 63\n56 64\n57 65\n58 66\n59 67\n60 68\n61 69\n62 70\n63 71\n64 72\n65 73\n66 74\n67 75\n68 76\n69 77\n70 78\n71 79\n72 80\n73 81\n74 82\n75 83\n76 84\n77 85\n78 86\n79 87\n80 88\n81 89\n82 90\n83 91\n84 92\n85 93\n86 94\n87 95\n88 96\n89 97\n90 98\n91 99\n92 100\n93 101\n94 102\n95 103\n96 104\n97 105\n98 106\n99 107\n100 108\n101 109\n102 110\n103 111\n104 112\n105 113\n106 114\n107 115\n108 116\n109 117\n110 118\n111 119\n112 120\n113 121\n114 122\n115 123\n116 124\n117 125\n118 126\n119 127\n120 128\n121 129\n122 130\n123 131\n124 132\n125 133\n126 134\n127 135\n128 136\n129 137\n130 138\n131 139\n132 140\n133 141\n134 142\n135 143\n136 144\n137 145\n138 146\n139 147\n140 148\n141 149\n142 150\n143 151\n144 152\n145 153\n146 154\n147 155\n148 156\n149 157\n150 158\n151 159\n152 160\n153 161\n154 162\n155 163\n156 164\n157 165\n158 166\n159 167\n160 168\n161 169\n162 170\n163 171\n164 172\n165 173\n166 174\n167 175\n168 176\n169 177\n170 178\n171 179\n172 180\n173 181\n174 182\n175 183\n176 184\n177 185\n178 186\n179 187\n180 188\n181 189\n182 190\n183 191\n184 192\n185 193\n186 194\n187 195\n188 196\n189 197\n190 198\n191 199\n192 200\n193 201\n194 202\n195 203\n196 204\n197 205\n198 206\n199 207\n200 208\n201 209\n202 210\n203 211\n204 212\n205 213\n206 214\n207 215\n208 216\n209 217\n210 218\n211 219\n212 220\n213 221\n214 222\n215 223\n216 224\n217 225\n218 226\n219 227\n220 228\n221 229\n222 230\n223 231\n224 232\n225 233\n226 234\n227 235\n228 236\n229 237\n230 238\n231 239\n232 240\n233 241\n234 242\n235 243\n236 244\n237 245\n238 246\n239 247\n240 248\n241 249\n242 250\n243 251\n244 252\n245 253\n246 254\n247 255\n248 256\n249 257\n250 258\n251 259\n252 260\n253 261\n254 262\n255 263\n256 264\n257 265\n258 266\n259 267\n260 268\n261 269\n262 270\n263 271\n264 272\n265 273\n266 274\n267 275\n268 276\n269 277\n270 278\n271 279\n272 280\n273 281\n274 282\n275 283\n276 284\n277 285\n278 286\n279 287\n280 288\n281 289\n282 290\n283 291\n284 292\n285 293\n286 294\n287 295\n288 296\n289 297\n290 298\n291 299\n292 300\n293 301\n294 302\n295 303\n296 304\n297 305\n298 306\n299 307\n300 308\n301 309\n302 310\n303 311\n304 312\n305 313\n306 314\n307 315\n308 316\n309 317\n310 318\n311 319\n312 320\n313 321\n314 322\n315 323\n316 324\n317 325\n318 326\n319 327\n320 328\n321 329\n322 330\n323 331\n324 332\n325 333\n326 334\n327 335\n328 336\n329 337\n330 338\n331 339\n332 340\n333 341\n334 342\n335 343\n336 344\n337 345\n338 346\n339 347\n340 348\n341 349\n342 350\n343 351\n344 352\n345 353\n346 354\n347 355\n348 356\n349 357\n350 358\n351 359\n352 360\n353 361\n354 362\n355 363\n356 364\n357 365\n358 366\n359 367\n360 368\n361 369\n362 370\n363 371\n364 372\n365 373\n366 374\n367 375\n368 376\n369 377\n370 378\n371 379\n372 380\n373 381\n374 382\n375 383\n376 384\n377 385\n378 386\n379 387\n380 388\n381 389\n382 390\n383 391\n384 392\n385 393\n386 394\n387 395\n388 396\n389 397\n390 398\n391 399\n392 400\n393 401\n394 402\n395 403\n396 404\n397 405\n398 406\n399 407\n400 408\n401 409\n402 410\n403 411\n404 412\n405 413\n406 414\n407 415\n408 416\n409 417\n410 418\n411 419\n412 420\n413 421\n414 422\n415 423\n416 424\n417 425\n418 426\n419 427\n420 428\n421 429\n422 430\n423 431\n424 432\n425 433\n426 434\n427 435\n428 436\n429 437\n430 438\n431 439\n432 440\n433 441\n434 442\n435 443\n436 444\n437 445\n438 446\n439 447\n440 448\n441 449\n442 450\n443 451\n444 452\n445 453\n446 454\n447 455\n448 456\n449 457\n450 458\n451 459\n452 460\n453 461\n454 462\n455 463\n456 464\n457 465\n458 466\n459 467\n460 468\n461 469\n462 470\n463 471\n464 472\n465 473\n466 474\n467 475\n468 476\n469 477\n470 478\n471 479\n472 480\n473 481\n474 482\n475 483\n476 484\n477 485\n478 486\n479 487\n480 488\n481 489\n482 490\n483 491\n484 492\n485 493\n486 494\n487 495\n488 496\n489 497\n490 498\n491 499\n492 500\n493 501\n494 502\n495 503\n496 504\n497 505\n498 506\n499 507\n500 508\n501 509\n502 510\n503 511\n504 512\n505 513\n506 514\n507 515\n508 516\n509 517\n510 518\n511 519\n512 520\n513 521\n514 522\n515 523\n516 524\n517 525\n518 526\n519 527\n520 528\n521 529\n522 530\n523 531\n524 532\n525 533\n526 534\n527 535\n528 536\n529 537\n530 538\n531 539\n532 540\n533 541\n534 542\n535 543\n536 544\n537 545\n538 546\n539 547\n540 548\n541 549\n542 550\n543 551\n544 552\n545 553\n546 554\n547 555\n548 556\n549 557\n550 558\n551 559\n552 560\n553 561\n554 562\n555 563\n556 564\n557 565\n558 566\n559 567\n560 568\n561 569\n562 570\n563 571\n564 572\n565 573\n566 574\n567 575\n568 576\n569 577\n570 578\n571 579\n572 580\n573 581\n574 582\n575 583\n576 584\n577 585\n578 586\n579 587\n580 588\n581 589\n582 590\n583 591\n584 592\n585 593\n586 594\n587 595\n588 596\n589 597\n590 598\n591 599\n592 600\n593 601\n594 602\n595 603\n596 604\n597 605\n598 606\n599 607\n600 608\n601 609\n602 610\n603 611\n604 612\n605 613\n606 614\n607 615\n608 616\n609 617\n610 618\n611 619\n612 620\n613 621\n614 622\n615 623\n616 624\n617 625\n618 626\n619 627\n620 628\n621 629\n622 630\n623 631\n624 632\n625 633\n626 634\n627 635\n628 636\n629 637\n630 638\n631 639\n632 640\n633 641\n634 642\n635 643\n636 644\n637 645\n638 646\n639 647\n640 648\n641 649\n642 650\n643 651\n644 652\n645 653\n646 654\n647 655\n648 656\n649 657\n650 658\n651 659\n652 660\n653 661\n654 662\n655 663\n656 664\n657 665\n658 666\n659 667\n660 668\n661 669\n662 670\n663 671\n664 672\n665 673\n666 674\n667 675\n668 676\n669 677\n670 678\n671 679\n672 680\n673 681\n674 682\n675 683\n676 684\n677 685\n678 686\n679 687\n680 688\n681 689\n682 690\n683 691\n684 692\n685 693\n686 694\n687 695\n688 696\n689 697\n690 698\n691 699\n692 700\n693 701\n694 702\n695 703\n696 704\n697 705\n698 706\n699 707\n700 708\n701 709\n702 710\n703 711\n704 712\n705 713\n706 714\n707 715\n708 716\n709 717\n710 718\n711 719\n712 720\n713 721\n714 722\n715 723\n716 724\n717 725\n718 726\n719 727\n720 728\n721 729\n722 730\n723 731\n724 732\n725 733\n726 734\n727 735\n728 736\n729 737\n730 738\n731 739\n732 740\n733 741\n734 742\n735 743\n736 744\n737 745\n738 746\n739 747\n740 748\n741 749\n742 750\n743 751\n744 752\n745 753\n746 754\n747 755\n748 756\n749 757\n750 758\n751 759\n752 760\n753 761\n754 762\n755 763\n756 764\n757 765\n758 766\n759 767\n760 768\n761 769\n762 770\n763 771\n764 772\n765 773\n766 774\n767 775\n768 776\n769 777\n770 778\n771 779\n772 780\n773 781\n774 782\n775 783\n776 784\n777 785\n778 786\n779 787\n780 788\n781 789\n782 790\n783 791\n784 792\n785 793\n786 794\n787 795\n788 796\n789 797\n790 798\n791 799\n792 800\n793 801\n794 802\n795 803\n796 804\n797 805\n798 806\n799 807\n800 808\n801 809\n802 810\n803 811\n804 812\n805 813\n806 814\n807 815\n808 816\n809 817\n810 818\n811 819\n812 820\n813 821\n814 822\n815 823\n816 824\n817 825\n818 826\n819 827\n820 828\n821 829\n822 830\n823 831\n824 832\n825 833\n826 834\n827 835\n828 836\n829 837\n830 838\n831 839\n832 840\n833 841\n834 842\n835 843\n836 844\n837 845\n838 846\n839 847\n840 848\n841 849\n842 850\n843 851\n844 852\n845 853\n846 854\n847 855\n848 856\n849 857\n850 858\n851 859\n852 860\n853 861\n854 862\n855 863\n856 864\n857 865\n858 866\n859 867\n860 868\n861 869\n862 870\n863 871\n864 872\n865 873\n866 874\n867 875\n868 876\n869 877\n870 878\n871 879\n872 880\n873 881\n874 882\n875 883\n876 884\n877 885\n878 886\n879 887\n880 888\n881 889\n882 890\n883 891\n884 892\n885 893\n886 894\n887 895\n888 896\n889 897\n890 898\n891 899\n892 900\n893 901\n894 902\n895 903\n896 904\n897 905\n898 906\n899 907\n900 908\n901 909\n902 910\n903 911\n904 912\n905 913\n906 914\n907 915\n908 916\n909 917\n910 918\n911 919\n912 920\n913 921\n914 922\n915 923\n916 924\n917 925\n918 926\n919 927\n920 928\n921 929\n922 930\n923 931\n924 932\n925 933\n926 934\n927 935\n928 936\n929 937\n930 938\n931 939\n932 940\n933 941\n934 942\n935 943\n936 944\n937 945\n938 946\n939 947\n940 948\n941 949\n942 950\n943 951\n944 952\n945 953\n946 954\n947 955\n948 956\n949 957\n950 958\n951 959\n952 960\n953 961\n954 962\n955 963\n956 964\n957 965\n958 966\n959 967\n960 968\n961 969\n962 970\n963 971\n964 972\n965 973\n966 974\n967 975\n968 976\n969 977\n970 978\n971 979\n972 980\n973 981\n974 982\n975 983\n976 984\n977 985\n978 986\n979 987\n980 988\n981 989\n982 990\n983 991\n984 992\n985 993\n986 994\n987 995\n988 996\n989 997\n990 998\n991 999\n992 1000\n",
"8\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n2 273\n3 274\n4 275\n5 276\n6 277\n7 278\n8 279\n9 280\n10 281\n11 282\n12 283\n13 284\n14 285\n15 286\n16 287\n17 288\n18 289\n19 290\n20 291\n21 292\n22 293\n23 294\n24 295\n25 296\n26 297\n27 298\n28 299\n29 300\n30 301\n31 302\n32 303\n33 304\n34 305\n35 306\n36 307\n37 308\n38 309\n39 310\n40 311\n41 312\n42 313\n43 314\n44 315\n45 316\n46 317\n47 318\n48 319\n49 320\n50 321\n51 322\n52 323\n53 324\n54 325\n55 326\n56 327\n57 328\n58 329\n59 330\n60 331\n61 332\n62 333\n63 334\n64 335\n65 336\n66 337\n67 338\n68 339\n69 340\n70 341\n71 342\n72 343\n73 344\n74 345\n75 346\n76 347\n77 348\n78 349\n79 350\n80 351\n81 352\n82 353\n83 354\n84 355\n85 356\n86 357\n87 358\n88 359\n89 360\n90 361\n91 362\n92 363\n93 364\n94 365\n95 366\n96 367\n97 368\n98 369\n99 370\n100 371\n101 372\n102 373\n103 374\n104 375\n105 376\n106 377\n107 378\n108 379\n109 380\n110 381\n111 382\n112 383\n113 384\n114 385\n115 386\n116 387\n117 388\n118 389\n119 390\n120 391\n121 392\n122 393\n123 394\n124 395\n125 396\n126 397\n127 398\n128 399\n129 400\n130 401\n131 402\n132 403\n133 404\n134 405\n135 406\n136 407\n137 408\n138 409\n139 410\n140 411\n141 412\n142 413\n143 414\n144 415\n145 416\n146 417\n147 418\n148 419\n149 420\n150 421\n151 422\n152 423\n153 424\n154 425\n155 426\n156 427\n157 428\n158 429\n159 430\n160 431\n161 432\n162 433\n163 434\n164 435\n165 436\n166 437\n167 438\n168 439\n169 440\n170 441\n171 442\n172 443\n173 444\n174 445\n175 446\n176 447\n177 448\n178 449\n179 450\n180 451\n181 452\n182 453\n183 454\n184 455\n185 456\n186 457\n187 458\n188 459\n189 460\n190 461\n191 462\n192 463\n193 464\n194 465\n195 466\n196 467\n197 468\n198 469\n199 470\n200 471\n201 472\n202 473\n203 474\n204 475\n205 476\n206 477\n207 478\n208 479\n209 480\n210 481\n211 482\n212 483\n213 484\n214 485\n215 486\n216 487\n217 488\n218 489\n219 490\n220 491\n221 492\n222 493\n223 494\n224 495\n225 496\n226 497\n227 498\n228 499\n229 500\n230 501\n231 502\n232 503\n233 504\n234 505\n235 506\n236 507\n237 508\n238 509\n239 510\n240 511\n241 512\n242 513\n243 514\n244 515\n245 516\n246 517\n247 518\n248 519\n249 520\n250 521\n251 522\n252 523\n253 524\n254 525\n255 526\n256 527\n257 528\n258 529\n259 530\n260 531\n261 532\n262 533\n263 534\n264 535\n265 536\n266 537\n267 538\n268 539\n269 540\n270 541\n271 542\n272 543\n273 544\n274 545\n275 546\n276 547\n277 548\n278 549\n279 550\n280 551\n281 552\n282 553\n283 554\n284 555\n285 556\n286 557\n287 558\n288 559\n289 560\n290 561\n291 562\n292 563\n293 564\n294 565\n295 566\n296 567\n297 568\n298 569\n299 570\n300 571\n301 572\n302 573\n303 574\n304 575\n305 576\n306 577\n307 578\n308 579\n309 580\n310 581\n311 582\n312 583\n313 584\n314 585\n315 586\n316 587\n317 588\n318 589\n319 590\n320 591\n321 592\n322 593\n323 594\n324 595\n325 596\n326 597\n327 598\n328 599\n329 600\n330 601\n331 602\n332 603\n333 604\n334 605\n335 606\n336 607\n337 608\n338 609\n339 610\n340 611\n341 612\n342 613\n343 614\n344 615\n345 616\n346 617\n347 618\n348 619\n349 620\n350 621\n351 622\n352 623\n353 624\n354 625\n355 626\n356 627\n357 628\n358 629\n359 630\n360 631\n361 632\n362 633\n363 634\n364 635\n365 636\n366 637\n367 638\n368 639\n369 640\n370 641\n371 642\n372 643\n373 644\n374 645\n375 646\n376 647\n377 648\n378 649\n379 650\n380 651\n381 652\n382 653\n383 654\n384 655\n385 656\n386 657\n387 658\n388 659\n389 660\n390 661\n391 662\n392 663\n393 664\n394 665\n395 666\n396 667\n397 668\n398 669\n399 670\n400 671\n401 672\n402 673\n403 674\n404 675\n405 676\n406 677\n407 678\n408 679\n409 680\n410 681\n411 682\n412 683\n413 684\n414 685\n415 686\n416 687\n417 688\n418 689\n419 690\n420 691\n421 692\n422 693\n423 694\n424 695\n425 696\n426 697\n427 698\n428 699\n429 700\n430 701\n431 702\n432 703\n433 704\n434 705\n435 706\n436 707\n437 708\n438 709\n439 710\n440 711\n441 712\n442 713\n443 714\n444 715\n445 716\n446 717\n447 718\n448 719\n449 720\n450 721\n451 722\n452 723\n453 724\n454 725\n455 726\n456 727\n457 728\n458 729\n459 730\n460 731\n461 732\n462 733\n463 734\n464 735\n465 736\n466 737\n467 738\n468 739\n469 740\n470 741\n471 742\n472 743\n473 744\n474 745\n475 746\n476 747\n477 748\n478 749\n479 750\n480 751\n481 752\n482 753\n483 754\n484 755\n485 756\n486 757\n487 758\n488 759\n489 760\n490 761\n491 762\n492 763\n493 764\n494 765\n495 766\n496 767\n497 768\n498 769\n499 770\n500 771\n501 772\n502 773\n503 774\n504 775\n505 776\n506 777\n507 778\n508 779\n509 780\n510 781\n511 782\n512 783\n513 784\n514 785\n515 786\n516 787\n517 788\n518 789\n519 790\n520 791\n521 792\n522 793\n523 794\n524 795\n525 796\n526 797\n527 798\n528 799\n529 800\n530 801\n531 802\n532 803\n533 804\n534 805\n535 806\n536 807\n537 808\n538 809\n539 810\n540 811\n541 812\n542 813\n543 814\n544 815\n545 816\n546 817\n547 818\n548 819\n549 820\n550 821\n551 822\n552 823\n553 824\n554 825\n555 826\n556 827\n557 828\n558 829\n559 830\n560 831\n561 832\n562 833\n563 834\n564 835\n565 836\n566 837\n567 838\n568 839\n569 840\n570 841\n571 842\n572 843\n573 844\n574 845\n575 846\n576 847\n577 848\n578 849\n579 850\n580 851\n581 852\n582 853\n583 854\n584 855\n585 856\n586 857\n587 858\n588 859\n589 860\n590 861\n591 862\n592 863\n593 864\n594 865\n595 866\n596 867\n597 868\n598 869\n599 870\n600 871\n601 872\n602 873\n603 874\n604 875\n605 876\n606 877\n607 878\n608 879\n609 880\n610 881\n611 882\n612 883\n613 884\n614 885\n615 886\n616 887\n617 888\n618 889\n619 890\n620 891\n621 892\n622 893\n623 894\n624 895\n625 896\n626 897\n627 898\n628 899\n629 900\n630 901\n631 902\n632 903\n633 904\n634 905\n635 906\n636 907\n637 908\n638 909\n639 910\n640 911\n641 912\n642 913\n643 914\n644 915\n645 916\n646 917\n647 918\n648 919\n649 920\n650 921\n651 922\n652 923\n653 924\n654 925\n655 926\n656 927\n657 928\n658 929\n659 930\n660 931\n661 932\n662 933\n663 934\n664 935\n665 936\n666 937\n667 938\n668 939\n669 940\n670 941\n671 942\n672 943\n673 944\n674 945\n675 946\n676 947\n677 948\n678 949\n679 950\n680 951\n681 952\n682 953\n683 954\n684 955\n685 956\n686 957\n687 958\n688 959\n689 960\n690 961\n691 962\n692 963\n693 964\n694 965\n695 966\n696 967\n697 968\n698 969\n699 970\n700 971\n701 972\n702 973\n703 974\n704 975\n705 976\n706 977\n707 978\n708 979\n709 980\n710 981\n711 982\n712 983\n713 984\n714 985\n715 986\n716 987\n717 988\n718 989\n719 990\n720 991\n721 992\n722 993\n723 994\n724 995\n725 996\n726 997\n727 998\n728 999\n729 1000\n730 1001\n731 1002\n732 1003\n733 1004\n734 1005\n735 1006\n736 1007\n737 1008\n738 1009\n739 1010\n740 1011\n741 1012\n742 1013\n743 1014\n744 1015\n745 1016\n746 1017\n747 1018\n748 1019\n749 1020\n750 1021\n751 1022\n752 1023\n753 1024\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n1 326\n1 327\n1 328\n1 329\n1 330\n1 331\n1 332\n1 333\n1 334\n1 335\n1 336\n1 337\n1 338\n1 339\n1 340\n1 341\n1 342\n1 343\n1 344\n1 345\n1 346\n1 347\n1 348\n1 349\n1 350\n1 351\n1 352\n1 353\n1 354\n1 355\n1 356\n1 357\n1 358\n1 359\n1 360\n1 361\n1 362\n1 363\n1 364\n1 365\n1 366\n1 367\n1 368\n1 369\n1 370\n1 371\n1 372\n1 373\n1 374\n1 375\n1 376\n1 377\n1 378\n1 379\n1 380\n1 381\n1 382\n1 383\n1 384\n1 385\n1 386\n1 387\n1 388\n1 389\n1 390\n1 391\n1 392\n1 393\n1 394\n1 395\n1 396\n1 397\n1 398\n1 399\n1 400\n1 401\n1 402\n1 403\n1 404\n1 405\n1 406\n1 407\n1 408\n1 409\n1 410\n1 411\n1 412\n1 413\n1 414\n1 415\n1 416\n1 417\n1 418\n1 419\n1 420\n1 421\n1 422\n1 423\n1 424\n1 425\n1 426\n1 427\n1 428\n1 429\n1 430\n1 431\n1 432\n1 433\n1 434\n1 435\n1 436\n1 437\n1 438\n1 439\n1 440\n1 441\n1 442\n1 443\n1 444\n1 445\n1 446\n1 447\n1 448\n1 449\n1 450\n1 451\n1 452\n1 453\n1 454\n1 455\n1 456\n1 457\n1 458\n1 459\n1 460\n1 461\n1 462\n1 463\n1 464\n1 465\n1 466\n1 467\n1 468\n1 469\n1 470\n1 471\n1 472\n1 473\n1 474\n1 475\n1 476\n1 477\n1 478\n1 479\n1 480\n1 481\n1 482\n1 483\n1 484\n1 485\n1 486\n1 487\n1 488\n1 489\n1 490\n1 491\n1 492\n1 493\n1 494\n1 495\n1 496\n1 497\n1 498\n1 499\n1 500\n1 501\n1 502\n1 503\n1 504\n1 505\n1 506\n1 507\n1 508\n1 509\n1 510\n1 511\n1 512\n1 513\n1 514\n1 515\n1 516\n1 517\n1 518\n1 519\n1 520\n1 521\n1 522\n1 523\n1 524\n1 525\n1 526\n1 527\n1 528\n1 529\n1 530\n1 531\n1 532\n1 533\n1 534\n1 535\n1 536\n1 537\n1 538\n1 539\n1 540\n1 541\n1 542\n1 543\n1 544\n1 545\n1 546\n1 547\n1 548\n1 549\n1 550\n1 551\n1 552\n1 553\n1 554\n1 555\n1 556\n1 557\n1 558\n1 559\n1 560\n1 561\n1 562\n1 563\n1 564\n1 565\n1 566\n1 567\n1 568\n1 569\n1 570\n1 571\n1 572\n1 573\n1 574\n1 575\n1 576\n1 577\n1 578\n1 579\n1 580\n2 581\n3 582\n4 583\n5 584\n6 585\n7 586\n8 587\n9 588\n10 589\n11 590\n12 591\n13 592\n14 593\n15 594\n16 595\n17 596\n18 597\n19 598\n20 599\n21 600\n22 601\n23 602\n24 603\n25 604\n26 605\n27 606\n28 607\n29 608\n30 609\n31 610\n32 611\n33 612\n34 613\n35 614\n36 615\n37 616\n38 617\n39 618\n40 619\n41 620\n42 621\n43 622\n44 623\n45 624\n46 625\n47 626\n48 627\n49 628\n50 629\n51 630\n52 631\n53 632\n54 633\n55 634\n56 635\n57 636\n58 637\n59 638\n60 639\n61 640\n62 641\n63 642\n64 643\n65 644\n66 645\n67 646\n68 647\n69 648\n70 649\n71 650\n72 651\n73 652\n74 653\n75 654\n76 655\n77 656\n78 657\n79 658\n80 659\n81 660\n82 661\n83 662\n84 663\n85 664\n86 665\n87 666\n88 667\n89 668\n90 669\n91 670\n92 671\n93 672\n94 673\n95 674\n96 675\n97 676\n98 677\n99 678\n100 679\n101 680\n102 681\n103 682\n104 683\n105 684\n106 685\n107 686\n108 687\n109 688\n110 689\n111 690\n112 691\n113 692\n114 693\n115 694\n116 695\n117 696\n118 697\n119 698\n120 699\n121 700\n122 701\n123 702\n124 703\n125 704\n126 705\n127 706\n128 707\n129 708\n130 709\n131 710\n132 711\n133 712\n134 713\n135 714\n136 715\n137 716\n138 717\n139 718\n140 719\n141 720\n142 721\n143 722\n144 723\n145 724\n146 725\n147 726\n148 727\n149 728\n150 729\n151 730\n152 731\n153 732\n154 733\n155 734\n156 735\n157 736\n158 737\n159 738\n160 739\n161 740\n162 741\n163 742\n164 743\n165 744\n166 745\n167 746\n168 747\n169 748\n170 749\n171 750\n172 751\n173 752\n174 753\n175 754\n176 755\n177 756\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n2 9\n3 10\n",
"108\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n2 22\n3 23\n4 24\n5 25\n6 26\n7 27\n8 28\n9 29\n10 30\n11 31\n12 32\n13 33\n14 34\n15 35\n16 36\n17 37\n18 38\n19 39\n20 40\n21 41\n22 42\n23 43\n24 44\n25 45\n26 46\n27 47\n28 48\n29 49\n30 50\n31 51\n32 52\n33 53\n34 54\n35 55\n36 56\n37 57\n38 58\n39 59\n40 60\n41 61\n42 62\n43 63\n44 64\n45 65\n46 66\n47 67\n48 68\n49 69\n50 70\n51 71\n52 72\n53 73\n54 74\n55 75\n56 76\n57 77\n58 78\n59 79\n60 80\n61 81\n62 82\n63 83\n64 84\n65 85\n66 86\n67 87\n68 88\n69 89\n70 90\n71 91\n72 92\n73 93\n74 94\n75 95\n76 96\n77 97\n78 98\n79 99\n80 100\n81 101\n82 102\n83 103\n84 104\n85 105\n86 106\n87 107\n88 108\n89 109\n90 110\n91 111\n92 112\n93 113\n94 114\n95 115\n96 116\n97 117\n98 118\n99 119\n100 120\n101 121\n102 122\n103 123\n104 124\n105 125\n106 126\n107 127\n108 128\n109 129\n110 130\n111 131\n112 132\n113 133\n114 134\n115 135\n116 136\n117 137\n118 138\n119 139\n120 140\n121 141\n122 142\n123 143\n124 144\n125 145\n126 146\n127 147\n128 148\n129 149\n130 150\n131 151\n132 152\n133 153\n134 154\n135 155\n136 156\n137 157\n138 158\n139 159\n140 160\n141 161\n142 162\n143 163\n144 164\n145 165\n146 166\n147 167\n148 168\n149 169\n150 170\n151 171\n152 172\n153 173\n154 174\n155 175\n156 176\n157 177\n158 178\n159 179\n160 180\n161 181\n162 182\n163 183\n164 184\n165 185\n166 186\n167 187\n168 188\n169 189\n170 190\n171 191\n172 192\n173 193\n174 194\n175 195\n176 196\n177 197\n178 198\n179 199\n180 200\n181 201\n182 202\n183 203\n184 204\n185 205\n186 206\n187 207\n188 208\n189 209\n190 210\n191 211\n192 212\n193 213\n194 214\n195 215\n196 216\n197 217\n198 218\n199 219\n200 220\n201 221\n202 222\n203 223\n204 224\n205 225\n206 226\n207 227\n208 228\n209 229\n210 230\n211 231\n212 232\n213 233\n214 234\n215 235\n216 236\n217 237\n218 238\n219 239\n220 240\n221 241\n222 242\n223 243\n224 244\n225 245\n226 246\n227 247\n228 248\n229 249\n230 250\n231 251\n232 252\n233 253\n234 254\n235 255\n236 256\n237 257\n238 258\n239 259\n240 260\n241 261\n242 262\n243 263\n244 264\n245 265\n246 266\n247 267\n248 268\n249 269\n250 270\n251 271\n252 272\n253 273\n254 274\n255 275\n256 276\n257 277\n258 278\n259 279\n260 280\n261 281\n262 282\n263 283\n264 284\n265 285\n266 286\n267 287\n268 288\n269 289\n270 290\n271 291\n272 292\n273 293\n274 294\n275 295\n276 296\n277 297\n278 298\n279 299\n280 300\n281 301\n282 302\n283 303\n284 304\n285 305\n286 306\n287 307\n288 308\n289 309\n290 310\n291 311\n292 312\n293 313\n294 314\n295 315\n296 316\n297 317\n298 318\n299 319\n300 320\n301 321\n302 322\n303 323\n304 324\n305 325\n306 326\n307 327\n308 328\n309 329\n310 330\n311 331\n312 332\n313 333\n314 334\n315 335\n316 336\n317 337\n318 338\n319 339\n320 340\n321 341\n322 342\n323 343\n324 344\n325 345\n326 346\n327 347\n328 348\n329 349\n330 350\n331 351\n332 352\n333 353\n334 354\n335 355\n336 356\n337 357\n338 358\n339 359\n340 360\n341 361\n342 362\n343 363\n344 364\n345 365\n346 366\n347 367\n348 368\n349 369\n350 370\n351 371\n352 372\n353 373\n354 374\n355 375\n356 376\n357 377\n358 378\n359 379\n360 380\n361 381\n362 382\n363 383\n364 384\n365 385\n366 386\n367 387\n368 388\n369 389\n370 390\n371 391\n372 392\n373 393\n374 394\n375 395\n376 396\n377 397\n378 398\n379 399\n380 400\n381 401\n382 402\n383 403\n384 404\n385 405\n386 406\n387 407\n388 408\n389 409\n390 410\n391 411\n392 412\n393 413\n394 414\n395 415\n396 416\n397 417\n398 418\n399 419\n400 420\n401 421\n402 422\n403 423\n404 424\n405 425\n406 426\n407 427\n408 428\n409 429\n410 430\n411 431\n412 432\n413 433\n414 434\n415 435\n416 436\n417 437\n418 438\n419 439\n420 440\n421 441\n422 442\n423 443\n424 444\n425 445\n426 446\n427 447\n428 448\n429 449\n430 450\n431 451\n432 452\n433 453\n434 454\n435 455\n436 456\n437 457\n438 458\n439 459\n440 460\n441 461\n442 462\n443 463\n444 464\n445 465\n446 466\n447 467\n448 468\n449 469\n450 470\n451 471\n452 472\n453 473\n454 474\n455 475\n456 476\n457 477\n458 478\n459 479\n460 480\n461 481\n462 482\n463 483\n464 484\n465 485\n466 486\n467 487\n468 488\n469 489\n470 490\n471 491\n472 492\n473 493\n474 494\n475 495\n476 496\n477 497\n478 498\n479 499\n480 500\n481 501\n482 502\n483 503\n484 504\n485 505\n486 506\n487 507\n488 508\n489 509\n490 510\n491 511\n492 512\n493 513\n494 514\n495 515\n496 516\n497 517\n498 518\n499 519\n500 520\n501 521\n502 522\n503 523\n504 524\n505 525\n506 526\n507 527\n508 528\n509 529\n510 530\n511 531\n512 532\n513 533\n514 534\n515 535\n516 536\n517 537\n518 538\n519 539\n520 540\n521 541\n522 542\n523 543\n524 544\n525 545\n526 546\n527 547\n528 548\n529 549\n530 550\n531 551\n532 552\n533 553\n534 554\n535 555\n536 556\n537 557\n538 558\n539 559\n540 560\n541 561\n542 562\n543 563\n544 564\n545 565\n546 566\n547 567\n548 568\n549 569\n550 570\n551 571\n552 572\n553 573\n554 574\n555 575\n556 576\n557 577\n558 578\n559 579\n560 580\n561 581\n562 582\n563 583\n564 584\n565 585\n566 586\n567 587\n568 588\n569 589\n570 590\n571 591\n572 592\n573 593\n574 594\n575 595\n576 596\n577 597\n578 598\n579 599\n580 600\n581 601\n582 602\n583 603\n584 604\n585 605\n586 606\n587 607\n588 608\n589 609\n590 610\n591 611\n592 612\n593 613\n594 614\n595 615\n596 616\n597 617\n598 618\n599 619\n600 620\n601 621\n602 622\n603 623\n604 624\n605 625\n606 626\n607 627\n608 628\n609 629\n610 630\n611 631\n612 632\n613 633\n614 634\n615 635\n616 636\n617 637\n618 638\n619 639\n620 640\n621 641\n622 642\n623 643\n624 644\n625 645\n626 646\n627 647\n628 648\n629 649\n630 650\n631 651\n632 652\n633 653\n634 654\n635 655\n636 656\n637 657\n638 658\n639 659\n640 660\n641 661\n642 662\n643 663\n644 664\n645 665\n646 666\n647 667\n648 668\n649 669\n650 670\n651 671\n652 672\n653 673\n654 674\n655 675\n656 676\n657 677\n658 678\n659 679\n660 680\n661 681\n662 682\n663 683\n664 684\n665 685\n666 686\n667 687\n668 688\n669 689\n670 690\n671 691\n672 692\n673 693\n674 694\n675 695\n676 696\n677 697\n678 698\n679 699\n680 700\n681 701\n682 702\n683 703\n684 704\n685 705\n686 706\n687 707\n688 708\n689 709\n690 710\n691 711\n692 712\n693 713\n694 714\n695 715\n696 716\n697 717\n698 718\n699 719\n700 720\n701 721\n702 722\n703 723\n704 724\n705 725\n706 726\n707 727\n708 728\n709 729\n710 730\n711 731\n712 732\n713 733\n714 734\n715 735\n716 736\n717 737\n718 738\n719 739\n720 740\n721 741\n722 742\n723 743\n724 744\n725 745\n726 746\n727 747\n728 748\n729 749\n730 750\n731 751\n732 752\n733 753\n734 754\n735 755\n736 756\n737 757\n738 758\n739 759\n740 760\n741 761\n742 762\n743 763\n744 764\n745 765\n746 766\n747 767\n748 768\n749 769\n750 770\n751 771\n752 772\n753 773\n754 774\n755 775\n756 776\n757 777\n758 778\n759 779\n760 780\n761 781\n762 782\n763 783\n764 784\n765 785\n766 786\n767 787\n768 788\n769 789\n770 790\n771 791\n772 792\n773 793\n774 794\n775 795\n776 796\n777 797\n778 798\n779 799\n780 800\n781 801\n782 802\n783 803\n784 804\n785 805\n786 806\n787 807\n788 808\n789 809\n790 810\n791 811\n792 812\n793 813\n794 814\n795 815\n796 816\n797 817\n798 818\n799 819\n800 820\n801 821\n802 822\n803 823\n804 824\n805 825\n806 826\n807 827\n808 828\n809 829\n810 830\n811 831\n812 832\n813 833\n814 834\n815 835\n816 836\n817 837\n818 838\n819 839\n820 840\n821 841\n822 842\n823 843\n824 844\n825 845\n826 846\n827 847\n828 848\n829 849\n830 850\n831 851\n832 852\n833 853\n834 854\n835 855\n836 856\n837 857\n838 858\n839 859\n840 860\n841 861\n842 862\n843 863\n844 864\n845 865\n846 866\n847 867\n848 868\n849 869\n850 870\n851 871\n852 872\n853 873\n854 874\n855 875\n856 876\n857 877\n858 878\n859 879\n860 880\n861 881\n862 882\n863 883\n864 884\n865 885\n866 886\n867 887\n868 888\n869 889\n870 890\n871 891\n872 892\n873 893\n874 894\n875 895\n876 896\n877 897\n878 898\n879 899\n880 900\n881 901\n882 902\n883 903\n884 904\n885 905\n886 906\n887 907\n888 908\n889 909\n890 910\n891 911\n892 912\n893 913\n894 914\n895 915\n896 916\n897 917\n898 918\n899 919\n900 920\n901 921\n902 922\n903 923\n904 924\n905 925\n906 926\n907 927\n908 928\n909 929\n910 930\n911 931\n912 932\n913 933\n914 934\n915 935\n916 936\n917 937\n918 938\n919 939\n920 940\n921 941\n922 942\n923 943\n924 944\n925 945\n926 946\n927 947\n928 948\n929 949\n930 950\n931 951\n932 952\n933 953\n934 954\n935 955\n936 956\n937 957\n938 958\n939 959\n940 960\n941 961\n942 962\n943 963\n944 964\n945 965\n946 966\n947 967\n948 968\n949 969\n950 970\n951 971\n952 972\n953 973\n954 974\n955 975\n956 976\n957 977\n958 978\n959 979\n960 980\n961 981\n962 982\n963 983\n964 984\n965 985\n966 986\n967 987\n968 988\n969 989\n970 990\n971 991\n972 992\n973 993\n974 994\n975 995\n976 996\n977 997\n978 998\n979 999\n980 1000\n981 1001\n982 1002\n983 1003\n984 1004\n985 1005\n986 1006\n987 1007\n988 1008\n989 1009\n990 1010\n991 1011\n992 1012\n993 1013\n994 1014\n995 1015\n996 1016\n997 1017\n998 1018\n999 1019\n1000 1020\n1001 1021\n1002 1022\n1003 1023\n1004 1024\n1005 1025\n1006 1026\n1007 1027\n1008 1028\n1009 1029\n1010 1030\n1011 1031\n1012 1032\n1013 1033\n1014 1034\n1015 1035\n1016 1036\n1017 1037\n1018 1038\n1019 1039\n1020 1040\n1021 1041\n1022 1042\n1023 1043\n1024 1044\n1025 1045\n1026 1046\n1027 1047\n1028 1048\n1029 1049\n1030 1050\n1031 1051\n1032 1052\n1033 1053\n1034 1054\n1035 1055\n1036 1056\n1037 1057\n1038 1058\n1039 1059\n1040 1060\n1041 1061\n1042 1062\n1043 1063\n1044 1064\n1045 1065\n1046 1066\n1047 1067\n1048 1068\n1049 1069\n1050 1070\n1051 1071\n",
"8\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n1 38\n1 39\n1 40\n1 41\n1 42\n1 43\n1 44\n1 45\n1 46\n1 47\n1 48\n1 49\n1 50\n1 51\n1 52\n1 53\n1 54\n1 55\n1 56\n1 57\n1 58\n1 59\n1 60\n1 61\n1 62\n1 63\n1 64\n1 65\n1 66\n1 67\n1 68\n1 69\n1 70\n1 71\n1 72\n1 73\n1 74\n1 75\n1 76\n1 77\n1 78\n1 79\n1 80\n1 81\n1 82\n1 83\n1 84\n1 85\n1 86\n1 87\n1 88\n1 89\n1 90\n1 91\n1 92\n1 93\n1 94\n1 95\n1 96\n1 97\n1 98\n1 99\n1 100\n1 101\n1 102\n1 103\n1 104\n1 105\n1 106\n1 107\n1 108\n1 109\n1 110\n1 111\n1 112\n1 113\n1 114\n1 115\n1 116\n1 117\n1 118\n1 119\n1 120\n1 121\n1 122\n1 123\n1 124\n1 125\n1 126\n1 127\n1 128\n1 129\n1 130\n1 131\n1 132\n1 133\n1 134\n1 135\n1 136\n1 137\n1 138\n1 139\n1 140\n1 141\n1 142\n1 143\n1 144\n1 145\n1 146\n1 147\n1 148\n1 149\n1 150\n1 151\n1 152\n1 153\n1 154\n1 155\n1 156\n1 157\n1 158\n1 159\n1 160\n1 161\n1 162\n1 163\n1 164\n1 165\n1 166\n1 167\n1 168\n1 169\n1 170\n1 171\n1 172\n1 173\n1 174\n1 175\n1 176\n1 177\n1 178\n1 179\n1 180\n1 181\n1 182\n1 183\n1 184\n1 185\n1 186\n1 187\n1 188\n1 189\n1 190\n1 191\n1 192\n1 193\n1 194\n1 195\n1 196\n1 197\n1 198\n1 199\n1 200\n1 201\n1 202\n1 203\n1 204\n1 205\n1 206\n1 207\n1 208\n1 209\n1 210\n1 211\n1 212\n1 213\n1 214\n1 215\n1 216\n1 217\n1 218\n1 219\n1 220\n1 221\n1 222\n1 223\n1 224\n1 225\n1 226\n1 227\n1 228\n1 229\n1 230\n1 231\n1 232\n1 233\n1 234\n1 235\n1 236\n1 237\n1 238\n1 239\n1 240\n1 241\n1 242\n1 243\n1 244\n1 245\n1 246\n1 247\n1 248\n1 249\n1 250\n1 251\n1 252\n1 253\n1 254\n1 255\n1 256\n1 257\n1 258\n1 259\n1 260\n1 261\n1 262\n1 263\n1 264\n1 265\n1 266\n1 267\n1 268\n1 269\n1 270\n1 271\n1 272\n1 273\n1 274\n1 275\n1 276\n1 277\n1 278\n1 279\n1 280\n1 281\n1 282\n1 283\n1 284\n1 285\n1 286\n1 287\n1 288\n1 289\n1 290\n1 291\n1 292\n1 293\n1 294\n1 295\n1 296\n1 297\n1 298\n1 299\n1 300\n1 301\n1 302\n1 303\n1 304\n1 305\n1 306\n1 307\n1 308\n1 309\n1 310\n1 311\n1 312\n1 313\n1 314\n1 315\n1 316\n1 317\n1 318\n1 319\n1 320\n1 321\n1 322\n1 323\n1 324\n1 325\n2 326\n3 327\n4 328\n5 329\n6 330\n7 331\n8 332\n9 333\n10 334\n11 335\n12 336\n13 337\n14 338\n15 339\n16 340\n17 341\n18 342\n19 343\n20 344\n21 345\n22 346\n23 347\n24 348\n25 349\n26 350\n27 351\n28 352\n29 353\n30 354\n31 355\n32 356\n33 357\n34 358\n35 359\n36 360\n37 361\n38 362\n39 363\n40 364\n41 365\n42 366\n43 367\n44 368\n45 369\n46 370\n47 371\n48 372\n49 373\n50 374\n51 375\n52 376\n53 377\n54 378\n55 379\n56 380\n57 381\n58 382\n59 383\n60 384\n61 385\n62 386\n63 387\n64 388\n65 389\n66 390\n67 391\n68 392\n69 393\n70 394\n71 395\n72 396\n73 397\n74 398\n75 399\n76 400\n77 401\n78 402\n79 403\n80 404\n81 405\n82 406\n83 407\n84 408\n85 409\n86 410\n87 411\n88 412\n89 413\n90 414\n91 415\n92 416\n93 417\n94 418\n95 419\n96 420\n97 421\n98 422\n99 423\n100 424\n101 425\n102 426\n103 427\n104 428\n105 429\n106 430\n107 431\n108 432\n109 433\n110 434\n111 435\n112 436\n113 437\n114 438\n115 439\n116 440\n117 441\n118 442\n119 443\n120 444\n121 445\n122 446\n123 447\n124 448\n125 449\n126 450\n127 451\n128 452\n129 453\n130 454\n131 455\n132 456\n133 457\n134 458\n135 459\n136 460\n137 461\n138 462\n139 463\n140 464\n141 465\n142 466\n143 467\n144 468\n145 469\n146 470\n147 471\n148 472\n149 473\n150 474\n151 475\n152 476\n153 477\n154 478\n155 479\n156 480\n157 481\n158 482\n159 483\n160 484\n161 485\n162 486\n163 487\n164 488\n165 489\n166 490\n167 491\n168 492\n169 493\n170 494\n171 495\n172 496\n173 497\n174 498\n175 499\n176 500\n177 501\n178 502\n179 503\n180 504\n181 505\n182 506\n183 507\n184 508\n185 509\n186 510\n187 511\n188 512\n189 513\n190 514\n191 515\n192 516\n193 517\n194 518\n195 519\n196 520\n197 521\n198 522\n199 523\n200 524\n201 525\n202 526\n203 527\n204 528\n205 529\n206 530\n207 531\n208 532\n209 533\n210 534\n211 535\n212 536\n213 537\n214 538\n215 539\n216 540\n217 541\n218 542\n219 543\n220 544\n221 545\n222 546\n223 547\n224 548\n225 549\n226 550\n227 551\n228 552\n229 553\n230 554\n231 555\n232 556\n233 557\n234 558\n235 559\n236 560\n237 561\n238 562\n239 563\n240 564\n241 565\n242 566\n243 567\n244 568\n245 569\n246 570\n247 571\n248 572\n249 573\n250 574\n251 575\n252 576\n253 577\n254 578\n255 579\n256 580\n257 581\n258 582\n259 583\n260 584\n261 585\n262 586\n263 587\n264 588\n265 589\n266 590\n267 591\n268 592\n269 593\n270 594\n271 595\n272 596\n273 597\n274 598\n275 599\n276 600\n277 601\n278 602\n279 603\n280 604\n281 605\n282 606\n283 607\n284 608\n285 609\n286 610\n287 611\n288 612\n289 613\n290 614\n291 615\n292 616\n293 617\n294 618\n295 619\n296 620\n297 621\n298 622\n299 623\n300 624\n301 625\n302 626\n303 627\n304 628\n305 629\n306 630\n307 631\n308 632\n309 633\n310 634\n311 635\n312 636\n313 637\n314 638\n315 639\n316 640\n317 641\n318 642\n319 643\n320 644\n321 645\n322 646\n323 647\n324 648\n325 649\n326 650\n327 651\n328 652\n329 653\n330 654\n331 655\n332 656\n333 657\n334 658\n335 659\n336 660\n337 661\n338 662\n339 663\n340 664\n341 665\n342 666\n343 667\n344 668\n345 669\n346 670\n347 671\n348 672\n349 673\n350 674\n351 675\n352 676\n353 677\n354 678\n355 679\n356 680\n357 681\n358 682\n359 683\n360 684\n361 685\n362 686\n363 687\n364 688\n365 689\n366 690\n367 691\n368 692\n369 693\n370 694\n371 695\n372 696\n373 697\n374 698\n375 699\n376 700\n377 701\n378 702\n379 703\n380 704\n381 705\n382 706\n383 707\n384 708\n385 709\n386 710\n387 711\n388 712\n389 713\n390 714\n391 715\n392 716\n393 717\n394 718\n395 719\n396 720\n397 721\n398 722\n399 723\n400 724\n401 725\n402 726\n403 727\n404 728\n405 729\n406 730\n407 731\n408 732\n409 733\n410 734\n411 735\n412 736\n413 737\n414 738\n415 739\n416 740\n417 741\n418 742\n419 743\n420 744\n421 745\n422 746\n423 747\n424 748\n425 749\n426 750\n427 751\n428 752\n429 753\n430 754\n431 755\n432 756\n433 757\n434 758\n435 759\n436 760\n437 761\n438 762\n439 763\n440 764\n441 765\n442 766\n443 767\n444 768\n445 769\n446 770\n447 771\n448 772\n449 773\n450 774\n451 775\n452 776\n453 777\n454 778\n455 779\n456 780\n457 781\n458 782\n459 783\n460 784\n461 785\n462 786\n463 787\n464 788\n465 789\n466 790\n467 791\n468 792\n469 793\n470 794\n471 795\n472 796\n473 797\n474 798\n475 799\n476 800\n477 801\n478 802\n479 803\n480 804\n481 805\n482 806\n483 807\n484 808\n485 809\n486 810\n487 811\n488 812\n489 813\n490 814\n491 815\n492 816\n493 817\n494 818\n495 819\n496 820\n497 821\n498 822\n499 823\n500 824\n501 825\n502 826\n503 827\n504 828\n505 829\n506 830\n507 831\n508 832\n509 833\n510 834\n511 835\n512 836\n513 837\n514 838\n515 839\n516 840\n517 841\n518 842\n519 843\n520 844\n521 845\n522 846\n523 847\n524 848\n525 849\n526 850\n527 851\n528 852\n529 853\n530 854\n531 855\n532 856\n533 857\n534 858\n535 859\n536 860\n537 861\n538 862\n539 863\n540 864\n541 865\n542 866\n543 867\n544 868\n545 869\n546 870\n547 871\n548 872\n549 873\n550 874\n551 875\n552 876\n553 877\n554 878\n555 879\n556 880\n557 881\n558 882\n559 883\n560 884\n561 885\n562 886\n563 887\n564 888\n565 889\n566 890\n567 891\n568 892\n569 893\n570 894\n571 895\n572 896\n573 897\n574 898\n575 899\n576 900\n577 901\n578 902\n579 903\n580 904\n581 905\n582 906\n583 907\n584 908\n585 909\n586 910\n587 911\n588 912\n589 913\n590 914\n591 915\n592 916\n593 917\n594 918\n595 919\n596 920\n597 921\n598 922\n599 923\n600 924\n601 925\n602 926\n603 927\n604 928\n605 929\n606 930\n607 931\n608 932\n609 933\n610 934\n611 935\n612 936\n613 937\n614 938\n615 939\n616 940\n617 941\n618 942\n619 943\n620 944\n621 945\n622 946\n623 947\n624 948\n625 949\n626 950\n627 951\n628 952\n629 953\n630 954\n631 955\n632 956\n633 957\n634 958\n635 959\n636 960\n637 961\n638 962\n639 963\n640 964\n641 965\n642 966\n643 967\n644 968\n645 969\n646 970\n647 971\n648 972\n649 973\n650 974\n651 975\n652 976\n653 977\n654 978\n655 979\n656 980\n657 981\n658 982\n659 983\n660 984\n661 985\n662 986\n663 987\n664 988\n665 989\n666 990\n667 991\n668 992\n669 993\n670 994\n671 995\n672 996\n",
"120\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n2 23\n3 24\n4 25\n5 26\n6 27\n7 28\n8 29\n9 30\n10 31\n11 32\n12 33\n13 34\n14 35\n15 36\n16 37\n17 38\n18 39\n19 40\n20 41\n21 42\n22 43\n23 44\n24 45\n25 46\n26 47\n27 48\n28 49\n29 50\n30 51\n31 52\n32 53\n33 54\n34 55\n35 56\n36 57\n37 58\n38 59\n39 60\n40 61\n41 62\n42 63\n43 64\n44 65\n45 66\n46 67\n47 68\n48 69\n49 70\n50 71\n51 72\n52 73\n53 74\n54 75\n55 76\n56 77\n57 78\n58 79\n59 80\n60 81\n61 82\n62 83\n63 84\n64 85\n65 86\n66 87\n67 88\n68 89\n69 90\n70 91\n71 92\n72 93\n73 94\n74 95\n75 96\n76 97\n77 98\n78 99\n79 100\n80 101\n81 102\n82 103\n83 104\n84 105\n85 106\n86 107\n87 108\n88 109\n89 110\n90 111\n91 112\n92 113\n93 114\n94 115\n95 116\n96 117\n97 118\n98 119\n99 120\n100 121\n101 122\n102 123\n103 124\n104 125\n105 126\n106 127\n107 128\n108 129\n109 130\n110 131\n111 132\n112 133\n113 134\n114 135\n115 136\n116 137\n117 138\n118 139\n119 140\n120 141\n121 142\n122 143\n123 144\n124 145\n125 146\n126 147\n127 148\n128 149\n129 150\n130 151\n131 152\n132 153\n133 154\n134 155\n135 156\n136 157\n137 158\n138 159\n139 160\n140 161\n141 162\n142 163\n143 164\n144 165\n145 166\n146 167\n147 168\n148 169\n149 170\n150 171\n151 172\n152 173\n153 174\n154 175\n155 176\n156 177\n157 178\n158 179\n159 180\n160 181\n161 182\n162 183\n163 184\n164 185\n165 186\n166 187\n167 188\n168 189\n169 190\n170 191\n171 192\n172 193\n173 194\n174 195\n175 196\n176 197\n177 198\n178 199\n179 200\n180 201\n181 202\n182 203\n183 204\n184 205\n185 206\n186 207\n187 208\n188 209\n189 210\n190 211\n191 212\n192 213\n193 214\n194 215\n195 216\n196 217\n197 218\n198 219\n199 220\n200 221\n201 222\n202 223\n203 224\n204 225\n205 226\n206 227\n207 228\n208 229\n209 230\n210 231\n211 232\n212 233\n213 234\n214 235\n215 236\n216 237\n217 238\n218 239\n219 240\n220 241\n221 242\n222 243\n223 244\n224 245\n225 246\n226 247\n227 248\n228 249\n229 250\n230 251\n231 252\n232 253\n233 254\n234 255\n235 256\n236 257\n237 258\n238 259\n239 260\n240 261\n241 262\n242 263\n243 264\n244 265\n245 266\n246 267\n247 268\n248 269\n249 270\n250 271\n251 272\n252 273\n253 274\n254 275\n255 276\n256 277\n257 278\n258 279\n259 280\n260 281\n261 282\n262 283\n263 284\n264 285\n265 286\n266 287\n267 288\n268 289\n269 290\n270 291\n271 292\n272 293\n273 294\n274 295\n275 296\n276 297\n277 298\n278 299\n279 300\n280 301\n281 302\n282 303\n283 304\n284 305\n285 306\n286 307\n287 308\n288 309\n289 310\n290 311\n291 312\n292 313\n293 314\n294 315\n295 316\n296 317\n297 318\n298 319\n299 320\n300 321\n301 322\n302 323\n303 324\n304 325\n305 326\n306 327\n307 328\n308 329\n309 330\n310 331\n311 332\n312 333\n313 334\n314 335\n315 336\n316 337\n317 338\n318 339\n319 340\n320 341\n321 342\n322 343\n323 344\n324 345\n325 346\n326 347\n327 348\n328 349\n329 350\n330 351\n331 352\n332 353\n333 354\n334 355\n335 356\n336 357\n337 358\n338 359\n339 360\n340 361\n341 362\n342 363\n343 364\n344 365\n345 366\n346 367\n347 368\n348 369\n349 370\n350 371\n351 372\n352 373\n353 374\n354 375\n355 376\n356 377\n357 378\n358 379\n359 380\n360 381\n361 382\n362 383\n363 384\n364 385\n365 386\n366 387\n367 388\n368 389\n369 390\n370 391\n371 392\n372 393\n373 394\n374 395\n375 396\n376 397\n377 398\n378 399\n379 400\n380 401\n381 402\n382 403\n383 404\n384 405\n385 406\n386 407\n387 408\n388 409\n389 410\n390 411\n391 412\n392 413\n393 414\n394 415\n395 416\n396 417\n397 418\n398 419\n399 420\n400 421\n401 422\n402 423\n403 424\n404 425\n405 426\n406 427\n407 428\n408 429\n409 430\n410 431\n411 432\n412 433\n413 434\n414 435\n415 436\n416 437\n417 438\n418 439\n419 440\n420 441\n421 442\n422 443\n423 444\n424 445\n425 446\n426 447\n427 448\n428 449\n429 450\n430 451\n431 452\n432 453\n433 454\n434 455\n435 456\n436 457\n437 458\n438 459\n439 460\n440 461\n441 462\n442 463\n443 464\n444 465\n445 466\n446 467\n447 468\n448 469\n449 470\n450 471\n451 472\n452 473\n453 474\n454 475\n455 476\n456 477\n457 478\n458 479\n459 480\n460 481\n461 482\n462 483\n463 484\n464 485\n465 486\n466 487\n467 488\n468 489\n469 490\n470 491\n471 492\n472 493\n473 494\n474 495\n475 496\n476 497\n477 498\n478 499\n479 500\n480 501\n481 502\n482 503\n483 504\n484 505\n485 506\n486 507\n487 508\n488 509\n489 510\n490 511\n491 512\n492 513\n493 514\n494 515\n495 516\n496 517\n497 518\n498 519\n499 520\n500 521\n501 522\n502 523\n503 524\n504 525\n505 526\n506 527\n507 528\n508 529\n509 530\n510 531\n511 532\n512 533\n513 534\n514 535\n515 536\n516 537\n517 538\n518 539\n519 540\n520 541\n521 542\n522 543\n523 544\n524 545\n525 546\n526 547\n527 548\n528 549\n529 550\n530 551\n531 552\n532 553\n533 554\n534 555\n535 556\n536 557\n537 558\n538 559\n539 560\n540 561\n541 562\n542 563\n543 564\n544 565\n545 566\n546 567\n547 568\n548 569\n549 570\n550 571\n551 572\n552 573\n553 574\n554 575\n555 576\n556 577\n557 578\n558 579\n559 580\n560 581\n561 582\n562 583\n563 584\n564 585\n565 586\n566 587\n567 588\n568 589\n569 590\n570 591\n571 592\n572 593\n573 594\n574 595\n575 596\n576 597\n577 598\n578 599\n579 600\n580 601\n581 602\n582 603\n583 604\n584 605\n585 606\n586 607\n587 608\n588 609\n589 610\n590 611\n591 612\n592 613\n593 614\n594 615\n595 616\n596 617\n597 618\n598 619\n599 620\n600 621\n601 622\n602 623\n603 624\n604 625\n605 626\n606 627\n607 628\n608 629\n609 630\n610 631\n611 632\n612 633\n613 634\n614 635\n615 636\n616 637\n617 638\n618 639\n619 640\n620 641\n621 642\n622 643\n623 644\n624 645\n625 646\n626 647\n627 648\n628 649\n629 650\n630 651\n631 652\n632 653\n633 654\n634 655\n635 656\n636 657\n637 658\n638 659\n639 660\n640 661\n641 662\n642 663\n643 664\n644 665\n645 666\n646 667\n647 668\n648 669\n649 670\n650 671\n651 672\n652 673\n653 674\n654 675\n655 676\n656 677\n657 678\n658 679\n659 680\n660 681\n661 682\n662 683\n663 684\n664 685\n665 686\n666 687\n667 688\n668 689\n669 690\n670 691\n671 692\n672 693\n673 694\n674 695\n675 696\n676 697\n677 698\n678 699\n679 700\n680 701\n681 702\n682 703\n683 704\n684 705\n685 706\n686 707\n687 708\n688 709\n689 710\n690 711\n691 712\n692 713\n693 714\n694 715\n695 716\n696 717\n697 718\n698 719\n699 720\n700 721\n701 722\n702 723\n703 724\n704 725\n705 726\n706 727\n707 728\n708 729\n709 730\n710 731\n711 732\n712 733\n713 734\n714 735\n715 736\n716 737\n717 738\n718 739\n719 740\n720 741\n721 742\n722 743\n723 744\n724 745\n725 746\n726 747\n727 748\n728 749\n729 750\n730 751\n731 752\n732 753\n733 754\n734 755\n735 756\n736 757\n737 758\n738 759\n739 760\n740 761\n741 762\n742 763\n743 764\n744 765\n745 766\n746 767\n747 768\n748 769\n749 770\n750 771\n751 772\n752 773\n753 774\n754 775\n755 776\n756 777\n757 778\n758 779\n759 780\n760 781\n761 782\n762 783\n763 784\n764 785\n765 786\n766 787\n767 788\n768 789\n769 790\n770 791\n771 792\n772 793\n773 794\n774 795\n775 796\n776 797\n777 798\n778 799\n779 800\n780 801\n781 802\n782 803\n783 804\n784 805\n785 806\n786 807\n787 808\n788 809\n789 810\n790 811\n791 812\n792 813\n793 814\n794 815\n795 816\n796 817\n797 818\n798 819\n799 820\n800 821\n801 822\n802 823\n803 824\n804 825\n805 826\n806 827\n807 828\n808 829\n809 830\n810 831\n811 832\n812 833\n813 834\n814 835\n815 836\n816 837\n817 838\n818 839\n819 840\n820 841\n821 842\n822 843\n823 844\n824 845\n825 846\n826 847\n827 848\n828 849\n829 850\n830 851\n831 852\n832 853\n833 854\n834 855\n835 856\n836 857\n837 858\n838 859\n839 860\n840 861\n841 862\n842 863\n843 864\n844 865\n845 866\n846 867\n847 868\n848 869\n849 870\n850 871\n851 872\n852 873\n853 874\n854 875\n855 876\n856 877\n857 878\n858 879\n859 880\n860 881\n861 882\n862 883\n863 884\n864 885\n865 886\n866 887\n867 888\n868 889\n869 890\n870 891\n871 892\n872 893\n873 894\n874 895\n875 896\n876 897\n877 898\n878 899\n879 900\n880 901\n881 902\n882 903\n883 904\n884 905\n885 906\n886 907\n887 908\n888 909\n889 910\n890 911\n891 912\n892 913\n893 914\n894 915\n895 916\n896 917\n897 918\n898 919\n899 920\n900 921\n901 922\n902 923\n903 924\n904 925\n905 926\n906 927\n907 928\n908 929\n909 930\n910 931\n911 932\n912 933\n913 934\n914 935\n915 936\n916 937\n917 938\n918 939\n919 940\n920 941\n921 942\n922 943\n923 944\n924 945\n925 946\n926 947\n927 948\n928 949\n929 950\n930 951\n931 952\n932 953\n933 954\n934 955\n935 956\n936 957\n937 958\n938 959\n939 960\n940 961\n941 962\n942 963\n943 964\n944 965\n945 966\n946 967\n947 968\n948 969\n949 970\n950 971\n951 972\n952 973\n953 974\n954 975\n955 976\n956 977\n957 978\n958 979\n959 980\n960 981\n961 982\n962 983\n963 984\n964 985\n965 986\n966 987\n967 988\n968 989\n969 990\n970 991\n971 992\n972 993\n973 994\n974 995\n975 996\n976 997\n977 998\n978 999\n979 1000\n980 1001\n981 1002\n982 1003\n983 1004\n984 1005\n985 1006\n986 1007\n987 1008\n988 1009\n989 1010\n990 1011\n991 1012\n992 1013\n993 1014\n994 1015\n995 1016\n996 1017\n997 1018\n998 1019\n999 1020\n1000 1021\n1001 1022\n1002 1023\n1003 1024\n1004 1025\n1005 1026\n1006 1027\n1007 1028\n1008 1029\n1009 1030\n1010 1031\n1011 1032\n1012 1033\n1013 1034\n1014 1035\n1015 1036\n1016 1037\n1017 1038\n1018 1039\n1019 1040\n1020 1041\n1021 1042\n1022 1043\n1023 1044\n1024 1045\n1025 1046\n1026 1047\n1027 1048\n1028 1049\n1029 1050\n1030 1051\n1031 1052\n1032 1053\n1033 1054\n1034 1055\n1035 1056\n1036 1057\n1037 1058\n1038 1059\n1039 1060\n1040 1061\n1041 1062\n1042 1063\n1043 1064\n1044 1065\n1045 1066\n1046 1067\n1047 1068\n1048 1069\n1049 1070\n1050 1071\n1051 1072\n1052 1073\n1053 1074\n1054 1075\n1055 1076\n1056 1077\n1057 1078\n1058 1079\n1059 1080\n1060 1081\n1061 1082\n1062 1083\n1063 1084\n1064 1085\n1065 1086\n1066 1087\n1067 1088\n1068 1089\n1069 1090\n1070 1091\n1071 1092\n1072 1093\n1073 1094\n1074 1095\n1075 1096\n1076 1097\n1077 1098\n1078 1099\n1079 1100\n1080 1101\n1081 1102\n1082 1103\n1083 1104\n1084 1105\n1085 1106\n1086 1107\n1087 1108\n1088 1109\n1089 1110\n1090 1111\n1091 1112\n1092 1113\n1093 1114\n1094 1115\n1095 1116\n1096 1117\n1097 1118\n1098 1119\n1099 1120\n1100 1121\n1101 1122\n1102 1123\n1103 1124\n1104 1125\n1105 1126\n1106 1127\n1107 1128\n1108 1129\n1109 1130\n1110 1131\n1111 1132\n1112 1133\n1113 1134\n1114 1135\n1115 1136\n1116 1137\n1117 1138\n1118 1139\n1119 1140\n1120 1141\n1121 1142\n1122 1143\n1123 1144\n1124 1145\n1125 1146\n1126 1147\n1127 1148\n1128 1149\n1129 1150\n1130 1151\n1131 1152\n1132 1153\n1133 1154\n1134 1155\n1135 1156\n1136 1157\n1137 1158\n1138 1159\n1139 1160\n1140 1161\n1141 1162\n1142 1163\n1143 1164\n1144 1165\n1145 1166\n1146 1167\n1147 1168\n1148 1169\n1149 1170\n1150 1171\n1151 1172\n1152 1173\n1153 1174\n1154 1175\n1155 1176\n1156 1177\n1157 1178\n1158 1179\n1159 1180\n1160 1181\n1161 1182\n1162 1183\n1163 1184\n1164 1185\n1165 1186\n1166 1187\n1167 1188\n1168 1189\n1169 1190\n1170 1191\n1171 1192\n1172 1193\n1173 1194\n1174 1195\n1175 1196\n1176 1197\n1177 1198\n1178 1199\n1179 1200\n1180 1201\n1181 1202\n1182 1203\n1183 1204\n1184 1205\n1185 1206\n1186 1207\n1187 1208\n1188 1209\n1189 1210\n1190 1211\n1191 1212\n1192 1213\n1193 1214\n1194 1215\n1195 1216\n1196 1217\n1197 1218\n1198 1219\n1199 1220\n1200 1221\n1201 1222\n1202 1223\n1203 1224\n1204 1225\n1205 1226\n1206 1227\n1207 1228\n1208 1229\n1209 1230\n1210 1231\n1211 1232\n1212 1233\n1213 1234\n1214 1235\n1215 1236\n1216 1237\n1217 1238\n1218 1239\n1219 1240\n1220 1241\n1221 1242\n1222 1243\n1223 1244\n1224 1245\n1225 1246\n1226 1247\n1227 1248\n1228 1249\n1229 1250\n1230 1251\n1231 1252\n1232 1253\n1233 1254\n1234 1255\n1235 1256\n1236 1257\n1237 1258\n1238 1259\n1239 1260\n1240 1261\n",
"8\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 37\n2 38\n3 39\n4 40\n5 41\n6 42\n7 43\n8 44\n9 45\n10 46\n11 47\n12 48\n13 49\n14 50\n15 51\n16 52\n17 53\n18 54\n19 55\n20 56\n21 57\n22 58\n23 59\n24 60\n25 61\n26 62\n27 63\n28 64\n29 65\n30 66\n31 67\n32 68\n33 69\n34 70\n35 71\n36 72\n37 73\n38 74\n39 75\n40 76\n41 77\n42 78\n43 79\n44 80\n45 81\n46 82\n47 83\n48 84\n49 85\n50 86\n51 87\n52 88\n53 89\n54 90\n55 91\n56 92\n57 93\n58 94\n59 95\n60 96\n61 97\n62 98\n63 99\n64 100\n65 101\n66 102\n67 103\n68 104\n69 105\n70 106\n71 107\n72 108\n73 109\n74 110\n75 111\n76 112\n77 113\n78 114\n79 115\n80 116\n81 117\n82 118\n83 119\n84 120\n85 121\n86 122\n87 123\n88 124\n89 125\n90 126\n91 127\n92 128\n93 129\n94 130\n95 131\n96 132\n97 133\n98 134\n99 135\n100 136\n101 137\n102 138\n103 139\n104 140\n",
"583\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n6 11\n7 12\n8 13\n9 14\n10 15\n11 16\n12 17\n13 18\n14 19\n15 20\n16 21\n17 22\n18 23\n19 24\n20 25\n21 26\n22 27\n23 28\n24 29\n25 30\n26 31\n27 32\n28 33\n29 34\n30 35\n31 36\n32 37\n33 38\n34 39\n35 40\n36 41\n37 42\n38 43\n39 44\n40 45\n41 46\n42 47\n43 48\n44 49\n45 50\n46 51\n47 52\n48 53\n49 54\n50 55\n51 56\n52 57\n53 58\n54 59\n55 60\n56 61\n57 62\n58 63\n59 64\n60 65\n61 66\n62 67\n63 68\n64 69\n65 70\n66 71\n67 72\n68 73\n69 74\n70 75\n71 76\n72 77\n73 78\n74 79\n75 80\n76 81\n77 82\n78 83\n79 84\n80 85\n81 86\n82 87\n83 88\n84 89\n85 90\n86 91\n87 92\n88 93\n89 94\n90 95\n91 96\n92 97\n93 98\n94 99\n95 100\n96 101\n97 102\n98 103\n99 104\n100 105\n101 106\n102 107\n103 108\n104 109\n105 110\n106 111\n107 112\n108 113\n109 114\n110 115\n111 116\n112 117\n113 118\n114 119\n115 120\n116 121\n117 122\n118 123\n119 124\n120 125\n121 126\n122 127\n123 128\n124 129\n125 130\n126 131\n127 132\n128 133\n129 134\n130 135\n131 136\n132 137\n133 138\n134 139\n135 140\n136 141\n137 142\n138 143\n139 144\n140 145\n141 146\n142 147\n143 148\n144 149\n145 150\n146 151\n147 152\n148 153\n149 154\n150 155\n151 156\n152 157\n153 158\n154 159\n155 160\n156 161\n157 162\n158 163\n159 164\n160 165\n161 166\n162 167\n163 168\n164 169\n165 170\n166 171\n167 172\n168 173\n169 174\n170 175\n171 176\n172 177\n173 178\n174 179\n175 180\n176 181\n177 182\n178 183\n179 184\n180 185\n181 186\n182 187\n183 188\n184 189\n185 190\n186 191\n187 192\n188 193\n189 194\n190 195\n191 196\n192 197\n193 198\n194 199\n195 200\n196 201\n197 202\n198 203\n199 204\n200 205\n201 206\n202 207\n203 208\n204 209\n205 210\n206 211\n207 212\n208 213\n209 214\n210 215\n211 216\n212 217\n213 218\n214 219\n215 220\n216 221\n217 222\n218 223\n219 224\n220 225\n221 226\n222 227\n223 228\n224 229\n225 230\n226 231\n227 232\n228 233\n229 234\n230 235\n231 236\n232 237\n233 238\n234 239\n235 240\n236 241\n237 242\n238 243\n239 244\n240 245\n241 246\n242 247\n243 248\n244 249\n245 250\n246 251\n247 252\n248 253\n249 254\n250 255\n251 256\n252 257\n253 258\n254 259\n255 260\n256 261\n257 262\n258 263\n259 264\n260 265\n261 266\n262 267\n263 268\n264 269\n265 270\n266 271\n267 272\n268 273\n269 274\n270 275\n271 276\n272 277\n273 278\n274 279\n275 280\n276 281\n277 282\n278 283\n279 284\n280 285\n281 286\n282 287\n283 288\n284 289\n285 290\n286 291\n287 292\n288 293\n289 294\n290 295\n291 296\n292 297\n293 298\n294 299\n295 300\n296 301\n297 302\n298 303\n299 304\n300 305\n301 306\n302 307\n303 308\n304 309\n305 310\n306 311\n307 312\n308 313\n309 314\n310 315\n311 316\n312 317\n313 318\n314 319\n315 320\n316 321\n317 322\n318 323\n319 324\n320 325\n321 326\n322 327\n323 328\n324 329\n325 330\n326 331\n327 332\n328 333\n329 334\n330 335\n331 336\n332 337\n333 338\n334 339\n335 340\n336 341\n337 342\n338 343\n339 344\n340 345\n341 346\n342 347\n343 348\n344 349\n345 350\n346 351\n347 352\n348 353\n349 354\n350 355\n351 356\n352 357\n353 358\n354 359\n355 360\n356 361\n357 362\n358 363\n359 364\n360 365\n361 366\n362 367\n363 368\n364 369\n365 370\n366 371\n367 372\n368 373\n369 374\n370 375\n371 376\n372 377\n373 378\n374 379\n375 380\n376 381\n377 382\n378 383\n379 384\n380 385\n381 386\n382 387\n383 388\n384 389\n385 390\n386 391\n387 392\n388 393\n389 394\n390 395\n391 396\n392 397\n393 398\n394 399\n395 400\n396 401\n397 402\n398 403\n399 404\n400 405\n401 406\n402 407\n403 408\n404 409\n405 410\n406 411\n407 412\n408 413\n409 414\n410 415\n411 416\n412 417\n413 418\n414 419\n415 420\n416 421\n417 422\n418 423\n419 424\n420 425\n421 426\n422 427\n423 428\n424 429\n425 430\n426 431\n427 432\n428 433\n429 434\n430 435\n431 436\n432 437\n433 438\n434 439\n435 440\n436 441\n437 442\n438 443\n439 444\n440 445\n441 446\n442 447\n443 448\n444 449\n445 450\n446 451\n447 452\n448 453\n449 454\n450 455\n451 456\n452 457\n453 458\n454 459\n455 460\n456 461\n457 462\n458 463\n459 464\n460 465\n461 466\n462 467\n463 468\n464 469\n465 470\n466 471\n467 472\n468 473\n469 474\n470 475\n471 476\n472 477\n473 478\n474 479\n475 480\n476 481\n477 482\n478 483\n479 484\n480 485\n481 486\n482 487\n483 488\n484 489\n485 490\n486 491\n487 492\n488 493\n489 494\n490 495\n491 496\n492 497\n493 498\n494 499\n495 500\n496 501\n497 502\n498 503\n499 504\n500 505\n501 506\n502 507\n503 508\n504 509\n505 510\n506 511\n507 512\n508 513\n509 514\n510 515\n511 516\n512 517\n513 518\n514 519\n515 520\n516 521\n517 522\n518 523\n519 524\n520 525\n521 526\n522 527\n523 528\n524 529\n525 530\n526 531\n527 532\n528 533\n529 534\n530 535\n531 536\n532 537\n533 538\n534 539\n535 540\n536 541\n537 542\n538 543\n539 544\n540 545\n541 546\n542 547\n543 548\n544 549\n545 550\n546 551\n547 552\n548 553\n549 554\n550 555\n551 556\n552 557\n553 558\n554 559\n555 560\n556 561\n557 562\n558 563\n559 564\n560 565\n561 566\n562 567\n563 568\n564 569\n565 570\n566 571\n567 572\n568 573\n569 574\n570 575\n571 576\n572 577\n573 578\n574 579\n575 580\n576 581\n577 582\n578 583\n579 584\n580 585\n581 586\n582 587\n583 588\n584 589\n585 590\n586 591\n587 592\n588 593\n589 594\n590 595\n591 596\n592 597\n593 598\n594 599\n595 600\n596 601\n597 602\n598 603\n599 604\n600 605\n601 606\n602 607\n603 608\n604 609\n605 610\n606 611\n607 612\n608 613\n609 614\n610 615\n611 616\n612 617\n613 618\n614 619\n615 620\n616 621\n617 622\n618 623\n619 624\n620 625\n621 626\n622 627\n623 628\n624 629\n625 630\n626 631\n627 632\n628 633\n629 634\n630 635\n631 636\n632 637\n633 638\n634 639\n635 640\n636 641\n637 642\n638 643\n639 644\n640 645\n641 646\n642 647\n643 648\n644 649\n645 650\n646 651\n647 652\n648 653\n649 654\n650 655\n651 656\n652 657\n653 658\n654 659\n655 660\n656 661\n657 662\n658 663\n659 664\n660 665\n661 666\n662 667\n663 668\n664 669\n665 670\n666 671\n667 672\n668 673\n669 674\n670 675\n671 676\n672 677\n673 678\n674 679\n675 680\n676 681\n677 682\n678 683\n679 684\n680 685\n681 686\n682 687\n683 688\n684 689\n685 690\n686 691\n687 692\n688 693\n689 694\n690 695\n691 696\n692 697\n693 698\n694 699\n695 700\n696 701\n697 702\n698 703\n699 704\n700 705\n701 706\n702 707\n703 708\n704 709\n705 710\n706 711\n707 712\n708 713\n709 714\n710 715\n711 716\n712 717\n713 718\n714 719\n715 720\n716 721\n717 722\n718 723\n719 724\n720 725\n721 726\n722 727\n723 728\n724 729\n725 730\n726 731\n727 732\n728 733\n729 734\n730 735\n731 736\n732 737\n733 738\n734 739\n735 740\n736 741\n737 742\n738 743\n739 744\n740 745\n741 746\n742 747\n743 748\n744 749\n745 750\n746 751\n747 752\n748 753\n749 754\n750 755\n751 756\n752 757\n753 758\n754 759\n755 760\n756 761\n757 762\n758 763\n759 764\n760 765\n761 766\n762 767\n763 768\n764 769\n765 770\n766 771\n767 772\n768 773\n769 774\n770 775\n771 776\n772 777\n773 778\n774 779\n775 780\n776 781\n777 782\n778 783\n779 784\n780 785\n781 786\n782 787\n783 788\n784 789\n785 790\n786 791\n787 792\n788 793\n789 794\n790 795\n791 796\n792 797\n793 798\n794 799\n795 800\n796 801\n797 802\n798 803\n799 804\n800 805\n801 806\n802 807\n803 808\n804 809\n805 810\n806 811\n807 812\n808 813\n809 814\n810 815\n811 816\n812 817\n813 818\n814 819\n815 820\n816 821\n817 822\n818 823\n819 824\n820 825\n821 826\n822 827\n823 828\n824 829\n825 830\n826 831\n827 832\n828 833\n829 834\n830 835\n831 836\n832 837\n833 838\n834 839\n835 840\n836 841\n837 842\n838 843\n839 844\n840 845\n841 846\n842 847\n843 848\n844 849\n845 850\n846 851\n847 852\n848 853\n849 854\n850 855\n851 856\n852 857\n853 858\n854 859\n855 860\n856 861\n857 862\n858 863\n859 864\n860 865\n861 866\n862 867\n863 868\n864 869\n865 870\n866 871\n867 872\n868 873\n869 874\n870 875\n871 876\n872 877\n873 878\n874 879\n875 880\n876 881\n877 882\n878 883\n879 884\n880 885\n881 886\n882 887\n883 888\n884 889\n885 890\n886 891\n887 892\n888 893\n889 894\n890 895\n891 896\n892 897\n893 898\n894 899\n895 900\n896 901\n897 902\n898 903\n899 904\n900 905\n901 906\n902 907\n903 908\n904 909\n905 910\n906 911\n907 912\n908 913\n909 914\n910 915\n911 916\n912 917\n913 918\n914 919\n915 920\n916 921\n917 922\n918 923\n919 924\n920 925\n921 926\n922 927\n923 928\n924 929\n925 930\n926 931\n927 932\n928 933\n929 934\n930 935\n931 936\n932 937\n933 938\n934 939\n935 940\n936 941\n937 942\n938 943\n939 944\n940 945\n941 946\n942 947\n943 948\n944 949\n945 950\n946 951\n947 952\n948 953\n949 954\n950 955\n951 956\n952 957\n953 958\n954 959\n955 960\n956 961\n957 962\n958 963\n959 964\n960 965\n961 966\n962 967\n963 968\n964 969\n965 970\n966 971\n967 972\n968 973\n969 974\n970 975\n971 976\n972 977\n973 978\n974 979\n975 980\n976 981\n977 982\n978 983\n979 984\n980 985\n981 986\n982 987\n983 988\n984 989\n985 990\n986 991\n987 992\n988 993\n989 994\n990 995\n991 996\n992 997\n993 998\n994 999\n995 1000\n996 1001\n997 1002\n998 1003\n999 1004\n1000 1005\n1001 1006\n1002 1007\n1003 1008\n1004 1009\n1005 1010\n1006 1011\n1007 1012\n1008 1013\n1009 1014\n1010 1015\n1011 1016\n1012 1017\n1013 1018\n1014 1019\n1015 1020\n1016 1021\n1017 1022\n1018 1023\n1019 1024\n1020 1025\n1021 1026\n1022 1027\n1023 1028\n1024 1029\n1025 1030\n1026 1031\n1027 1032\n1028 1033\n1029 1034\n1030 1035\n1031 1036\n1032 1037\n1033 1038\n1034 1039\n1035 1040\n1036 1041\n1037 1042\n1038 1043\n1039 1044\n1040 1045\n1041 1046\n1042 1047\n1043 1048\n1044 1049\n1045 1050\n1046 1051\n1047 1052\n1048 1053\n1049 1054\n1050 1055\n1051 1056\n1052 1057\n1053 1058\n1054 1059\n1055 1060\n1056 1061\n1057 1062\n1058 1063\n1059 1064\n1060 1065\n1061 1066\n1062 1067\n1063 1068\n1064 1069\n1065 1070\n1066 1071\n1067 1072\n1068 1073\n1069 1074\n1070 1075\n1071 1076\n1072 1077\n1073 1078\n1074 1079\n1075 1080\n1076 1081\n1077 1082\n1078 1083\n1079 1084\n1080 1085\n1081 1086\n1082 1087\n1083 1088\n1084 1089\n1085 1090\n1086 1091\n1087 1092\n1088 1093\n1089 1094\n1090 1095\n1091 1096\n1092 1097\n1093 1098\n1094 1099\n1095 1100\n1096 1101\n1097 1102\n1098 1103\n1099 1104\n1100 1105\n1101 1106\n1102 1107\n1103 1108\n1104 1109\n1105 1110\n1106 1111\n1107 1112\n1108 1113\n1109 1114\n1110 1115\n1111 1116\n1112 1117\n1113 1118\n1114 1119\n1115 1120\n1116 1121\n1117 1122\n1118 1123\n1119 1124\n1120 1125\n1121 1126\n1122 1127\n1123 1128\n1124 1129\n1125 1130\n1126 1131\n1127 1132\n1128 1133\n1129 1134\n1130 1135\n1131 1136\n1132 1137\n1133 1138\n1134 1139\n1135 1140\n1136 1141\n1137 1142\n1138 1143\n1139 1144\n1140 1145\n1141 1146\n1142 1147\n1143 1148\n1144 1149\n1145 1150\n1146 1151\n1147 1152\n1148 1153\n1149 1154\n1150 1155\n1151 1156\n1152 1157\n1153 1158\n1154 1159\n1155 1160\n1156 1161\n1157 1162\n1158 1163\n1159 1164\n1160 1165\n1161 1166\n1162 1167\n1163 1168\n1164 1169\n1165 1170\n1166 1171\n1167 1172\n1168 1173\n1169 1174\n1170 1175\n1171 1176\n1172 1177\n1173 1178\n1174 1179\n1175 1180\n1176 1181\n1177 1182\n1178 1183\n1179 1184\n1180 1185\n1181 1186\n1182 1187\n1183 1188\n1184 1189\n1185 1190\n1186 1191\n1187 1192\n1188 1193\n1189 1194\n1190 1195\n1191 1196\n1192 1197\n1193 1198\n1194 1199\n1195 1200\n1196 1201\n1197 1202\n1198 1203\n1199 1204\n1200 1205\n1201 1206\n1202 1207\n1203 1208\n1204 1209\n1205 1210\n1206 1211\n1207 1212\n1208 1213\n1209 1214\n1210 1215\n1211 1216\n1212 1217\n1213 1218\n1214 1219\n1215 1220\n1216 1221\n1217 1222\n1218 1223\n1219 1224\n1220 1225\n1221 1226\n1222 1227\n1223 1228\n1224 1229\n1225 1230\n1226 1231\n1227 1232\n1228 1233\n1229 1234\n1230 1235\n1231 1236\n1232 1237\n1233 1238\n1234 1239\n1235 1240\n1236 1241\n1237 1242\n1238 1243\n1239 1244\n1240 1245\n1241 1246\n1242 1247\n1243 1248\n1244 1249\n1245 1250\n1246 1251\n1247 1252\n1248 1253\n1249 1254\n1250 1255\n1251 1256\n1252 1257\n1253 1258\n1254 1259\n1255 1260\n1256 1261\n1257 1262\n1258 1263\n1259 1264\n1260 1265\n1261 1266\n1262 1267\n1263 1268\n1264 1269\n1265 1270\n1266 1271\n1267 1272\n1268 1273\n1269 1274\n1270 1275\n1271 1276\n1272 1277\n1273 1278\n1274 1279\n1275 1280\n1276 1281\n1277 1282\n1278 1283\n1279 1284\n1280 1285\n1281 1286\n1282 1287\n1283 1288\n1284 1289\n1285 1290\n1286 1291\n1287 1292\n1288 1293\n1289 1294\n1290 1295\n1291 1296\n1292 1297\n1293 1298\n1294 1299\n1295 1300\n1296 1301\n1297 1302\n1298 1303\n1299 1304\n1300 1305\n1301 1306\n1302 1307\n1303 1308\n1304 1309\n1305 1310\n1306 1311\n1307 1312\n1308 1313\n1309 1314\n1310 1315\n1311 1316\n1312 1317\n1313 1318\n1314 1319\n1315 1320\n1316 1321\n1317 1322\n1318 1323\n1319 1324\n1320 1325\n1321 1326\n1322 1327\n1323 1328\n1324 1329\n1325 1330\n1326 1331\n1327 1332\n1328 1333\n1329 1334\n1330 1335\n1331 1336\n1332 1337\n1333 1338\n1334 1339\n1335 1340\n1336 1341\n1337 1342\n1338 1343\n1339 1344\n1340 1345\n1341 1346\n1342 1347\n1343 1348\n1344 1349\n1345 1350\n1346 1351\n1347 1352\n1348 1353\n1349 1354\n1350 1355\n1351 1356\n1352 1357\n1353 1358\n1354 1359\n1355 1360\n1356 1361\n1357 1362\n1358 1363\n1359 1364\n1360 1365\n1361 1366\n1362 1367\n1363 1368\n1364 1369\n1365 1370\n1366 1371\n1367 1372\n1368 1373\n1369 1374\n1370 1375\n1371 1376\n1372 1377\n1373 1378\n1374 1379\n1375 1380\n1376 1381\n1377 1382\n1378 1383\n1379 1384\n1380 1385\n1381 1386\n1382 1387\n1383 1388\n1384 1389\n1385 1390\n1386 1391\n1387 1392\n1388 1393\n1389 1394\n1390 1395\n1391 1396\n1392 1397\n1393 1398\n1394 1399\n1395 1400\n1396 1401\n1397 1402\n1398 1403\n1399 1404\n1400 1405\n1401 1406\n1402 1407\n1403 1408\n1404 1409\n1405 1410\n1406 1411\n1407 1412\n1408 1413\n1409 1414\n1410 1415\n1411 1416\n1412 1417\n1413 1418\n1414 1419\n1415 1420\n1416 1421\n1417 1422\n1418 1423\n1419 1424\n1420 1425\n1421 1426\n1422 1427\n1423 1428\n1424 1429\n1425 1430\n1426 1431\n1427 1432\n1428 1433\n1429 1434\n1430 1435\n1431 1436\n1432 1437\n1433 1438\n1434 1439\n1435 1440\n1436 1441\n1437 1442\n1438 1443\n1439 1444\n1440 1445\n1441 1446\n1442 1447\n1443 1448\n1444 1449\n1445 1450\n1446 1451\n1447 1452\n1448 1453\n1449 1454\n1450 1455\n1451 1456\n1452 1457\n",
"4\n1 2\n1 3\n1 4\n1 5\n1 6\n2 7\n3 8\n4 9\n5 10\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Arkady needs your help again! This time he decided to build his own high-speed Internet exchange point. It should consist of n nodes connected with minimum possible number of wires into one network (a wire directly connects two nodes). Exactly k of the nodes should be exit-nodes, that means that each of them should be connected to exactly one other node of the network, while all other nodes should be connected to at least two nodes in order to increase the system stability.
Arkady wants to make the system as fast as possible, so he wants to minimize the maximum distance between two exit-nodes. The distance between two nodes is the number of wires a package needs to go through between those two nodes.
Help Arkady to find such a way to build the network that the distance between the two most distant exit-nodes is as small as possible.
Input
The first line contains two integers n and k (3 ≤ n ≤ 2·105, 2 ≤ k ≤ n - 1) — the total number of nodes and the number of exit-nodes.
Note that it is always possible to build at least one network with n nodes and k exit-nodes within the given constraints.
Output
In the first line print the minimum possible distance between the two most distant exit-nodes. In each of the next n - 1 lines print two integers: the ids of the nodes connected by a wire. The description of each wire should be printed exactly once. You can print wires and wires' ends in arbitrary order. The nodes should be numbered from 1 to n. Exit-nodes can have any ids.
If there are multiple answers, print any of them.
Examples
Input
3 2
Output
2
1 2
2 3
Input
5 3
Output
3
1 2
2 3
3 4
3 5
Note
In the first example the only network is shown on the left picture.
In the second example one of optimal networks is shown on the right picture.
Exit-nodes are highlighted.
<image>
### Input:
5 3
### Output:
3
1 2
1 3
1 4
2 5
### Input:
3 2
### Output:
2
1 2
1 3
### Code:
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**9+7
Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
n,k = Ri()
lis = [i for i in range(k)]
ans = []
cur = k
totans = 0
while True:
tlis = []
while len(lis):
if cur == n-1: break
# temp =
ans.append((lis[-1], cur))
tlis.append(cur)
cur+=1
lis.pop()
if len(lis) != 0:
for i in tlis:
ans.append((i, cur))
for i in lis:
ans.append((i, cur))
if len(tlis) == 1:
totans+=2
totans = totans+(totans-1)
elif len(tlis) >= 2:
totans+=2
totans = totans*2
else:
# print(totans)
totans+=1
totans = 2*totans
break
lis = tlis
totans+=1
print(totans)
for i in ans:
print(i[0]+1, i[1]+1)
|
849_B. Tell Your World_28398
|
Connect the countless points with lines, till we reach the faraway yonder.
There are n points on a coordinate plane, the i-th of which being (i, yi).
Determine whether it's possible to draw two parallel and non-overlapping lines, such that every point in the set lies on exactly one of them, and each of them passes through at least one point in the set.
Input
The first line of input contains a positive integer n (3 ≤ n ≤ 1 000) — the number of points.
The second line contains n space-separated integers y1, y2, ..., yn ( - 109 ≤ yi ≤ 109) — the vertical coordinates of each point.
Output
Output "Yes" (without quotes) if it's possible to fulfill the requirements, and "No" otherwise.
You can print each letter in any case (upper or lower).
Examples
Input
5
7 5 8 6 9
Output
Yes
Input
5
-1 -2 0 0 -5
Output
No
Input
5
5 4 3 2 1
Output
No
Input
5
1000000000 0 0 0 0
Output
Yes
Note
In the first example, there are five points: (1, 7), (2, 5), (3, 8), (4, 6) and (5, 9). It's possible to draw a line that passes through points 1, 3, 5, and another one that passes through points 2, 4 and is parallel to the first one.
In the second example, while it's possible to draw two lines that cover all points, they cannot be made parallel.
In the third example, it's impossible to satisfy both requirements at the same time.
|
def run():
n = int(input())
a = [int(x) for x in input().split()]
_s = set(a)
if len(_s) == 1:
print('No')
return
if len(_s) == 2:
print('Yes')
return
def check(dy, base):
st = [False] * n
for i in range(n):
if (a[i] - a[base]) * 2 == dy * (i - base):
st[i] = True
for i, s in enumerate(st):
if not s:
newbase = i
break
else:
return False
base = newbase
for i in range(n):
if (a[i] - a[base]) * 2 == dy * (i - base):
st[i] = True
return not (False in st)
if check((a[1]-a[0])*2, 0) or check((a[2]-a[1])*2, 1) or check((a[2]-a[0]), 0):
print('Yes')
else:
print('No')
run()
|
{
"input": [
"5\n7 5 8 6 9\n",
"5\n-1 -2 0 0 -5\n",
"5\n1000000000 0 0 0 0\n",
"5\n5 4 3 2 1\n",
"5\n-954618456 -522919664 -248330428 -130850748 300848044\n",
"6\n1 2 4 5 7 9\n",
"5\n7 5 9 10 8\n",
"5\n7 5 8 6 3\n",
"5\n1 2 3 3 3\n",
"4\n1 3 4 4\n",
"10\n-6568 -5920 -5272 -4624 -2435 -635 -2680 -2032 -1384 6565\n",
"4\n-253090305 36298498 374072642 711846786\n",
"10\n4846 6705 2530 5757 5283 -944 -2102 -3260 -4418 2913\n",
"5\n1 2 6 10 17\n",
"4\n0 0 4 0\n",
"5\n2 1 0 1 2\n",
"6\n0 0 1 2 3 4\n",
"5\n-186772848 -235864239 -191561068 -193955178 -243046569\n",
"4\n1 0 1 4\n",
"5\n1 6 7 4 9\n",
"5\n1 2 -3 4 -1\n",
"3\n-1000000000 0 1000000000\n",
"3\n998 244 353\n",
"5\n1000000000 1 0 -999999999 -1000000000\n",
"4\n1 3 3 6\n",
"5\n-1 -1 -1 -1 1\n",
"4\n100 50 50 1000000\n",
"8\n1 12 3 14 5 16 7 8\n",
"7\n0 0 2 3 4 5 5\n",
"4\n2 2 4 5\n",
"4\n-9763 530 3595 6660\n",
"3\n1000000000 1000000000 -1000000000\n",
"7\n1 2 2 1 2 2 1\n",
"20\n319410377 286827025 254243673 221660321 189076969 156493617 123910265 91326913 58743561 26160209 -6423143 -39006495 -71589847 -104173199 -136756551 -169339903 -201923255 -234506607 -267089959 -299673311\n",
"5\n1 2 9 4 5\n",
"4\n1 0 3 0\n",
"4\n0 0 1 3\n",
"5\n7 5 8 6 8\n",
"6\n1 2 1 3 4 5\n",
"7\n1 2 -1 0 1 6 7\n",
"4\n100 50 50 10000000\n",
"4\n100 2 3 4\n",
"20\n-975467170 758268840 -975467171 758268839 -975467172 758268838 -975467173 758268837 -975467174 758268836 -975467175 758268835 -975467176 758268834 -975467177 758268833 -975467178 758268832 -975467179 758268831\n",
"5\n-954618456 -522919664 -248330428 -130850748 191871394\n",
"4\n1 0 2 4\n",
"6\n1 2 4 2 7 9\n",
"5\n8 5 9 10 8\n",
"5\n7 5 8 2 3\n",
"5\n1 2 6 3 3\n",
"10\n-6568 -5920 -8871 -4624 -2435 -635 -2680 -2032 -1384 6565\n",
"10\n4846 6705 2530 5757 7569 -944 -2102 -3260 -4418 2913\n",
"5\n1 2 6 18 17\n",
"5\n-186772848 -235864239 -41387515 -193955178 -243046569\n",
"5\n1 6 0 4 9\n",
"5\n1 2 -3 4 -2\n",
"3\n-1334827446 0 1000000000\n",
"3\n650 244 353\n",
"5\n1000000001 1 0 -999999999 -1000000000\n",
"8\n1 12 3 14 8 16 7 8\n",
"7\n0 0 2 3 1 5 5\n",
"4\n2 2 2 5\n",
"3\n1000000000 1000000000 -227897416\n",
"7\n1 2 2 1 1 2 1\n",
"20\n319410377 286827025 254243673 221660321 189076969 156493617 123910265 91326913 58743561 26160209 -11606501 -39006495 -71589847 -104173199 -136756551 -169339903 -201923255 -234506607 -267089959 -299673311\n",
"5\n1 2 9 4 8\n",
"4\n0 -1 1 3\n",
"5\n10 5 8 6 8\n",
"6\n1 4 1 3 4 5\n",
"7\n1 4 -1 0 1 6 7\n",
"20\n-975467170 758268840 -975467171 758268839 -975467172 758268838 -975467173 758268837 -975467174 758268836 -975467175 758268835 -975467176 758268834 -975467177 758268833 -975467178 758268832 -975467179 1082851919\n",
"5\n1000000100 0 0 0 0\n",
"5\n5 4 3 2 0\n",
"5\n-954618456 -522919664 -458263692 -130850748 191871394\n",
"6\n1 2 4 1 7 9\n",
"5\n15 5 9 10 8\n",
"5\n7 5 8 4 3\n",
"5\n2 2 6 3 3\n",
"10\n-6568 -5920 -8871 -4624 -2435 -635 -2680 -2032 -614 6565\n",
"10\n4846 6705 2530 5757 7569 -944 -2102 -3260 -4418 291\n",
"5\n1 2 6 22 17\n",
"5\n-186772848 -235864239 -29968495 -193955178 -243046569\n",
"5\n1 11 0 4 9\n",
"5\n2 2 -3 4 -2\n",
"3\n-1334827446 -1 1000000000\n",
"3\n896 244 353\n",
"5\n1000000001 1 -1 -999999999 -1000000000\n",
"8\n1 12 3 14 8 21 7 8\n",
"7\n0 0 2 3 0 5 5\n",
"4\n2 2 3 5\n",
"3\n1000000001 1000000000 -227897416\n",
"7\n1 2 2 1 1 0 1\n",
"20\n319410377 286827025 254243673 221660321 189076969 156493617 123910265 91326913 58743561 26160209 -11606501 -39006495 -71589847 -104173199 -136756551 -169339903 -201923255 -234506607 -461921277 -299673311\n",
"5\n1 0 9 4 8\n",
"4\n0 -1 2 3\n",
"5\n10 5 8 6 5\n",
"6\n1 4 1 3 4 9\n",
"7\n1 4 -1 0 1 6 9\n",
"20\n-975467170 758268840 -975467171 758268839 -975467172 758268838 -975467173 758268837 -975467174 758268836 -975467175 758268835 -975467176 758268834 -975467177 967684266 -975467178 758268832 -975467179 1082851919\n",
"5\n5 4 1 2 0\n",
"5\n-954618456 -522919664 -427019021 -130850748 191871394\n",
"6\n1 2 4 1 0 9\n",
"5\n15 1 9 10 8\n",
"5\n7 5 15 4 3\n",
"5\n2 2 6 4 3\n",
"10\n-6568 -5920 -8871 -5841 -2435 -635 -2680 -2032 -614 6565\n",
"10\n4846 6705 2530 5757 7569 -532 -2102 -3260 -4418 291\n",
"5\n1 2 6 22 27\n",
"5\n-186772848 -235864239 -25766025 -193955178 -243046569\n",
"5\n1 19 0 4 9\n",
"5\n2 0 -3 4 -2\n",
"3\n-1334827446 0 1001000000\n",
"3\n896 244 69\n",
"5\n1000001001 1 -1 -999999999 -1000000000\n",
"8\n1 12 3 14 8 21 7 11\n",
"7\n0 -1 2 3 0 5 5\n",
"3\n1000100001 1000000000 -227897416\n",
"7\n1 2 2 1 1 -1 1\n",
"20\n319410377 286827025 320654998 221660321 189076969 156493617 123910265 91326913 58743561 26160209 -11606501 -39006495 -71589847 -104173199 -136756551 -169339903 -201923255 -234506607 -461921277 -299673311\n",
"5\n0 0 9 4 8\n",
"5\n10 5 8 6 6\n",
"6\n1 4 1 3 4 7\n",
"7\n1 2 -1 0 1 6 9\n",
"20\n-975467170 758268840 -975467171 758268839 -975467172 758268838 -975467173 758268837 -975467174 1015089897 -975467175 758268835 -975467176 758268834 -975467177 967684266 -975467178 758268832 -975467179 1082851919\n",
"5\n5 4 2 2 0\n",
"5\n-954618456 -522919664 -427019021 -177751682 191871394\n",
"6\n1 2 5 1 0 9\n",
"5\n15 1 11 10 8\n",
"5\n7 10 15 4 3\n",
"5\n2 2 6 8 3\n",
"10\n-6568 -5920 -8871 -5841 -2435 -635 -1977 -2032 -614 6565\n",
"10\n4846 6705 1988 5757 7569 -532 -2102 -3260 -4418 291\n",
"5\n1 2 6 32 27\n",
"5\n-186772848 -235864239 -30207311 -193955178 -243046569\n"
],
"output": [
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Connect the countless points with lines, till we reach the faraway yonder.
There are n points on a coordinate plane, the i-th of which being (i, yi).
Determine whether it's possible to draw two parallel and non-overlapping lines, such that every point in the set lies on exactly one of them, and each of them passes through at least one point in the set.
Input
The first line of input contains a positive integer n (3 ≤ n ≤ 1 000) — the number of points.
The second line contains n space-separated integers y1, y2, ..., yn ( - 109 ≤ yi ≤ 109) — the vertical coordinates of each point.
Output
Output "Yes" (without quotes) if it's possible to fulfill the requirements, and "No" otherwise.
You can print each letter in any case (upper or lower).
Examples
Input
5
7 5 8 6 9
Output
Yes
Input
5
-1 -2 0 0 -5
Output
No
Input
5
5 4 3 2 1
Output
No
Input
5
1000000000 0 0 0 0
Output
Yes
Note
In the first example, there are five points: (1, 7), (2, 5), (3, 8), (4, 6) and (5, 9). It's possible to draw a line that passes through points 1, 3, 5, and another one that passes through points 2, 4 and is parallel to the first one.
In the second example, while it's possible to draw two lines that cover all points, they cannot be made parallel.
In the third example, it's impossible to satisfy both requirements at the same time.
### Input:
5
7 5 8 6 9
### Output:
Yes
### Input:
5
-1 -2 0 0 -5
### Output:
No
### Code:
def run():
n = int(input())
a = [int(x) for x in input().split()]
_s = set(a)
if len(_s) == 1:
print('No')
return
if len(_s) == 2:
print('Yes')
return
def check(dy, base):
st = [False] * n
for i in range(n):
if (a[i] - a[base]) * 2 == dy * (i - base):
st[i] = True
for i, s in enumerate(st):
if not s:
newbase = i
break
else:
return False
base = newbase
for i in range(n):
if (a[i] - a[base]) * 2 == dy * (i - base):
st[i] = True
return not (False in st)
if check((a[1]-a[0])*2, 0) or check((a[2]-a[1])*2, 1) or check((a[2]-a[0]), 0):
print('Yes')
else:
print('No')
run()
|
870_E. Points, Lines and Ready-made Titles_28402
|
You are given n distinct points on a plane with integral coordinates. For each point you can either draw a vertical line through it, draw a horizontal line through it, or do nothing.
You consider several coinciding straight lines as a single one. How many distinct pictures you can get? Print the answer modulo 109 + 7.
Input
The first line contains single integer n (1 ≤ n ≤ 105) — the number of points.
n lines follow. The (i + 1)-th of these lines contains two integers xi, yi ( - 109 ≤ xi, yi ≤ 109) — coordinates of the i-th point.
It is guaranteed that all points are distinct.
Output
Print the number of possible distinct pictures modulo 109 + 7.
Examples
Input
4
1 1
1 2
2 1
2 2
Output
16
Input
2
-1 -1
0 1
Output
9
Note
In the first example there are two vertical and two horizontal lines passing through the points. You can get pictures with any subset of these lines. For example, you can get the picture containing all four lines in two ways (each segment represents a line containing it).
The first way: <image> The second way: <image>
In the second example you can work with two points independently. The number of pictures is 32 = 9.
|
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n = mint()
p = [0]*n
x = dict()
y = dict()
for i in range(n):
a = tuple(mints())
p[i] = a
if a[0] in x:
x[a[0]].append(i)
else:
x[a[0]] = [i]
if a[1] in y:
y[a[1]].append(i)
else:
y[a[1]] = [i]
del(pow)
r = 1
q = [0]*n
w = [True]*n
ql = 0
qr = 0
for i in range(n):
if w[i]:
w[i] = False
q[qr] = i
qr += 1
qlb = ql
e = 0
xs = set()
ys = set()
while ql < qr:
v = q[ql]
ql += 1
a = p[v]
if a[0] not in xs:
xs.add(a[0])
e -= 1
for u in x[a[0]]:
e += 1
if w[u]:
w[u] = False
q[qr] = u
qr += 1
if a[1] not in ys:
ys.add(a[1])
e -= 1
for u in y[a[1]]:
e += 1
if w[u]:
w[u] = False
q[qr] = u
qr += 1
vc = ql-qlb
#print(vc,e,vc-1)
if vc-1 == e:
r = (r*(pow(2,vc+1,1000000007)-1))%1000000007
else:
r = (r*(pow(2,len(xs)+len(ys),1000000007)))%1000000007
print(r)
|
{
"input": [
"2\n-1 -1\n0 1\n",
"4\n1 1\n1 2\n2 1\n2 2\n",
"6\n0 2\n-1 1\n1 -2\n2 1\n-2 1\n-2 0\n",
"6\n-1 2\n0 -1\n-1 -2\n0 1\n-1 0\n1 0\n",
"1\n0 0\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n88335251 -77293021\n970294418 -43296260\n-155983273 850521645\n-852404258 -77293021\n518823261 -77293021\n-89661323 -43296260\n-155983273 -406914114\n",
"4\n1 0\n0 0\n0 1\n1 -1\n",
"7\n0 0\n2 2\n-2 2\n-1 2\n-1 -2\n-2 -2\n-2 -1\n",
"30\n4 3\n4 0\n0 -1\n-2 4\n3 4\n-1 1\n-3 -2\n-2 0\n-1 2\n3 -4\n-3 2\n1 -4\n-4 -4\n2 -1\n1 -2\n1 -1\n1 2\n3 0\n-2 1\n3 -3\n-4 -2\n2 -4\n1 3\n3 -1\n-2 2\n0 -4\n-2 3\n-4 2\n-1 3\n3 2\n",
"9\n1 1\n2 2\n3 3\n1 2\n2 1\n3 1\n1 3\n3 2\n2 3\n",
"6\n-2 1\n-1 -2\n-2 -2\n-2 2\n1 2\n2 -2\n",
"6\n1 -2\n-2 -1\n-1 1\n1 2\n0 -1\n-2 0\n",
"4\n1 -2\n2 1\n-1 2\n0 1\n",
"4\n2 1\n0 2\n-2 1\n0 0\n",
"3\n2 0\n2 1\n1 -2\n",
"4\n-2 -1\n0 0\n1 -2\n1 0\n",
"6\n-1 2\n0 -1\n0 -2\n0 1\n-1 0\n1 0\n",
"1\n0 -1\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n88335251 -80040028\n970294418 -43296260\n-155983273 850521645\n-852404258 -77293021\n518823261 -77293021\n-89661323 -43296260\n-155983273 -406914114\n",
"4\n1 0\n0 0\n0 1\n1 -2\n",
"7\n0 0\n2 2\n-2 2\n0 2\n-1 -2\n-2 -2\n-2 -1\n",
"30\n4 3\n4 0\n0 -1\n-2 4\n3 4\n-1 1\n-3 -2\n-2 0\n-1 2\n3 -4\n-3 2\n1 -4\n-4 -4\n2 -1\n1 -2\n1 -1\n1 2\n3 0\n-2 1\n3 -3\n-4 -2\n2 -4\n1 3\n3 -1\n-2 2\n-1 -4\n-2 3\n-4 2\n-1 3\n3 2\n",
"6\n-2 1\n-1 -2\n-2 0\n-2 2\n1 2\n2 -2\n",
"6\n1 -2\n-4 -1\n-1 1\n1 2\n0 -1\n-2 0\n",
"4\n0 -2\n2 1\n-1 2\n0 1\n",
"3\n2 0\n2 1\n0 -2\n",
"4\n-2 -1\n0 1\n1 -2\n1 0\n",
"2\n-2 -1\n0 1\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n88335251 -80040028\n970294418 -43296260\n-155983273 850521645\n-852404258 -77293021\n518823261 -77293021\n-89661323 -21885159\n-155983273 -406914114\n",
"7\n0 0\n2 2\n-2 3\n0 2\n-1 -2\n-2 -2\n-2 -1\n",
"6\n-2 1\n-1 0\n-2 0\n-2 2\n1 2\n2 -2\n",
"6\n1 -2\n-4 -1\n-1 1\n1 2\n0 -1\n-1 0\n",
"4\n-1 -2\n2 1\n-1 2\n0 1\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n88335251 -80040028\n970294418 -43296260\n-155983273 850521645\n-852404258 -125749655\n518823261 -77293021\n-89661323 -21885159\n-155983273 -406914114\n",
"6\n-2 1\n-1 -1\n-2 0\n-2 2\n1 2\n2 -2\n",
"4\n2 -1\n-1 2\n-2 1\n0 0\n",
"4\n2 0\n0 2\n-2 1\n0 0\n",
"4\n1 1\n1 2\n2 1\n0 2\n",
"6\n-1 2\n0 -1\n0 -2\n0 1\n-1 0\n1 -1\n",
"1\n-1 -1\n",
"4\n2 0\n-1 2\n-2 1\n0 0\n",
"3\n2 0\n0 1\n0 -2\n",
"4\n-2 -1\n1 1\n1 -2\n1 0\n",
"2\n-2 -1\n-1 1\n",
"4\n1 1\n1 2\n2 1\n0 3\n",
"1\n-1 0\n",
"6\n1 -2\n-4 -1\n-1 1\n1 2\n1 -1\n-1 0\n",
"4\n-2 -2\n2 1\n-1 2\n0 1\n",
"3\n2 -1\n0 1\n0 -2\n",
"2\n-2 -1\n0 2\n",
"4\n1 1\n0 2\n2 1\n0 3\n",
"1\n-2 0\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n87058696 -80040028\n970294418 -43296260\n-155983273 850521645\n-852404258 -125749655\n518823261 -77293021\n-89661323 -21885159\n-155983273 -406914114\n",
"6\n1 -2\n-4 -1\n-1 1\n1 2\n1 0\n-1 0\n",
"4\n-2 -2\n2 2\n-1 2\n0 1\n",
"4\n2 -1\n-1 2\n-2 2\n0 0\n",
"3\n2 -1\n0 1\n0 0\n",
"2\n-3 -1\n0 2\n",
"4\n1 1\n-1 2\n2 1\n0 3\n",
"1\n1 0\n",
"10\n504155727 -77293021\n-155983273 -43296260\n-548837441 -43296260\n87058696 -80040028\n1006418476 -43296260\n-155983273 850521645\n-852404258 -125749655\n518823261 -77293021\n-89661323 -21885159\n-155983273 -406914114\n",
"6\n1 -2\n-7 -1\n-1 1\n1 2\n1 0\n-1 0\n",
"4\n-2 -1\n2 1\n-1 2\n0 1\n"
],
"output": [
"9\n",
"16\n",
"279\n",
"217\n",
"3\n",
"3937\n",
"31\n",
"192\n",
"262144\n",
"64\n",
"127\n",
"315\n",
"63\n",
"49\n",
"21\n",
"45\n",
"225\n",
"3\n",
"5715\n",
"31\n",
"255\n",
"262144\n",
"217\n",
"441\n",
"45\n",
"21\n",
"63\n",
"9\n",
"8505\n",
"465\n",
"189\n",
"343\n",
"49\n",
"11907\n",
"279\n",
"81\n",
"45\n",
"31\n",
"217\n",
"3\n",
"63\n",
"21\n",
"45\n",
"9\n",
"45\n",
"3\n",
"217\n",
"63\n",
"21\n",
"9\n",
"49\n",
"3\n",
"11907\n",
"189\n",
"63\n",
"63\n",
"21\n",
"9\n",
"63\n",
"3\n",
"11907\n",
"189\n",
"63\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given n distinct points on a plane with integral coordinates. For each point you can either draw a vertical line through it, draw a horizontal line through it, or do nothing.
You consider several coinciding straight lines as a single one. How many distinct pictures you can get? Print the answer modulo 109 + 7.
Input
The first line contains single integer n (1 ≤ n ≤ 105) — the number of points.
n lines follow. The (i + 1)-th of these lines contains two integers xi, yi ( - 109 ≤ xi, yi ≤ 109) — coordinates of the i-th point.
It is guaranteed that all points are distinct.
Output
Print the number of possible distinct pictures modulo 109 + 7.
Examples
Input
4
1 1
1 2
2 1
2 2
Output
16
Input
2
-1 -1
0 1
Output
9
Note
In the first example there are two vertical and two horizontal lines passing through the points. You can get pictures with any subset of these lines. For example, you can get the picture containing all four lines in two ways (each segment represents a line containing it).
The first way: <image> The second way: <image>
In the second example you can work with two points independently. The number of pictures is 32 = 9.
### Input:
2
-1 -1
0 1
### Output:
9
### Input:
4
1 1
1 2
2 1
2 2
### Output:
16
### Code:
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n = mint()
p = [0]*n
x = dict()
y = dict()
for i in range(n):
a = tuple(mints())
p[i] = a
if a[0] in x:
x[a[0]].append(i)
else:
x[a[0]] = [i]
if a[1] in y:
y[a[1]].append(i)
else:
y[a[1]] = [i]
del(pow)
r = 1
q = [0]*n
w = [True]*n
ql = 0
qr = 0
for i in range(n):
if w[i]:
w[i] = False
q[qr] = i
qr += 1
qlb = ql
e = 0
xs = set()
ys = set()
while ql < qr:
v = q[ql]
ql += 1
a = p[v]
if a[0] not in xs:
xs.add(a[0])
e -= 1
for u in x[a[0]]:
e += 1
if w[u]:
w[u] = False
q[qr] = u
qr += 1
if a[1] not in ys:
ys.add(a[1])
e -= 1
for u in y[a[1]]:
e += 1
if w[u]:
w[u] = False
q[qr] = u
qr += 1
vc = ql-qlb
#print(vc,e,vc-1)
if vc-1 == e:
r = (r*(pow(2,vc+1,1000000007)-1))%1000000007
else:
r = (r*(pow(2,len(xs)+len(ys),1000000007)))%1000000007
print(r)
|
897_D. Ithea Plays With Chtholly_28406
|
This is an interactive problem. Refer to the Interaction section below for better understanding.
Ithea and Chtholly want to play a game in order to determine who can use the kitchen tonight.
<image>
Initially, Ithea puts n clear sheets of paper in a line. They are numbered from 1 to n from left to right.
This game will go on for m rounds. In each round, Ithea will give Chtholly an integer between 1 and c, and Chtholly needs to choose one of the sheets to write down this number (if there is already a number before, she will erase the original one and replace it with the new one).
Chtholly wins if, at any time, all the sheets are filled with a number and the n numbers are in non-decreasing order looking from left to right from sheet 1 to sheet n, and if after m rounds she still doesn't win, she loses the game.
Chtholly really wants to win the game as she wants to cook something for Willem. But she doesn't know how to win the game. So Chtholly finds you, and your task is to write a program to receive numbers that Ithea gives Chtholly and help her make the decision on which sheet of paper write this number.
Input
The first line contains 3 integers n, m and c (<image>, <image> means <image> rounded up) — the number of sheets, the number of rounds and the largest possible number Ithea can give to Chtholly respectively. The remaining parts of input are given throughout the interaction process.
Interaction
In each round, your program needs to read one line containing a single integer pi (1 ≤ pi ≤ c), indicating the number given to Chtholly.
Your program should then output a line containing an integer between 1 and n, indicating the number of sheet to write down this number in.
After outputting each line, don't forget to flush the output. For example:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
If Chtholly wins at the end of a round, no more input will become available and your program should terminate normally. It can be shown that under the constraints, it's always possible for Chtholly to win the game.
Example
Input
2 4 4
2
1
3
Output
1
2
2
Note
In the example, Chtholly initially knew there were 2 sheets, 4 rounds and each number was between 1 and 4. She then received a 2 and decided to write it in the 1st sheet. Then she received a 1 and wrote it in the 2nd sheet. At last, she received a 3 and replaced 1 with 3 in the 2nd sheet. At this time all the sheets were filled with a number and they were non-decreasing, so she won the game.
Note that it is required that your program terminate immediately after Chtholly wins and do not read numbers from the input for the remaining rounds. If not, undefined behaviour may arise and it won't be sure whether your program will be accepted or rejected. Also because of this, please be careful when hacking others' codes. In the sample, Chtholly won the game after the 3rd round, so it is required that your program doesn't read the number of the remaining 4th round.
The input format for hacking:
* The first line contains 3 integers n, m and c;
* The following m lines each contains an integer between 1 and c, indicating the number given to Chtholly in each round.
|
import sys
n, m, c = map(int, input().split())
free = n
nums = [0] * n
for i in range(m):
pi = int(input())
if(pi > c//2):
current = n - 1
while(nums[current] > 0 and nums[current] >= pi and current >= 0):current -= 1
if(current == -1):current = 0
if(nums[current] == 0):free -= 1
nums[current] = pi
print(current + 1)
else:
current = 0
while(current < n and nums[current] > 0 and nums[current] <= pi):current += 1
if(current == n):current = n - 1
if(nums[current] == 0):free -=1
nums[current] = pi
print(current + 1)
if(free == 0):break
|
{
"input": [
"2 4 4\n2\n1\n3\n",
"4 4 2\n2\n2\n2\n1\n",
"3 6 3\n3\n3\n2\n2\n1\n1\n",
"2 2 1\n1\n1\n",
"3 6 3\n1\n2\n1\n3\n1\n3\n",
"4 8 4\n2\n3\n2\n3\n2\n3\n2\n3\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n12\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n11\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n20\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n15\n15\n2\n6\n18\n12\n20\n10\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n10\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n6\n6\n6\n6\n6\n6\n6\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n3\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n1\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 8 4\n4\n4\n4\n4\n4\n4\n4\n4\n",
"4 4 2\n1\n2\n1\n2\n",
"4 8 3\n2\n1\n2\n1\n2\n1\n1\n1\n",
"4 8 3\n3\n2\n3\n2\n3\n2\n3\n1\n",
"3 3 1\n1\n1\n1\n",
"3 6 3\n2\n2\n3\n3\n1\n1\n",
"3 3 2\n1\n2\n1\n",
"4 4 2\n1\n2\n2\n1\n",
"2 2 2\n2\n1\n",
"2 2 2\n1\n2\n",
"2 4 4\n2\n1\n3\n4\n",
"3 3 2\n2\n1\n2\n",
"4 8 3\n2\n3\n2\n3\n3\n3\n3\n1\n",
"10 120 15\n6\n11\n9\n11\n3\n12\n11\n12\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n7\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n9\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n2\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"2 2 2\n2\n2\n",
"4 8 4\n3\n4\n3\n3\n4\n4\n1\n2\n",
"3 6 3\n2\n2\n1\n1\n3\n3\n",
"3 3 2\n2\n2\n1\n",
"3 3 2\n2\n1\n1\n",
"4 4 3\n2\n2\n2\n1\n",
"3 6 3\n3\n3\n2\n2\n0\n1\n",
"3 6 3\n1\n2\n1\n3\n1\n2\n",
"4 8 4\n2\n1\n2\n3\n2\n3\n2\n3\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n12\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n11\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n20\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n18\n12\n20\n10\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n6\n6\n6\n6\n6\n6\n6\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n3\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n1\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 8 4\n4\n1\n4\n4\n4\n4\n4\n4\n",
"4 4 3\n1\n2\n1\n2\n",
"4 16 3\n3\n2\n3\n2\n3\n2\n3\n1\n",
"3 10 3\n2\n2\n3\n3\n1\n1\n",
"4 8 3\n2\n3\n2\n3\n3\n3\n6\n1\n",
"10 120 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n7\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n9\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n2\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"2 3 2\n2\n1\n1\n",
"4 4 3\n2\n2\n1\n1\n",
"4 10 3\n2\n2\n3\n3\n1\n1\n",
"3 8 5\n2\n2\n1\n1\n3\n3\n",
"10 100 20\n11\n20\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n6\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n4\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n1\n4\n13\n25\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n7\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n29\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n23\n5\n7\n9\n15\n14\n37\n0\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n25\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n4\n8\n3\n11\n13\n5\n12\n11\n9\n6\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n1\n4\n13\n25\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n13\n12\n8\n",
"4 8 3\n2\n1\n2\n1\n1\n1\n1\n1\n",
"3 8 3\n2\n2\n1\n1\n3\n3\n",
"4 8 4\n2\n1\n2\n3\n2\n3\n2\n1\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n12\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n11\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n18\n12\n20\n10\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n6\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n3\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n1\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 8 3\n2\n1\n2\n2\n1\n1\n1\n1\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n7\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n9\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n2\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"4 8 4\n2\n1\n2\n3\n2\n3\n2\n0\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n12\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n11\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n18\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n6\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n3\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 8 3\n2\n1\n2\n2\n0\n1\n1\n1\n",
"4 14 3\n2\n2\n3\n3\n1\n1\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n7\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n2\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"3 8 5\n2\n2\n1\n1\n3\n0\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n11\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n18\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n6\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 13 3\n2\n1\n2\n2\n0\n1\n1\n1\n",
"4 24 3\n2\n2\n3\n3\n1\n1\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n7\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n18\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n5\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"4 13 3\n2\n1\n2\n2\n0\n0\n1\n1\n",
"4 37 3\n2\n2\n3\n3\n1\n1\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n4\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n6\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n25\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n11\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n6\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n3\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n1\n4\n13\n13\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n16\n5\n7\n9\n15\n14\n37\n0\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n25\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n2\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n1\n4\n13\n25\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n8\n12\n8\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n16\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n23\n5\n7\n9\n15\n14\n37\n0\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n25\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n20\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n6\n5\n5\n4\n4\n4\n4\n4\n4\n4\n4\n4\n3\n2\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"10 100 20\n4\n1\n15\n2\n11\n1\n18\n9\n17\n5\n17\n12\n20\n6\n14\n19\n20\n3\n6\n14\n13\n17\n17\n10\n11\n8\n6\n6\n19\n16\n20\n6\n14\n5\n6\n19\n29\n11\n12\n1\n18\n10\n20\n8\n6\n12\n18\n16\n9\n10\n13\n17\n19\n7\n15\n7\n19\n1\n9\n10\n12\n5\n4\n23\n5\n7\n9\n15\n14\n37\n0\n3\n12\n10\n3\n6\n1\n16\n15\n18\n6\n19\n4\n17\n10\n15\n2\n6\n25\n12\n20\n16\n5\n13\n9\n11\n20\n20\n4\n16\n",
"10 100 20\n11\n20\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n5\n5\n5\n5\n6\n5\n5\n4\n4\n7\n4\n4\n4\n4\n4\n4\n3\n2\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n",
"10 47 15\n6\n11\n9\n11\n3\n12\n11\n9\n4\n8\n3\n11\n13\n5\n12\n11\n9\n3\n10\n9\n9\n13\n13\n5\n6\n11\n3\n15\n8\n8\n10\n13\n7\n6\n4\n14\n9\n10\n5\n13\n4\n1\n8\n6\n13\n1\n3\n4\n9\n12\n2\n7\n3\n3\n5\n2\n2\n9\n2\n4\n2\n2\n11\n12\n15\n13\n6\n2\n11\n1\n8\n3\n13\n6\n15\n6\n4\n3\n4\n15\n15\n9\n5\n8\n3\n6\n14\n14\n5\n5\n4\n4\n14\n1\n12\n4\n12\n9\n11\n7\n4\n4\n5\n1\n4\n13\n25\n4\n5\n8\n3\n4\n2\n15\n3\n10\n9\n13\n12\n8\n",
"10 100 20\n11\n20\n11\n11\n11\n11\n11\n11\n11\n10\n10\n10\n10\n10\n10\n10\n10\n11\n9\n9\n9\n9\n9\n9\n9\n9\n9\n8\n8\n8\n8\n8\n8\n8\n8\n8\n7\n7\n7\n7\n7\n7\n7\n7\n7\n4\n6\n6\n6\n6\n6\n9\n6\n6\n5\n5\n10\n5\n5\n5\n6\n5\n5\n4\n4\n7\n4\n4\n4\n4\n4\n4\n3\n2\n3\n3\n3\n3\n3\n3\n5\n2\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n1\n1\n1\n1\n1\n1\n12\n"
],
"output": [
"1\n1\n2\n",
"4\n3\n2\n1\n",
"3\n2\n1\n",
"2\n1\n",
"1\n3\n2\n",
"1\n4\n2\n3\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n3\n2\n1\n",
"1\n4\n2\n3\n",
"4\n1\n3\n2\n",
"4\n3\n3\n2\n2\n1\n",
"3\n2\n1\n",
"3\n2\n3\n2\n1\n",
"1\n3\n2\n",
"1\n4\n3\n2\n",
"2\n1\n",
"1\n2\n",
"1\n1\n2\n",
"3\n1\n2\n",
"4\n4\n3\n3\n2\n1\n",
"1\n10\n9\n9\n1\n10\n8\n9\n1\n7\n2\n7\n10\n3\n8\n6\n5\n3\n5\n4\n",
"2\n1\n",
"4\n4\n3\n2\n3\n2\n1\n",
"3\n2\n1\n",
"3\n2\n1\n",
"3\n1\n2\n",
"4\n3\n2\n1\n",
"3\n2\n1\n",
"1\n3\n2\n",
"1\n1\n2\n4\n3\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n1\n3\n2\n",
"1\n4\n2\n3\n",
"4\n3\n3\n2\n2\n1\n",
"3\n2\n3\n2\n1\n",
"4\n4\n3\n3\n2\n1\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"2\n1\n",
"4\n3\n1\n2\n",
"4\n3\n4\n3\n1\n2\n",
"1\n2\n1\n2\n3\n",
"10\n10\n9\n8\n7\n6\n5\n4\n3\n1\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n2\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n10\n2\n9\n2\n10\n3\n3\n3\n9\n8\n10\n4\n8\n9\n9\n3\n5\n7\n6\n",
"1\n10\n9\n9\n1\n10\n8\n7\n2\n6\n2\n7\n10\n3\n9\n6\n5\n4\n",
"4\n1\n3\n2\n",
"3\n2\n1\n",
"1\n1\n2\n4\n3\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n1\n3\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n2\n4\n3\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n1\n3\n2\n",
"4\n3\n4\n3\n1\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n2\n1\n2\n3\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n1\n3\n2\n",
"4\n3\n4\n3\n1\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"4\n1\n3\n2\n",
"4\n3\n4\n3\n1\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"1\n10\n9\n9\n1\n10\n8\n7\n1\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n10\n9\n8\n7\n6\n5\n4\n3\n1\n2\n",
"1\n1\n10\n2\n9\n2\n10\n3\n9\n3\n8\n7\n10\n4\n7\n9\n9\n3\n5\n6\n",
"10\n10\n9\n8\n7\n6\n5\n4\n3\n1\n2\n",
"1\n10\n9\n9\n1\n10\n8\n7\n2\n6\n2\n7\n10\n3\n9\n6\n5\n3\n5\n4\n",
"10\n10\n9\n8\n7\n6\n5\n4\n3\n1\n2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This is an interactive problem. Refer to the Interaction section below for better understanding.
Ithea and Chtholly want to play a game in order to determine who can use the kitchen tonight.
<image>
Initially, Ithea puts n clear sheets of paper in a line. They are numbered from 1 to n from left to right.
This game will go on for m rounds. In each round, Ithea will give Chtholly an integer between 1 and c, and Chtholly needs to choose one of the sheets to write down this number (if there is already a number before, she will erase the original one and replace it with the new one).
Chtholly wins if, at any time, all the sheets are filled with a number and the n numbers are in non-decreasing order looking from left to right from sheet 1 to sheet n, and if after m rounds she still doesn't win, she loses the game.
Chtholly really wants to win the game as she wants to cook something for Willem. But she doesn't know how to win the game. So Chtholly finds you, and your task is to write a program to receive numbers that Ithea gives Chtholly and help her make the decision on which sheet of paper write this number.
Input
The first line contains 3 integers n, m and c (<image>, <image> means <image> rounded up) — the number of sheets, the number of rounds and the largest possible number Ithea can give to Chtholly respectively. The remaining parts of input are given throughout the interaction process.
Interaction
In each round, your program needs to read one line containing a single integer pi (1 ≤ pi ≤ c), indicating the number given to Chtholly.
Your program should then output a line containing an integer between 1 and n, indicating the number of sheet to write down this number in.
After outputting each line, don't forget to flush the output. For example:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
If Chtholly wins at the end of a round, no more input will become available and your program should terminate normally. It can be shown that under the constraints, it's always possible for Chtholly to win the game.
Example
Input
2 4 4
2
1
3
Output
1
2
2
Note
In the example, Chtholly initially knew there were 2 sheets, 4 rounds and each number was between 1 and 4. She then received a 2 and decided to write it in the 1st sheet. Then she received a 1 and wrote it in the 2nd sheet. At last, she received a 3 and replaced 1 with 3 in the 2nd sheet. At this time all the sheets were filled with a number and they were non-decreasing, so she won the game.
Note that it is required that your program terminate immediately after Chtholly wins and do not read numbers from the input for the remaining rounds. If not, undefined behaviour may arise and it won't be sure whether your program will be accepted or rejected. Also because of this, please be careful when hacking others' codes. In the sample, Chtholly won the game after the 3rd round, so it is required that your program doesn't read the number of the remaining 4th round.
The input format for hacking:
* The first line contains 3 integers n, m and c;
* The following m lines each contains an integer between 1 and c, indicating the number given to Chtholly in each round.
### Input:
2 4 4
2
1
3
### Output:
1
1
2
### Input:
4 4 2
2
2
2
1
### Output:
4
3
2
1
### Code:
import sys
n, m, c = map(int, input().split())
free = n
nums = [0] * n
for i in range(m):
pi = int(input())
if(pi > c//2):
current = n - 1
while(nums[current] > 0 and nums[current] >= pi and current >= 0):current -= 1
if(current == -1):current = 0
if(nums[current] == 0):free -= 1
nums[current] = pi
print(current + 1)
else:
current = 0
while(current < n and nums[current] > 0 and nums[current] <= pi):current += 1
if(current == n):current = n - 1
if(nums[current] == 0):free -=1
nums[current] = pi
print(current + 1)
if(free == 0):break
|
940_E. Cashback_28412
|
Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.
You are given an array a of length n and an integer c.
The value of some array b of length k is the sum of its elements except for the <image> smallest. For example, the value of the array [3, 1, 6, 5, 2] with c = 2 is 3 + 6 + 5 = 14.
Among all possible partitions of a into contiguous subarrays output the smallest possible sum of the values of these subarrays.
Input
The first line contains integers n and c (1 ≤ n, c ≤ 100 000).
The second line contains n integers ai (1 ≤ ai ≤ 109) — elements of a.
Output
Output a single integer — the smallest possible sum of values of these subarrays of some partition of a.
Examples
Input
3 5
1 2 3
Output
6
Input
12 10
1 1 10 10 10 10 10 10 9 10 10 10
Output
92
Input
7 2
2 3 6 4 5 7 1
Output
17
Input
8 4
1 3 4 5 5 3 4 1
Output
23
Note
In the first example any partition yields 6 as the sum.
In the second example one of the optimal partitions is [1, 1], [10, 10, 10, 10, 10, 10, 9, 10, 10, 10] with the values 2 and 90 respectively.
In the third example one of the optimal partitions is [2, 3], [6, 4, 5, 7], [1] with the values 3, 13 and 1 respectively.
In the fourth example one of the optimal partitions is [1], [3, 4, 5, 5, 3, 4], [1] with the values 1, 21 and 1 respectively.
|
from heapq import *
f = lambda: map(int, input().split())
n, c = f()
a = list(f()) + [0] * c
b = [0] * (n + c)
s = 0
h = [(0, -1)]
for i in range(n):
s += a[i] - a[i - c]
heappush(h, (a[i], i))
while h[0][1] <= i - c: heappop(h)
b[i] = min(b[i - 1] + a[i], b[i - c] + s - h[0][0])
print(b[n - 1])
|
{
"input": [
"3 5\n1 2 3\n",
"7 2\n2 3 6 4 5 7 1\n",
"8 4\n1 3 4 5 5 3 4 1\n",
"12 10\n1 1 10 10 10 10 10 10 9 10 10 10\n",
"15 10\n4 5 5 5 5 5 5 5 5 5 5 5 5 5 1\n",
"15 5\n1 67 1 100 67 34 67 34 34 1 1 34 34 1 67\n",
"15 5\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"9 10\n20 54 35 72 35 35 64 39 34\n",
"14 10\n16 82 72 72 72 72 72 72 72 72 72 72 81 71\n",
"15 10\n31 91 91 91 91 91 91 91 91 99 91 91 91 91 90\n",
"100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 1611 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 9756 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 7547 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 3668 6876 7116\n",
"13 10\n94 95 95 95 95 95 95 95 95 95 95 95 76\n",
"10 10\n48 87 96 87 87 87 87 87 87 86\n",
"15 10\n94 87 72 62 55 53 51 50 48 41 39 24 15 7 2\n",
"15 10\n2 3 3 3 3 3 3 3 3 3 3 3 3 3 1\n",
"100 25\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 5\n3 4 9 4 2 6 3 3 9 4 4 1 9 9 9 6 10 9 3 7 7 1 5 7 1 8 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 5 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 1 2\n",
"11 10\n58 97 93 74 59 59 76 59 59 59 30\n",
"15 15\n47 48 48 48 48 48 48 48 48 48 48 48 48 48 25\n",
"15 5\n11 15 16 24 24 28 36 40 49 49 53 55 66 73 100\n",
"1 1\n1\n",
"12 10\n76 77 82 77 97 77 77 77 77 77 77 48\n",
"15 10\n4 5 5 5 5 5 9 5 5 5 5 5 5 5 1\n",
"15 5\n1 67 1 100 67 34 67 34 34 1 1 50 34 1 67\n",
"9 10\n20 54 35 72 35 41 64 39 34\n",
"15 10\n31 91 91 91 91 91 91 91 91 99 91 91 91 91 118\n",
"100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 1611 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 9756 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 10553 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 3668 6876 7116\n",
"13 10\n94 95 95 95 95 95 95 95 133 95 95 95 76\n",
"10 10\n53 87 96 87 87 87 87 87 87 86\n",
"15 10\n94 87 72 62 55 53 51 50 48 41 39 24 15 6 2\n",
"15 10\n2 5 3 3 3 3 3 3 3 3 3 3 3 3 1\n",
"100 25\n1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 5\n3 4 9 4 2 6 3 3 9 4 4 1 9 9 9 6 10 9 3 7 7 1 5 7 1 15 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 5 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 1 2\n",
"11 11\n58 97 93 74 59 59 76 59 59 59 30\n",
"15 15\n47 48 48 48 48 48 0 48 48 48 48 48 48 48 25\n",
"15 7\n11 15 16 24 24 28 36 40 49 49 53 55 66 73 100\n",
"1 1\n0\n",
"12 14\n76 77 82 77 97 77 77 77 77 77 77 48\n",
"7 2\n2 2 6 4 5 7 1\n",
"8 4\n0 3 4 5 5 3 4 1\n",
"12 10\n1 1 10 15 10 10 10 10 9 10 10 10\n",
"15 10\n4 5 5 5 5 5 9 5 5 5 5 5 5 2 1\n",
"15 5\n1 133 1 100 67 34 67 34 34 1 1 50 34 1 67\n",
"100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 636 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 9756 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 10553 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 3668 6876 7116\n",
"13 10\n94 95 95 95 95 95 95 95 113 95 95 95 76\n",
"10 10\n53 87 96 87 87 87 87 87 87 111\n",
"15 10\n94 87 72 62 55 53 90 50 48 41 39 24 15 6 2\n",
"100 5\n3 4 9 4 2 6 3 3 9 4 4 1 9 9 9 6 10 9 3 7 7 1 5 7 1 15 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 10 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 1 2\n",
"11 11\n58 97 93 74 34 59 76 59 59 59 30\n",
"15 7\n11 15 16 24 24 28 36 40 68 49 53 55 66 73 100\n",
"12 14\n76 77 82 77 97 77 77 77 77 77 108 48\n",
"8 4\n0 3 8 5 5 3 4 1\n",
"15 5\n1 133 1 100 84 34 67 34 34 1 1 50 34 1 67\n",
"15 10\n31 91 91 91 91 20 91 91 91 99 95 91 91 91 118\n",
"100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 636 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 9756 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 10553 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 4511 6876 7116\n",
"13 10\n94 95 95 95 95 95 186 95 113 95 95 95 76\n",
"10 10\n53 87 96 87 87 110 87 87 87 111\n",
"15 10\n2 5 3 3 1 5 3 3 3 3 3 3 3 3 1\n",
"100 5\n3 4 9 4 2 6 3 3 9 4 4 1 9 9 9 6 10 9 3 7 7 1 5 7 1 15 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 10 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 0 2\n",
"11 11\n58 97 93 74 34 59 76 59 59 59 43\n",
"15 7\n11 15 16 23 24 28 36 40 68 49 53 55 66 73 100\n",
"12 14\n76 77 82 77 97 77 77 77 104 77 108 48\n",
"8 4\n0 3 8 0 5 3 4 1\n",
"15 5\n1 133 1 100 84 34 67 34 34 1 2 50 34 1 67\n",
"100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 636 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 3740 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 10553 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 4511 6876 7116\n",
"13 10\n94 95 95 95 95 95 186 95 37 95 95 95 76\n",
"10 10\n53 148 96 87 87 110 87 87 87 111\n",
"15 10\n2 5 3 3 1 5 3 3 3 3 3 3 5 3 1\n",
"100 5\n3 4 9 4 2 6 3 3 9 4 2 1 9 9 9 6 10 9 3 7 7 1 5 7 1 15 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 10 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 0 2\n",
"11 11\n58 97 93 80 34 59 76 59 59 59 43\n",
"15 7\n11 15 16 23 24 28 66 40 68 49 53 55 66 73 100\n",
"12 14\n76 77 110 77 97 77 77 77 104 77 108 48\n",
"15 10\n31 91 91 91 91 20 91 91 91 99 91 91 91 91 118\n",
"15 10\n2 5 3 3 1 3 3 3 3 3 3 3 3 3 1\n",
"100 25\n1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\n",
"15 10\n4 5 5 5 5 5 9 5 5 2 5 5 5 2 1\n",
"100 25\n1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\n",
"15 10\n4 5 5 5 5 5 9 5 5 2 5 5 8 2 1\n",
"15 10\n31 91 91 91 91 12 91 91 91 99 95 91 91 91 118\n",
"100 25\n1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\n",
"8 4\n0 3 8 0 5 6 4 1\n"
],
"output": [
"6\n",
"17\n",
"23\n",
"92\n",
"65\n",
"508\n",
"12\n",
"388\n",
"898\n",
"1221\n",
"543544\n",
"1120\n",
"791\n",
"659\n",
"39\n",
"96\n",
"488\n",
"665\n",
"671\n",
"547\n",
"0\n",
"842\n",
"69\n",
"524\n",
"394\n",
"1249\n",
"546550\n",
"1158\n",
"791\n",
"658\n",
"41\n",
"96\n",
"495\n",
"693\n",
"648\n",
"575\n",
"0\n",
"919\n",
"16\n",
"22\n",
"97\n",
"66\n",
"590\n",
"546438\n",
"1138\n",
"816\n",
"697\n",
"500\n",
"668\n",
"594\n",
"950\n",
"26\n",
"607\n",
"1253\n",
"547281\n",
"1229\n",
"839\n",
"43\n",
"499\n",
"677\n",
"593\n",
"977\n",
"23\n",
"608\n",
"541265\n",
"1211\n",
"900\n",
"45\n",
"497\n",
"683\n",
"623\n",
"1005\n",
"1249\n",
"41\n",
"97\n",
"66\n",
"96\n",
"69\n",
"1253\n",
"96\n",
"26\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.
You are given an array a of length n and an integer c.
The value of some array b of length k is the sum of its elements except for the <image> smallest. For example, the value of the array [3, 1, 6, 5, 2] with c = 2 is 3 + 6 + 5 = 14.
Among all possible partitions of a into contiguous subarrays output the smallest possible sum of the values of these subarrays.
Input
The first line contains integers n and c (1 ≤ n, c ≤ 100 000).
The second line contains n integers ai (1 ≤ ai ≤ 109) — elements of a.
Output
Output a single integer — the smallest possible sum of values of these subarrays of some partition of a.
Examples
Input
3 5
1 2 3
Output
6
Input
12 10
1 1 10 10 10 10 10 10 9 10 10 10
Output
92
Input
7 2
2 3 6 4 5 7 1
Output
17
Input
8 4
1 3 4 5 5 3 4 1
Output
23
Note
In the first example any partition yields 6 as the sum.
In the second example one of the optimal partitions is [1, 1], [10, 10, 10, 10, 10, 10, 9, 10, 10, 10] with the values 2 and 90 respectively.
In the third example one of the optimal partitions is [2, 3], [6, 4, 5, 7], [1] with the values 3, 13 and 1 respectively.
In the fourth example one of the optimal partitions is [1], [3, 4, 5, 5, 3, 4], [1] with the values 1, 21 and 1 respectively.
### Input:
3 5
1 2 3
### Output:
6
### Input:
7 2
2 3 6 4 5 7 1
### Output:
17
### Code:
from heapq import *
f = lambda: map(int, input().split())
n, c = f()
a = list(f()) + [0] * c
b = [0] * (n + c)
s = 0
h = [(0, -1)]
for i in range(n):
s += a[i] - a[i - c]
heappush(h, (a[i], i))
while h[0][1] <= i - c: heappop(h)
b[i] = min(b[i - 1] + a[i], b[i - c] + s - h[0][0])
print(b[n - 1])
|
96_B. Lucky Numbers (easy)_28416
|
Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.
One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.
Input
The only line contains a positive integer n (1 ≤ n ≤ 109). This number doesn't have leading zeroes.
Output
Output the least super lucky number that is more than or equal to n.
Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.
Examples
Input
4500
Output
4747
Input
47
Output
47
|
gh=set()
def rep(n,four,seven):
global gh
if n>10000000000 :return
if (four==seven):gh|={n}
rep(n*10+4,four+1,seven)
rep(n*10+7,four,seven+1)
rep(0,0,0)
gh=sorted(gh)
def bin_s(a):
lo=0;hi=len(gh);ans=0
while lo<=hi:
mid=(lo+hi)//2
if gh[mid]>=a:ans=gh[mid];hi=mid-1
else:lo=mid+1
return ans
print(bin_s(int(input())))
|
{
"input": [
"4500\n",
"47\n",
"447777\n",
"444000000\n",
"99\n",
"48\n",
"7773\n",
"7748\n",
"10\n",
"1\n",
"7474747\n",
"50\n",
"4\n",
"147474747\n",
"444444444\n",
"4700007\n",
"87584777\n",
"123\n",
"4777\n",
"19\n",
"1024\n",
"12\n",
"74477744\n",
"491020945\n",
"99999999\n",
"85469\n",
"474\n",
"1007\n",
"888999577\n",
"73\n",
"100\n",
"777777\n",
"47474774\n",
"74710000\n",
"70070077\n",
"2145226\n",
"74777443\n",
"47474749\n",
"467549754\n",
"7\n",
"7474\n",
"4587\n",
"5556585\n",
"555\n",
"1000000000\n",
"999999999\n",
"100000\n",
"70\n",
"77777777\n",
"3696\n",
"9\n",
"74700\n",
"734904893\n",
"3\n",
"13610\n",
"2606\n",
"14388274\n",
"63\n",
"7627\n",
"20\n",
"6\n",
"174446465\n",
"642273025\n",
"2896627\n",
"113236598\n",
"8783\n",
"13\n",
"151\n",
"2\n",
"18021447\n",
"289763961\n",
"162196004\n",
"65072\n",
"417\n",
"495\n",
"667961893\n",
"126\n",
"101\n",
"1413183\n",
"4293860\n",
"91582417\n",
"96581809\n",
"372783\n",
"146158462\n",
"39422007\n",
"909851506\n",
"11245\n",
"2998\n",
"6998206\n",
"1000100000\n",
"492963911\n",
"101000\n",
"28\n",
"107083084\n",
"2096\n",
"60360\n",
"2059\n",
"16\n",
"541447802\n",
"5\n",
"3146\n",
"33\n",
"13953863\n",
"11\n",
"273889958\n",
"305496855\n",
"2621539\n",
"15515374\n",
"111\n",
"287\n",
"14\n",
"7110283\n",
"428420186\n",
"195316478\n",
"42040\n",
"402\n",
"579\n",
"1211766791\n",
"39\n",
"1389220\n",
"381831\n",
"34892475\n",
"118807601\n",
"162567\n",
"153773674\n",
"29385491\n",
"1101704081\n",
"17414\n",
"6738403\n",
"1010000000\n",
"889611598\n",
"100010\n",
"8\n",
"188870328\n",
"432\n",
"1755\n",
"25\n",
"22\n",
"787738391\n",
"44\n",
"3916\n",
"26\n",
"12641310\n",
"504830410\n",
"593897243\n",
"3181856\n",
"3992010\n",
"10855\n"
],
"output": [
"4747\n",
"47\n",
"474477\n",
"4444477777\n",
"4477\n",
"74\n",
"444777\n",
"444777\n",
"47\n",
"47\n",
"44447777\n",
"74\n",
"47\n",
"4444477777\n",
"4444477777\n",
"44447777\n",
"4444477777\n",
"4477\n",
"7447\n",
"47\n",
"4477\n",
"47\n",
"74477744\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"4477\n",
"4477\n",
"4444477777\n",
"74\n",
"4477\n",
"44447777\n",
"47474774\n",
"74744477\n",
"74444777\n",
"44447777\n",
"74777444\n",
"47474774\n",
"4444477777\n",
"47\n",
"7474\n",
"4747\n",
"44447777\n",
"4477\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"74\n",
"4444477777\n",
"4477\n",
"47\n",
"444777\n",
"4444477777\n",
"47\n",
"444777\n",
"4477\n",
"44447777\n",
"74\n",
"7744\n",
"47\n",
"47\n",
"4444477777\n",
"4444477777\n",
"44447777\n",
"4444477777\n",
"444777\n",
"47\n",
"4477\n",
"47\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"4477\n",
"4477\n",
"4444477777\n",
"4477\n",
"4477\n",
"44447777\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"4444477777\n",
"44447777\n",
"4444477777\n",
"444777\n",
"4477\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"47\n",
"4444477777\n",
"4477\n",
"444777\n",
"4477\n",
"47\n",
"4444477777\n",
"47\n",
"4477\n",
"47\n",
"44447777\n",
"47\n",
"4444477777\n",
"4444477777\n",
"44447777\n",
"44447777\n",
"4477\n",
"4477\n",
"47\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"4477\n",
"4477\n",
"4444477777\n",
"47\n",
"44447777\n",
"444777\n",
"44447777\n",
"4444477777\n",
"444777\n",
"4444477777\n",
"44447777\n",
"4444477777\n",
"444777\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"444777\n",
"47\n",
"4444477777\n",
"4477\n",
"4477\n",
"47\n",
"47\n",
"4444477777\n",
"47\n",
"4477\n",
"47\n",
"44447777\n",
"4444477777\n",
"4444477777\n",
"44447777\n",
"44447777\n",
"444777\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.
One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.
Input
The only line contains a positive integer n (1 ≤ n ≤ 109). This number doesn't have leading zeroes.
Output
Output the least super lucky number that is more than or equal to n.
Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.
Examples
Input
4500
Output
4747
Input
47
Output
47
### Input:
4500
### Output:
4747
### Input:
47
### Output:
47
### Code:
gh=set()
def rep(n,four,seven):
global gh
if n>10000000000 :return
if (four==seven):gh|={n}
rep(n*10+4,four+1,seven)
rep(n*10+7,four,seven+1)
rep(0,0,0)
gh=sorted(gh)
def bin_s(a):
lo=0;hi=len(gh);ans=0
while lo<=hi:
mid=(lo+hi)//2
if gh[mid]>=a:ans=gh[mid];hi=mid-1
else:lo=mid+1
return ans
print(bin_s(int(input())))
|
994_B. Knights of a Polygonal Table_28420
|
Unlike Knights of a Round Table, Knights of a Polygonal Table deprived of nobility and happy to kill each other. But each knight has some power and a knight can kill another knight if and only if his power is greater than the power of victim. However, even such a knight will torment his conscience, so he can kill no more than k other knights. Also, each knight has some number of coins. After a kill, a knight can pick up all victim's coins.
Now each knight ponders: how many coins he can have if only he kills other knights?
You should answer this question for each knight.
Input
The first line contains two integers n and k (1 ≤ n ≤ 10^5, 0 ≤ k ≤ min(n-1,10)) — the number of knights and the number k from the statement.
The second line contains n integers p_1, p_2 ,…,p_n (1 ≤ p_i ≤ 10^9) — powers of the knights. All p_i are distinct.
The third line contains n integers c_1, c_2 ,…,c_n (0 ≤ c_i ≤ 10^9) — the number of coins each knight has.
Output
Print n integers — the maximum number of coins each knight can have it only he kills other knights.
Examples
Input
4 2
4 5 9 7
1 2 11 33
Output
1 3 46 36
Input
5 1
1 2 3 4 5
1 2 3 4 5
Output
1 3 5 7 9
Input
1 0
2
3
Output
3
Note
Consider the first example.
* The first knight is the weakest, so he can't kill anyone. That leaves him with the only coin he initially has.
* The second knight can kill the first knight and add his coin to his own two.
* The third knight is the strongest, but he can't kill more than k = 2 other knights. It is optimal to kill the second and the fourth knights: 2+11+33 = 46.
* The fourth knight should kill the first and the second knights: 33+1+2 = 36.
In the second example the first knight can't kill anyone, while all the others should kill the one with the index less by one than their own.
In the third example there is only one knight, so he can't kill anyone.
|
n,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
d={}
l=[]
for i in range(n):
x=a[i]
y=b[i]
l.append((x,y))
l.sort()
ans=[]
j=0
if k==0:
print(*b)
else:
for i in range(n):
if i<k:
ans.append(l[i][1])
ans.sort()
d[l[i][0]]=sum(ans)
else:
d[l[i][0]]=sum(ans)+l[i][1]
if min(ans)<l[i][1]:
ind=ans.index(min(ans))
ans[ind]=l[i][1]
for i in range(n):
print(d[a[i]],end=' ')
|
{
"input": [
"5 1\n1 2 3 4 5\n1 2 3 4 5\n",
"1 0\n2\n3\n",
"4 2\n4 5 9 7\n1 2 11 33\n",
"3 0\n1 2 3\n10 20 30\n",
"2 0\n2 3\n3 3\n",
"11 10\n1 2 3 4 5 6 7 8 9 10 11\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"10 5\n1 2 3 4 5 6 7 8 9 10\n1 1 1 1 1 1 1 1 1 1\n",
"7 1\n2 3 4 5 7 8 9\n0 3 7 9 5 8 9\n",
"3 0\n3 2 1\n1 2 3\n",
"4 2\n4 5 9 7\n2 2 11 33\n",
"3 2\n1 2 3\n1 1 1\n",
"7 3\n1 2 3 4 5 6 7\n3 3 3 8 8 8 8\n",
"4 0\n4 5 9 7\n1 2 11 33\n",
"5 4\n1 2 3 4 5\n1 1 1 1 1\n",
"6 3\n1 2 3 4 5 6\n1 1 1 1 1 1\n",
"3 0\n1 2 3\n5 5 5\n",
"4 0\n4 5 9 7\n1 2 3 4\n",
"7 3\n1 2 3 4 5 6 7\n3 3 3 4 5 6 7\n",
"4 3\n1 2 3 4\n5 5 5 5\n",
"7 2\n2 4 6 7 8 9 10\n10 8 4 8 4 5 9\n",
"5 3\n4 5 7 9 11\n10 10 10 10 10\n",
"5 3\n1 2 3 4 5\n7 7 7 7 7\n",
"2 0\n1 3\n3 3\n",
"11 10\n1 2 3 4 5 6 7 8 9 10 11\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1100000000\n",
"10 1\n1 2 3 4 5 6 7 8 9 10\n1 1 1 1 1 1 1 1 1 1\n",
"3 0\n3 2 1\n0 2 3\n",
"3 2\n1 4 3\n1 1 1\n",
"7 3\n1 2 3 4 5 6 7\n3 4 3 8 8 8 8\n",
"4 0\n4 5 9 6\n1 2 11 33\n",
"5 4\n1 2 3 4 8\n1 1 1 1 1\n",
"6 3\n1 2 3 4 5 6\n1 2 1 1 1 1\n",
"3 0\n1 2 3\n5 5 3\n",
"7 3\n1 2 3 4 5 6 7\n3 3 1 4 5 6 7\n",
"4 3\n1 2 3 4\n5 1 5 5\n",
"7 2\n2 4 6 7 8 9 16\n10 8 4 8 4 5 9\n",
"1 0\n2\n0\n",
"4 2\n4 3 9 7\n1 2 11 33\n",
"2 0\n1 3\n0 3\n",
"11 10\n1 2 3 4 5 6 7 8 9 10 11\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1101000000\n",
"3 1\n3 2 1\n0 2 3\n",
"7 3\n1 2 0 4 5 6 7\n3 4 3 8 8 8 8\n",
"4 0\n4 5 9 6\n1 1 11 33\n",
"5 4\n1 2 0 4 8\n1 1 1 1 1\n",
"3 0\n1 2 3\n5 5 0\n",
"7 3\n1 2 3 4 5 6 7\n3 2 1 4 5 6 7\n",
"7 2\n2 4 6 7 3 9 16\n10 8 4 8 4 5 9\n",
"4 2\n4 3 9 7\n1 1 11 33\n",
"5 4\n1 2 0 4 8\n1 1 1 2 1\n",
"3 0\n1 2 3\n5 2 0\n",
"7 3\n1 2 3 4 5 6 7\n3 2 2 4 5 6 7\n",
"4 3\n1 2 5 4\n5 1 5 5\n",
"7 2\n2 4 6 7 3 18 16\n10 8 4 8 4 5 9\n",
"5 4\n1 2 0 4 8\n1 2 1 1 1\n",
"3 0\n1 2 3\n5 1 0\n",
"7 3\n1 2 3 4 5 11 7\n3 2 2 4 5 6 7\n",
"5 4\n1 2 0 4 8\n1 2 0 1 1\n",
"7 3\n1 2 3 4 5 11 7\n3 2 2 4 5 6 2\n",
"4 0\n4 3 17 7\n1 1 11 50\n",
"7 3\n1 2 3 4 5 11 7\n3 2 2 4 1 6 2\n",
"7 1\n1 2 3 4 5 11 7\n3 2 2 4 1 6 2\n",
"7 1\n1 2 3 4 5 11 7\n3 2 2 4 2 6 2\n",
"7 1\n1 2 3 4 5 11 7\n3 2 2 4 2 2 2\n",
"7 1\n1 2 3 4 5 11 9\n3 2 2 4 1 2 2\n",
"7 2\n0 2 3 4 5 11 9\n3 2 2 4 1 2 2\n",
"7 2\n0 2 3 4 5 11 9\n3 2 2 4 1 2 3\n",
"10 5\n1 2 3 4 5 6 7 8 9 10\n1 1 1 1 1 1 0 1 1 1\n",
"4 2\n4 5 9 7\n2 4 11 33\n",
"3 2\n1 2 3\n2 1 1\n",
"4 0\n4 5 9 7\n1 2 17 33\n",
"6 3\n1 2 3 4 5 6\n1 1 1 1 0 1\n",
"3 0\n1 2 5\n5 5 5\n",
"7 3\n1 2 3 4 5 6 7\n4 3 3 4 5 6 7\n",
"4 3\n1 2 3 4\n6 5 5 5\n",
"7 2\n2 4 6 7 8 9 10\n10 8 3 8 4 5 9\n",
"5 3\n4 5 7 9 11\n10 10 10 10 2\n",
"5 3\n1 2 3 4 9\n7 7 7 7 7\n",
"5 1\n1 2 3 4 5\n1 2 2 4 5\n",
"4 2\n4 5 9 7\n1 2 11 50\n",
"11 10\n1 2 3 4 5 6 7 8 9 10 11\n1000000000 1000000000 1000000000 1000000000 1000000000 1000010000 1000000000 1000000000 1000000000 1000000000 1100000000\n",
"3 2\n1 4 3\n2 1 1\n",
"5 4\n1 2 3 4 8\n0 1 1 1 1\n",
"3 0\n1 2 3\n5 5 1\n",
"4 3\n1 2 3 4\n3 1 5 5\n",
"7 2\n2 4 6 7 8 9 16\n10 9 4 8 4 5 9\n",
"4 3\n0 2 3 4\n5 1 5 5\n",
"1 0\n0\n0\n",
"2 0\n2 3\n0 3\n",
"4 0\n1 5 9 6\n1 1 11 33\n",
"4 2\n4 3 17 7\n1 1 11 33\n",
"4 3\n1 2 9 4\n5 1 5 5\n",
"4 0\n4 3 17 7\n1 1 11 33\n",
"7 1\n1 2 3 4 5 11 9\n3 2 2 4 2 2 2\n",
"7 1\n0 2 3 4 5 11 9\n3 2 2 4 1 2 2\n",
"3 0\n5 2 1\n0 2 3\n",
"6 3\n1 2 3 4 5 9\n1 2 1 1 1 1\n"
],
"output": [
"1 3 5 7 9\n",
"3\n",
"1 3 46 36\n",
"10 20 30\n",
"3 3\n",
"1000000000 2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000\n",
"1 2 3 4 5 6 6 6 6 6\n",
"0 3 10 16 14 17 18\n",
"1 2 3\n",
"2 4 46 37\n",
"1 2 3\n",
"3 6 9 17 22 27 32\n",
"1 2 11 33\n",
"1 2 3 4 5\n",
"1 2 3 4 4 4\n",
"5 5 5\n",
"1 2 3 4\n",
"3 6 9 13 15 18 22\n",
"5 10 15 20\n",
"10 18 22 26 22 23 27\n",
"10 20 30 40 40\n",
"7 14 21 28 28\n",
"3 3\n",
"1000000000 2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11100000000\n",
"1 2 2 2 2 2 2 2 2 2\n",
"0 2 3\n",
"1 3 2\n",
"3 7 10 18 23 28 32\n",
"1 2 11 33\n",
"1 2 3 4 5\n",
"1 3 4 5 5 5\n",
"5 5 3\n",
"3 6 7 11 15 18 22\n",
"5 6 11 16\n",
"10 18 22 26 22 23 27\n",
"0\n",
"3 2 46 36\n",
"0 3\n",
"1000000000 2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11101000000\n",
"3 5 3\n",
"6 10 3 18 23 28 32\n",
"1 1 11 33\n",
"2 3 1 4 5\n",
"5 5 0\n",
"3 5 6 10 14 18 22\n",
"10 22 22 26 14 23 27\n",
"2 1 45 35\n",
"2 3 1 5 6\n",
"5 2 0\n",
"3 5 7 11 14 18 22\n",
"5 6 16 11\n",
"10 22 22 26 14 24 27\n",
"2 4 1 5 6\n",
"5 1 0\n",
"3 5 7 11 14 22 19\n",
"1 3 0 4 5\n",
"3 5 7 11 14 18 14\n",
"1 1 11 50\n",
"3 5 7 11 10 15 11\n",
"3 5 5 7 5 10 6\n",
"3 5 5 7 6 10 6\n",
"3 5 5 7 6 6 6\n",
"3 5 5 7 5 6 6\n",
"3 5 7 9 8 9 9\n",
"3 5 7 9 8 9 10\n",
"1 2 3 4 5 6 5 6 6 6\n",
"2 6 48 39\n",
"2 3 4\n",
"1 2 17 33\n",
"1 2 3 4 3 4\n",
"5 5 5\n",
"4 7 10 14 16 19 22\n",
"6 11 16 21\n",
"10 18 21 26 22 23 27\n",
"10 20 30 40 32\n",
"7 14 21 28 28\n",
"1 3 4 6 9\n",
"1 3 63 53\n",
"1000000000 2000000000 3000000000 4000000000 5000000000 6000010000 7000010000 8000010000 9000010000 10000010000 11100010000\n",
"2 4 3\n",
"0 1 2 3 4\n",
"5 5 1\n",
"3 4 9 14\n",
"10 19 23 27 23 24 28\n",
"5 6 11 16\n",
"0\n",
"0 3\n",
"1 1 11 33\n",
"2 1 45 35\n",
"5 6 16 11\n",
"1 1 11 33\n",
"3 5 5 7 6 6 6\n",
"3 5 5 7 5 6 6\n",
"0 2 3\n",
"1 3 4 5 5 5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Unlike Knights of a Round Table, Knights of a Polygonal Table deprived of nobility and happy to kill each other. But each knight has some power and a knight can kill another knight if and only if his power is greater than the power of victim. However, even such a knight will torment his conscience, so he can kill no more than k other knights. Also, each knight has some number of coins. After a kill, a knight can pick up all victim's coins.
Now each knight ponders: how many coins he can have if only he kills other knights?
You should answer this question for each knight.
Input
The first line contains two integers n and k (1 ≤ n ≤ 10^5, 0 ≤ k ≤ min(n-1,10)) — the number of knights and the number k from the statement.
The second line contains n integers p_1, p_2 ,…,p_n (1 ≤ p_i ≤ 10^9) — powers of the knights. All p_i are distinct.
The third line contains n integers c_1, c_2 ,…,c_n (0 ≤ c_i ≤ 10^9) — the number of coins each knight has.
Output
Print n integers — the maximum number of coins each knight can have it only he kills other knights.
Examples
Input
4 2
4 5 9 7
1 2 11 33
Output
1 3 46 36
Input
5 1
1 2 3 4 5
1 2 3 4 5
Output
1 3 5 7 9
Input
1 0
2
3
Output
3
Note
Consider the first example.
* The first knight is the weakest, so he can't kill anyone. That leaves him with the only coin he initially has.
* The second knight can kill the first knight and add his coin to his own two.
* The third knight is the strongest, but he can't kill more than k = 2 other knights. It is optimal to kill the second and the fourth knights: 2+11+33 = 46.
* The fourth knight should kill the first and the second knights: 33+1+2 = 36.
In the second example the first knight can't kill anyone, while all the others should kill the one with the index less by one than their own.
In the third example there is only one knight, so he can't kill anyone.
### Input:
5 1
1 2 3 4 5
1 2 3 4 5
### Output:
1 3 5 7 9
### Input:
1 0
2
3
### Output:
3
### Code:
n,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
d={}
l=[]
for i in range(n):
x=a[i]
y=b[i]
l.append((x,y))
l.sort()
ans=[]
j=0
if k==0:
print(*b)
else:
for i in range(n):
if i<k:
ans.append(l[i][1])
ans.sort()
d[l[i][0]]=sum(ans)
else:
d[l[i][0]]=sum(ans)+l[i][1]
if min(ans)<l[i][1]:
ind=ans.index(min(ans))
ans[ind]=l[i][1]
for i in range(n):
print(d[a[i]],end=' ')
|
p02634 AtCoder Grand Contest 046 - Extension_28433
|
We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:
* Assume that the grid currently has a horizontal rows and b vertical columns. Choose "vertical" or "horizontal".
* If we choose "vertical", insert one row at the top of the grid, resulting in an (a+1) \times b grid.
* If we choose "horizontal", insert one column at the right end of the grid, resulting in an a \times (b+1) grid.
* Then, paint one of the added squares black, and the other squares white.
Assume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.
Constraints
* 1 \leq A \leq C \leq 3000
* 1 \leq B \leq D \leq 3000
* A, B, C, and D are integers.
Input
Input is given from Standard Input in the following format:
A B C D
Output
Print the number of ways in which the squares can be painted in the end, modulo 998244353.
Examples
Input
1 1 2 2
Output
3
Input
2 1 3 4
Output
65
Input
31 41 59 265
Output
387222020
|
a, b, c, d = map(int,input().split())
mod = 998244353
A = [[0] * (d+1) for i in range(c+1)]
A[a][b] = 1
for i in range(a, c+1):
for j in range(b, d+1):
A[i][j] = (A[i][j] + A[i][j-1] * i + A[i-1][j] * j ) % mod
if i!=a and j!=b:
A[i][j] = (A[i][j] - A[i-1][j-1] * (i-1)*(j-1)) % mod
print(A[c][d])
# print(A)
|
{
"input": [
"2 1 3 4",
"31 41 59 265",
"1 1 2 2",
"2 0 3 4",
"54 41 59 265",
"1 0 2 2",
"2 0 3 0",
"54 41 59 202",
"1 0 2 3",
"2 0 3 1",
"41 41 59 202",
"2 0 3 2",
"50 41 59 202",
"1 0 2 1",
"2 0 6 2",
"4 0 6 2",
"4 0 6 4",
"4 0 6 7",
"3 0 6 7",
"2 0 3 3",
"31 41 59 430",
"2 0 3 8",
"54 55 59 265",
"1 -1 2 2",
"53 41 59 202",
"41 77 59 202",
"2 1 3 2",
"55 41 59 202",
"2 0 6 3",
"4 0 6 6",
"20 6 33 12",
"3 0 6 13",
"31 1 33 2",
"22 -2 27 0",
"22 -2 37 0",
"2 1 3 3",
"1 41 59 430",
"2 1 2 4",
"2 0 6 8",
"56 55 59 265",
"2 -1 2 1",
"41 77 64 202",
"2 1 6 2",
"55 60 59 202",
"4 0 6 3",
"1 1 2 9",
"22 -2 27 -1",
"1 41 57 430",
"2 0 2 4",
"4 0 6 8",
"8 55 59 265",
"2 1 9 2",
"55 60 82 202",
"3 0 6 3",
"1 -1 6 1",
"1 41 57 658",
"4 0 6 11",
"8 55 67 265",
"2 0 9 2",
"55 60 82 289",
"1 0 6 3",
"3 -1 3 6",
"6 1 33 6",
"1 41 105 658",
"8 69 67 265",
"89 41 89 91",
"44 141 64 202",
"2 -1 9 2",
"69 60 82 289",
"1 0 6 2",
"3 -2 3 6",
"9 1 33 6",
"8 127 67 265",
"89 41 89 165",
"2 -2 9 2",
"69 60 100 289",
"3 -1 3 4",
"2 1 33 6",
"0 2 27 2",
"1 1 3 4",
"31 41 59 79",
"1 1 3 5",
"31 27 59 79",
"2 1 3 5",
"31 27 59 78",
"3 1 3 5",
"31 8 59 78",
"3 1 3 4",
"31 2 59 78",
"31 2 111 78",
"2 1 3 6",
"31 3 111 78",
"2 1 2 6",
"31 5 111 78",
"2 1 4 6",
"31 5 111 52",
"2 2 4 6",
"31 2 111 52",
"31 2 111 5",
"31 2 110 5",
"8 2 110 5",
"2 3 011 3",
"4 3 011 5"
],
"output": [
"65",
"387222020",
"3",
"130\n",
"630730430\n",
"3\n",
"0\n",
"436335769\n",
"7\n",
"2\n",
"424344021\n",
"10\n",
"153856517\n",
"1\n",
"94\n",
"76\n",
"7212\n",
"2752636\n",
"5710332\n",
"38\n",
"544744202\n",
"12610\n",
"9644323\n",
"998244352\n",
"148357892\n",
"745049221\n",
"5\n",
"318847346\n",
"1544\n",
"401228\n",
"712060372\n",
"742885543\n",
"127\n",
"998243437\n",
"996999149\n",
"19\n",
"485000080\n",
"8\n",
"57087860\n",
"281238708\n",
"4\n",
"789276898\n",
"47\n",
"83527542\n",
"828\n",
"511\n",
"998244269\n",
"889484649\n",
"16\n",
"18274924\n",
"491282403\n",
"383\n",
"24092690\n",
"1278\n",
"998244350\n",
"59959374\n",
"759715512\n",
"760055692\n",
"766\n",
"854025171\n",
"1145\n",
"2187\n",
"193878945\n",
"122679717\n",
"506230183\n",
"539238403\n",
"923601205\n",
"1096\n",
"680621959\n",
"63\n",
"6561\n",
"174606617\n",
"926346472\n",
"136372116\n",
"998187281\n",
"394269194\n",
"243\n",
"547709964\n",
"134217728\n",
"108\n",
"595583270\n",
"359\n",
"601137163\n",
"211\n",
"254945721\n",
"81\n",
"377073578\n",
"27\n",
"850452065\n",
"818593055\n",
"665\n",
"566727388\n",
"32\n",
"196791621\n",
"7893\n",
"36674389\n",
"3300\n",
"646829554\n",
"686942251\n",
"149760297\n",
"490540261\n",
"19683\n",
"3240552\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:
* Assume that the grid currently has a horizontal rows and b vertical columns. Choose "vertical" or "horizontal".
* If we choose "vertical", insert one row at the top of the grid, resulting in an (a+1) \times b grid.
* If we choose "horizontal", insert one column at the right end of the grid, resulting in an a \times (b+1) grid.
* Then, paint one of the added squares black, and the other squares white.
Assume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.
Constraints
* 1 \leq A \leq C \leq 3000
* 1 \leq B \leq D \leq 3000
* A, B, C, and D are integers.
Input
Input is given from Standard Input in the following format:
A B C D
Output
Print the number of ways in which the squares can be painted in the end, modulo 998244353.
Examples
Input
1 1 2 2
Output
3
Input
2 1 3 4
Output
65
Input
31 41 59 265
Output
387222020
### Input:
2 1 3 4
### Output:
65
### Input:
31 41 59 265
### Output:
387222020
### Code:
a, b, c, d = map(int,input().split())
mod = 998244353
A = [[0] * (d+1) for i in range(c+1)]
A[a][b] = 1
for i in range(a, c+1):
for j in range(b, d+1):
A[i][j] = (A[i][j] + A[i][j-1] * i + A[i-1][j] * j ) % mod
if i!=a and j!=b:
A[i][j] = (A[i][j] - A[i-1][j-1] * (i-1)*(j-1)) % mod
print(A[c][d])
# print(A)
|
p02765 AtCoder Beginner Contest 156 - Beginner_28437
|
Takahashi is a member of a programming competition site, ButCoder.
Each member of ButCoder is assigned two values: Inner Rating and Displayed Rating.
The Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \times (10 - K) when the member has participated in K contests.
Takahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.
Constraints
* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq R \leq 4111
Input
Input is given from Standard Input in the following format:
N R
Output
Print his Inner Rating.
Examples
Input
2 2919
Output
3719
Input
22 3051
Output
3051
|
N, R = map(int, input().split())
print(R + max(0, 100 * (10 - N)))
|
{
"input": [
"2 2919",
"22 3051",
"2 4162",
"17 3051",
"1 4162",
"17 3619",
"1 1703",
"1 1051",
"0 1051",
"0 1885",
"76 6963",
"0 1615",
"76 3451",
"0 2265",
"76 835",
"-1 2265",
"76 1018",
"1 2265",
"76 170",
"0 503",
"-1 503",
"6 170",
"1 503",
"6 319",
"0 245",
"9 319",
"0 6",
"9 540",
"0 12",
"9 206",
"1 12",
"15 206",
"2 12",
"6 206",
"2 19",
"9 81",
"2 1",
"1 81",
"3 1",
"2 81",
"3 0",
"1 139",
"1 0",
"1 2",
"1 -1",
"2 2",
"2 -1",
"2 4",
"2 -2",
"3 4",
"1 -2",
"2 8",
"2 -4",
"0 1",
"3 -4",
"1 1",
"1 -4",
"1 4",
"4 -4",
"0 4",
"4 -2",
"0 2",
"3 -2",
"2 5",
"4 -1",
"2 6",
"2 0",
"3 2",
"4 2",
"4 0",
"4 4",
"3 -1",
"3 3",
"2 -3",
"3 5",
"2 -5",
"0 -1",
"4 -5",
"0 0",
"0 -5",
"-1 0",
"0 -8",
"-1 1",
"0 -16",
"-2 1",
"0 -25",
"-2 2",
"0 -17",
"-2 0",
"0 -28",
"1 3",
"-1 -28",
"1 5",
"-1 -19",
"1 7",
"2 7",
"-1 -22",
"3 7",
"-1 -27",
"3 6",
"-1 -32",
"3 12"
],
"output": [
"3719",
"3051",
"4962\n",
"3051\n",
"5062\n",
"3619\n",
"2603\n",
"1951\n",
"2051\n",
"2885\n",
"6963\n",
"2615\n",
"3451\n",
"3265\n",
"835\n",
"3365\n",
"1018\n",
"3165\n",
"170\n",
"1503\n",
"1603\n",
"570\n",
"1403\n",
"719\n",
"1245\n",
"419\n",
"1006\n",
"640\n",
"1012\n",
"306\n",
"912\n",
"206\n",
"812\n",
"606\n",
"819\n",
"181\n",
"801\n",
"981\n",
"701\n",
"881\n",
"700\n",
"1039\n",
"900\n",
"902\n",
"899\n",
"802\n",
"799\n",
"804\n",
"798\n",
"704\n",
"898\n",
"808\n",
"796\n",
"1001\n",
"696\n",
"901\n",
"896\n",
"904\n",
"596\n",
"1004\n",
"598\n",
"1002\n",
"698\n",
"805\n",
"599\n",
"806\n",
"800\n",
"702\n",
"602\n",
"600\n",
"604\n",
"699\n",
"703\n",
"797\n",
"705\n",
"795\n",
"999\n",
"595\n",
"1000\n",
"995\n",
"1100\n",
"992\n",
"1101\n",
"984\n",
"1201\n",
"975\n",
"1202\n",
"983\n",
"1200\n",
"972\n",
"903\n",
"1072\n",
"905\n",
"1081\n",
"907\n",
"807\n",
"1078\n",
"707\n",
"1073\n",
"706\n",
"1068\n",
"712\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Takahashi is a member of a programming competition site, ButCoder.
Each member of ButCoder is assigned two values: Inner Rating and Displayed Rating.
The Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \times (10 - K) when the member has participated in K contests.
Takahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.
Constraints
* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq R \leq 4111
Input
Input is given from Standard Input in the following format:
N R
Output
Print his Inner Rating.
Examples
Input
2 2919
Output
3719
Input
22 3051
Output
3051
### Input:
2 2919
### Output:
3719
### Input:
22 3051
### Output:
3051
### Code:
N, R = map(int, input().split())
print(R + max(0, 100 * (10 - N)))
|
p02900 AtCoder Beginner Contest 142 - Disjoint Set of Common Divisors_28441
|
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1
|
import fractions
a,b=map(int,input().split())
g=fractions.gcd(a,b)
#print(g)
ans=1
i=2
while i*i<=g:
if(g%i==0):
ans+=1
while g%i==0:
g/=i
i=i+1
if(g!=1):ans+=1
print(ans)
|
{
"input": [
"1 2019",
"12 18",
"420 660",
"2 2019",
"420 324",
"3 2019",
"19 18",
"19 16",
"420 71",
"6 2019",
"19 9",
"420 47",
"6 949",
"31 9",
"411 47",
"6 1591",
"40 9",
"411 17",
"8 1591",
"66 9",
"442 17",
"4 1591",
"66 17",
"313 17",
"3 1591",
"79 17",
"313 19",
"3 1324",
"154 17",
"22 19",
"6 1324",
"178 17",
"3 19",
"8 1324",
"178 13",
"3 38",
"8 2254",
"328 13",
"5 2254",
"28 13",
"5 3453",
"28 5",
"10 3453",
"44 5",
"10 6430",
"44 4",
"16 6430",
"83 4",
"16 3854",
"73 4",
"16 7064",
"73 8",
"11 7064",
"73 5",
"11 11968",
"16 11968",
"16 8817",
"16 15382",
"16 15958",
"31 15958",
"27 15958",
"27 4794",
"33 4794",
"4 4794",
"5 4794",
"3 4794",
"3 4371",
"3 7306",
"4 7306",
"8 7306",
"17 18",
"420 1226",
"2 1692",
"19 36",
"420 456",
"3 3712",
"10 16",
"836 71",
"6 2844",
"36 9",
"688 47",
"11 949",
"411 20",
"5 1591",
"34 9",
"430 17",
"7 1591",
"42 9",
"620 17",
"2 1591",
"66 13",
"180 17",
"6 980",
"71 17",
"409 19",
"5 1324",
"154 25",
"23 19",
"6 1354",
"261 17",
"1 19",
"9 1324",
"178 4"
],
"output": [
"1",
"3",
"4",
"1\n",
"3\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"3\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"3\n",
"1\n",
"2\n",
"1\n",
"3\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1
### Input:
1 2019
### Output:
1
### Input:
12 18
### Output:
3
### Code:
import fractions
a,b=map(int,input().split())
g=fractions.gcd(a,b)
#print(g)
ans=1
i=2
while i*i<=g:
if(g%i==0):
ans+=1
while g%i==0:
g/=i
i=i+1
if(g!=1):ans+=1
print(ans)
|
p03035 AtCoder Beginner Contest 127 - Ferris Wheel_28445
|
Takahashi, who is A years old, is riding a Ferris wheel.
It costs B yen (B is an even number) to ride the Ferris wheel if you are 13 years old or older, but children between 6 and 12 years old (inclusive) can ride it for half the cost, and children who are 5 years old or younger are free of charge. (Yen is the currency of Japan.)
Find the cost of the Ferris wheel for Takahashi.
Constraints
* 0 ≤ A ≤ 100
* 2 ≤ B ≤ 1000
* B is an even number.
Input
Input is given from Standard Input in the following format:
A B
Output
Print the cost of the Ferris wheel for Takahashi.
Examples
Input
30 100
Output
100
Input
12 100
Output
50
Input
0 100
Output
0
|
a,b = map(int,input().split())
if a > 12:
print(b)
elif a < 6:
print(0)
else:
print(b//2)
|
{
"input": [
"0 100",
"30 100",
"12 100",
"-1 100",
"15 100",
"6 111",
"9 100",
"16 110",
"17 101",
"25 111",
"59 011",
"89 001",
"30 010",
"9 010",
"1 100",
"-2 100",
"17 100",
"2 100",
"-2 000",
"2 101",
"0 000",
"-2 001",
"3 101",
"0 001",
"1 001",
"3 111",
"-1 001",
"1 101",
"2 111",
"1 011",
"1 000",
"4 101",
"1 010",
"2 000",
"4 001",
"1 110",
"3 100",
"4 011",
"0 101",
"3 110",
"4 111",
"-1 101",
"3 010",
"0 110",
"3 000",
"5 111",
"0 010",
"5 000",
"9 111",
"0 111",
"5 001",
"9 110",
"2 011",
"10 001",
"1 111",
"3 001",
"-1 010",
"2 001",
"3 011",
"-1 011",
"6 101",
"6 110",
"0 011",
"11 111",
"2 110",
"-1 111",
"-2 011",
"4 110",
"-1 110",
"-4 011",
"7 110",
"2 010",
"-4 010",
"10 110",
"-1 000",
"-4 000",
"12 110",
"-6 000",
"-4 001",
"-2 110",
"-3 011",
"20 110",
"-2 010",
"-3 010",
"27 110",
"-3 001",
"-3 110",
"17 110",
"-4 101",
"-3 100",
"-2 101",
"-6 100",
"26 101",
"-4 100",
"-10 100",
"25 101",
"-8 101",
"-10 000",
"-8 100",
"-16 000",
"38 111",
"-12 100",
"-16 100"
],
"output": [
"0",
"100",
"50",
"0\n",
"100\n",
"55\n",
"50\n",
"110\n",
"101\n",
"111\n",
"11\n",
"1\n",
"10\n",
"5\n",
"0\n",
"0\n",
"100\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"55\n",
"0\n",
"0\n",
"55\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"50\n",
"55\n",
"0\n",
"55\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"55\n",
"0\n",
"0\n",
"55\n",
"0\n",
"0\n",
"55\n",
"0\n",
"0\n",
"0\n",
"0\n",
"110\n",
"0\n",
"0\n",
"110\n",
"0\n",
"0\n",
"110\n",
"0\n",
"0\n",
"0\n",
"0\n",
"101\n",
"0\n",
"0\n",
"101\n",
"0\n",
"0\n",
"0\n",
"0\n",
"111\n",
"0\n",
"0\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Takahashi, who is A years old, is riding a Ferris wheel.
It costs B yen (B is an even number) to ride the Ferris wheel if you are 13 years old or older, but children between 6 and 12 years old (inclusive) can ride it for half the cost, and children who are 5 years old or younger are free of charge. (Yen is the currency of Japan.)
Find the cost of the Ferris wheel for Takahashi.
Constraints
* 0 ≤ A ≤ 100
* 2 ≤ B ≤ 1000
* B is an even number.
Input
Input is given from Standard Input in the following format:
A B
Output
Print the cost of the Ferris wheel for Takahashi.
Examples
Input
30 100
Output
100
Input
12 100
Output
50
Input
0 100
Output
0
### Input:
0 100
### Output:
0
### Input:
30 100
### Output:
100
### Code:
a,b = map(int,input().split())
if a > 12:
print(b)
elif a < 6:
print(0)
else:
print(b//2)
|
p03176 Educational DP Contest - Flowers_28449
|
There are N flowers arranged in a row. For each i (1 \leq i \leq N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively. Here, h_1, h_2, \ldots, h_N are all distinct.
Taro is pulling out some flowers so that the following condition is met:
* The heights of the remaining flowers are monotonically increasing from left to right.
Find the maximum possible sum of the beauties of the remaining flowers.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 × 10^5
* 1 \leq h_i \leq N
* h_1, h_2, \ldots, h_N are all distinct.
* 1 \leq a_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
h_1 h_2 \ldots h_N
a_1 a_2 \ldots a_N
Output
Print the maximum possible sum of the beauties of the remaining flowers.
Examples
Input
4
3 1 4 2
10 20 30 40
Output
60
Input
1
1
10
Output
10
Input
5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000
Output
5000000000
Input
9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5
Output
31
|
class Bit:
def __init__(self, n):
self.size = n
self.tree = [0] * (n + 1)
def sum(self, i):
s = 0
while i > 0:
s = max(s, self.tree[i])
i -= i & -i
return s
def add(self, i, x):
while i <= self.size:
self.tree[i] = max(x, self.tree[i])
i += i & -i
N, = map(int, input().split())
Hs = map(int, input().split())
As = map(int, input().split())
bit = Bit(N)
for h, a in zip(Hs, As):
a0 = bit.sum(h)
bit.add(h, a0+a)
print(bit.sum(N))
|
{
"input": [
"5\n1 2 3 4 5\n1000000000 1000000000 1000000000 1000000000 1000000000",
"4\n3 1 4 2\n10 20 30 40",
"1\n1\n10",
"9\n4 2 5 8 3 6 1 7 9\n6 8 8 4 6 3 5 7 5",
"5\n1 2 3 4 5\n1000000000 1000000010 1000000000 1000000000 1000000000",
"4\n3 1 4 2\n10 20 2 40",
"9\n4 2 5 8 3 6 1 7 9\n6 8 8 4 6 5 5 7 5",
"5\n1 2 3 4 5\n1000000000 1000000010 1000000000 1010000000 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n6 8 8 4 6 4 5 7 5",
"5\n1 2 3 4 5\n1000000000 1000000010 1000100000 1010000000 1000000000",
"4\n3 1 4 2\n20 20 2 26",
"4\n3 1 4 2\n15 25 2 40",
"5\n1 2 3 4 5\n1010000000 1000000010 1000100000 1010000000 1000000000",
"5\n1 2 3 4 5\n1010000000 0000000010 1000100000 1010000000 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n6 8 13 4 6 3 5 7 5",
"5\n1 2 3 4 5\n1000010000 1000000010 1000000000 1000000000 1000000000",
"4\n3 1 4 2\n10 39 2 40",
"9\n4 2 5 8 3 6 1 7 9\n6 13 8 4 6 5 5 7 5",
"4\n3 1 4 2\n20 20 2 37",
"4\n3 1 4 2\n15 25 2 64",
"5\n1 2 3 4 5\n1010000000 1000010010 1000100000 1010000000 1000000000",
"5\n1 2 3 4 5\n1010010000 0000000010 1000100000 1010000000 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n6 8 13 4 6 3 5 12 5",
"4\n3 1 4 2\n15 13 2 64",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1010000000 1000000000",
"4\n3 1 4 2\n18 20 0 24",
"5\n1 2 3 4 5\n1010011000 0000000010 1000100000 1010000000 1000000000",
"4\n3 1 4 2\n15 6 2 64",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1011000000 1000000000",
"4\n3 1 4 2\n18 5 0 24",
"4\n3 1 3 2\n20 6 0 37",
"4\n3 1 4 2\n18 5 0 35",
"9\n4 2 5 8 3 6 1 7 9\n6 12 8 4 6 3 5 7 5",
"5\n1 2 3 4 5\n1000000000 1000000010 1000000000 1000000000 1001000000",
"5\n1 2 3 4 5\n1000000000 1000000010 1000000000 1010000000 1001000000",
"9\n4 2 5 8 3 6 1 7 9\n6 8 5 4 6 4 5 7 5",
"5\n1 2 3 4 5\n1000000000 1000000000 1000100000 1010000000 1000000000",
"4\n3 1 4 2\n20 32 2 26",
"5\n1 2 3 4 5\n1010000000 0000000010 0000100000 1010000000 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n6 12 8 4 6 5 5 7 5",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1010000001 1000000000",
"5\n1 2 3 4 5\n1010010000 0000100010 1000100000 1010000000 1000000000",
"4\n3 1 3 2\n6 12 0 37",
"5\n1 2 3 4 5\n1000000000 1000000010 1000100000 1000000000 1001000000",
"5\n1 2 3 4 5\n1000000000 1000000000 1000100000 0010000000 1000000000",
"5\n1 2 3 4 5\n1010010000 0000100010 1000100000 1010000001 1000000000",
"4\n3 1 3 2\n5 22 2 37",
"5\n1 2 3 4 5\n1000000000 1000000010 0000100000 1000000000 1001000000",
"5\n1 2 3 4 5\n1000000000 1000000000 1000100000 0010000000 0000000000",
"4\n3 1 3 2\n18 20 1 6",
"4\n3 1 3 2\n5 11 2 37",
"4\n4 1 4 2\n23 8 0 64",
"5\n1 2 3 4 5\n1000000000 1000000000 1000100000 0010000000 0001000000",
"4\n3 1 3 2\n9 15 2 40",
"5\n1 2 3 4 5\n1000000000 1000000000 1000100000 0010000000 0001000001",
"4\n4 1 4 2\n23 8 1 42",
"4\n4 1 4 2\n23 12 2 42",
"5\n1 2 3 4 5\n1000000000 1000000000 1000000000 1000000000 1100000000",
"5\n1 2 3 4 5\n1000000000 1000000010 1100000000 1000000000 1000000000",
"5\n1 2 3 4 5\n1000000000 1000000010 1000100000 1010000000 1000000100",
"5\n1 2 3 4 5\n1010000000 0000000010 1000100000 1110000000 1000000000",
"5\n1 2 3 4 5\n1010000000 1000010010 1000100000 1011000000 1000000000",
"4\n3 1 4 2\n15 4 2 64",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1010000010 1000000000",
"5\n1 2 3 4 5\n1010011000 0000000010 1000100000 1110000000 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n9 8 13 4 6 3 4 12 5",
"4\n3 1 4 2\n18 1 0 24",
"4\n3 1 3 2\n20 6 0 22",
"4\n3 1 4 2\n12 6 2 118",
"4\n3 1 3 2\n6 6 0 7",
"5\n1 2 3 4 5\n1000000000 1000000000 1000000010 1000000001 1000000000",
"5\n1 2 3 4 5\n1000000000 1000000010 1000000000 1011000000 1001000000",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1010000001 1000000001",
"4\n3 1 4 2\n47 20 0 24",
"4\n3 1 3 2\n20 2 0 37",
"5\n1 2 3 4 5\n1010010000 0000100010 1100100000 1010000001 1000000000",
"5\n1 2 3 4 5\n1000000000 1000000010 0000100000 1001000000 1001000000",
"4\n3 1 3 2\n7 38 2 40",
"4\n3 1 4 2\n3 39 1 30",
"4\n3 1 3 2\n5 30 4 37",
"5\n1 2 3 4 5\n1000000000 1100000010 1100000000 1000000000 1000000000",
"5\n1 2 3 4 5\n0000000000 1000000010 1000100000 1010000000 1000000100",
"5\n1 2 3 4 5\n1010000000 1000000010 0000000000 1010000000 1000000000",
"5\n1 2 3 4 5\n1010000000 1000010010 1000100000 1011000000 1100000000",
"4\n3 1 4 2\n21 20 0 2",
"4\n3 1 4 2\n15 4 2 78",
"5\n1 2 3 4 5\n1010000000 1000011011 1000100000 1010000010 1000000000",
"5\n1 2 3 4 5\n1010011010 0000000010 1000100000 1110000000 1000000000",
"4\n3 1 4 2\n12 3 2 118",
"4\n4 1 4 2\n12 6 4 124",
"5\n1 2 3 4 5\n1000000000 1000000000 0000000010 1000000001 1000000000",
"9\n4 2 5 8 3 6 1 7 9\n6 2 10 4 6 5 5 7 3",
"4\n3 1 4 2\n26 19 2 26",
"5\n1 2 3 4 5\n1010000000 1000011010 1000100000 1010000001 1010000001",
"4\n3 1 4 2\n7 40 2 26",
"4\n4 1 4 2\n15 10 0 64",
"5\n1 2 3 4 5\n0000000000 1000000010 1000100010 1010000000 1000000100",
"5\n1 2 3 4 5\n1010000000 1000000010 0000000000 1010000000 1000000010",
"5\n1 2 3 4 5\n1010000000 1000010010 1000100001 1011000000 1000000000",
"4\n3 1 4 2\n21 15 0 2",
"5\n1 2 3 4 5\n1010000000 1000001010 1000100000 1010000010 1000000000",
"5\n1 2 3 4 5\n1000000000 0000000000 0000000010 1000000001 1000000000",
"5\n1 2 3 4 5\n1000000000 1000000010 0000100000 1001000000 1000000001",
"5\n1 2 3 4 5\n0000000000 1000000010 1000100010 1010000000 1000010100"
],
"output": [
"5000000000",
"60",
"10",
"31",
"5000000010\n",
"60\n",
"33\n",
"5010000010\n",
"32\n",
"5010100010\n",
"46\n",
"65\n",
"5020100010\n",
"4020100010\n",
"36\n",
"5000010010\n",
"79\n",
"38\n",
"57\n",
"89\n",
"5020110010\n",
"4020110010\n",
"41\n",
"77\n",
"5020111010\n",
"44\n",
"4020111010\n",
"70\n",
"5021111010\n",
"29\n",
"43\n",
"40\n",
"35\n",
"5001000010\n",
"5011000010\n",
"30\n",
"5010100000\n",
"58\n",
"3020100010\n",
"37\n",
"5020111011\n",
"4020210010\n",
"49\n",
"5001100010\n",
"4010100000\n",
"4020210011\n",
"59\n",
"4001100010\n",
"3010100000\n",
"26\n",
"48\n",
"72\n",
"3011100000\n",
"55\n",
"3011100001\n",
"50\n",
"54\n",
"5100000000\n",
"5100000010\n",
"5010100110\n",
"4120100010\n",
"5021110010\n",
"68\n",
"5020111020\n",
"4120111010\n",
"42\n",
"25\n",
"28\n",
"124\n",
"13\n",
"5000000011\n",
"5012000010\n",
"5020111012\n",
"47\n",
"39\n",
"4120210011\n",
"4002100010\n",
"78\n",
"69\n",
"67\n",
"5200000010\n",
"4010100110\n",
"4020000010\n",
"5121110010\n",
"22\n",
"82\n",
"5020111021\n",
"4120111020\n",
"121\n",
"130\n",
"4000000011\n",
"31\n",
"45\n",
"5030111012\n",
"66\n",
"74\n",
"4010100120\n",
"4020000020\n",
"5021110011\n",
"21\n",
"5020101020\n",
"3000000011\n",
"4001100011\n",
"4010110120\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N flowers arranged in a row. For each i (1 \leq i \leq N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively. Here, h_1, h_2, \ldots, h_N are all distinct.
Taro is pulling out some flowers so that the following condition is met:
* The heights of the remaining flowers are monotonically increasing from left to right.
Find the maximum possible sum of the beauties of the remaining flowers.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 × 10^5
* 1 \leq h_i \leq N
* h_1, h_2, \ldots, h_N are all distinct.
* 1 \leq a_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
h_1 h_2 \ldots h_N
a_1 a_2 \ldots a_N
Output
Print the maximum possible sum of the beauties of the remaining flowers.
Examples
Input
4
3 1 4 2
10 20 30 40
Output
60
Input
1
1
10
Output
10
Input
5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000
Output
5000000000
Input
9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5
Output
31
### Input:
5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000
### Output:
5000000000
### Input:
4
3 1 4 2
10 20 30 40
### Output:
60
### Code:
class Bit:
def __init__(self, n):
self.size = n
self.tree = [0] * (n + 1)
def sum(self, i):
s = 0
while i > 0:
s = max(s, self.tree[i])
i -= i & -i
return s
def add(self, i, x):
while i <= self.size:
self.tree[i] = max(x, self.tree[i])
i += i & -i
N, = map(int, input().split())
Hs = map(int, input().split())
As = map(int, input().split())
bit = Bit(N)
for h, a in zip(Hs, As):
a0 = bit.sum(h)
bit.add(h, a0+a)
print(bit.sum(N))
|
p03324 AtCoder Beginner Contest 100 - Ringo's Favorite Numbers_28453
|
Today, the memorable AtCoder Beginner Contest 100 takes place. On this occasion, Takahashi would like to give an integer to Ringo.
As the name of the contest is AtCoder Beginner Contest 100, Ringo would be happy if he is given a positive integer that can be divided by 100 exactly D times.
Find the N-th smallest integer that would make Ringo happy.
Constraints
* D is 0, 1 or 2.
* N is an integer between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
D N
Output
Print the N-th smallest integer that can be divided by 100 exactly D times.
Examples
Input
0 5
Output
5
Input
1 11
Output
1100
Input
2 85
Output
850000
|
D, N = map(int, input().split(" "))
print(((100**D)*(N+(N//100))))
|
{
"input": [
"2 85",
"1 11",
"0 5",
"2 37",
"2 11",
"-1 5",
"2 40",
"2 19",
"-1 9",
"2 57",
"3 19",
"0 9",
"2 86",
"0 19",
"-1 2",
"2 63",
"-1 19",
"2 71",
"-1 35",
"2 84",
"-1 66",
"1 84",
"-1 43",
"1 63",
"-1 8",
"-2 8",
"1 9",
"1 5",
"2 35",
"2 1",
"-2 5",
"4 40",
"0 37",
"-1 15",
"2 26",
"1 19",
"0 15",
"0 22",
"2 12",
"0 30",
"4 71",
"-1 -1",
"1 48",
"-1 10",
"-1 49",
"0 8",
"-3 8",
"1 1",
"2 38",
"4 1",
"-2 -1",
"6 40",
"0 50",
"-2 15",
"0 26",
"1 18",
"0 4",
"-1 22",
"3 12",
"1 30",
"-1 -2",
"1 14",
"-1 1",
"0 49",
"-1 16",
"-3 13",
"2 2",
"2 39",
"7 1",
"-4 0",
"3 40",
"0 98",
"-4 15",
"-1 26",
"2 18",
"0 1",
"-2 22",
"1 12",
"1 23",
"-2 -2",
"1 17",
"0 2",
"0 94",
"-1 21",
"-3 11",
"0 3",
"2 56",
"9 1",
"-4 -1",
"1 40",
"-1 98",
"-3 15",
"-2 26",
"4 18",
"0 -1",
"-2 10",
"0 12",
"1 -1",
"-2 -4",
"2 17",
"1 2",
"1 94",
"-1 54"
],
"output": [
"850000",
"1100",
"5",
"370000\n",
"110000\n",
"0.05\n",
"400000\n",
"190000\n",
"0.09\n",
"570000\n",
"19000000\n",
"9\n",
"860000\n",
"19\n",
"0.02\n",
"630000\n",
"0.19\n",
"710000\n",
"0.35\n",
"840000\n",
"0.66\n",
"8400\n",
"0.43\n",
"6300\n",
"0.08\n",
"0.0008\n",
"900\n",
"500\n",
"350000\n",
"10000\n",
"0.0005\n",
"4000000000\n",
"37\n",
"0.15\n",
"260000\n",
"1900\n",
"15\n",
"22\n",
"120000\n",
"30\n",
"7100000000\n",
"-0.01\n",
"4800\n",
"0.1\n",
"0.49\n",
"8\n",
"8e-06\n",
"100\n",
"380000\n",
"100000000\n",
"-0.0001\n",
"40000000000000\n",
"50\n",
"0.0015\n",
"26\n",
"1800\n",
"4\n",
"0.22\n",
"12000000\n",
"3000\n",
"-0.02\n",
"1400\n",
"0.01\n",
"49\n",
"0.16\n",
"1.3e-05\n",
"20000\n",
"390000\n",
"100000000000000\n",
"0.0\n",
"40000000\n",
"98\n",
"1.5e-07\n",
"0.26\n",
"180000\n",
"1\n",
"0.0022\n",
"1200\n",
"2300\n",
"-0.0002\n",
"1700\n",
"2\n",
"94\n",
"0.21\n",
"1.1e-05\n",
"3\n",
"560000\n",
"1000000000000000000\n",
"-1e-08\n",
"4000\n",
"0.98\n",
"1.5e-05\n",
"0.0026\n",
"1800000000\n",
"-1\n",
"0.001\n",
"12\n",
"-100\n",
"-0.0004\n",
"170000\n",
"200\n",
"9400\n",
"0.54\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Today, the memorable AtCoder Beginner Contest 100 takes place. On this occasion, Takahashi would like to give an integer to Ringo.
As the name of the contest is AtCoder Beginner Contest 100, Ringo would be happy if he is given a positive integer that can be divided by 100 exactly D times.
Find the N-th smallest integer that would make Ringo happy.
Constraints
* D is 0, 1 or 2.
* N is an integer between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
D N
Output
Print the N-th smallest integer that can be divided by 100 exactly D times.
Examples
Input
0 5
Output
5
Input
1 11
Output
1100
Input
2 85
Output
850000
### Input:
2 85
### Output:
850000
### Input:
1 11
### Output:
1100
### Code:
D, N = map(int, input().split(" "))
print(((100**D)*(N+(N//100))))
|
p03478 AtCoder Beginner Contest 083 - Some Sums_28457
|
Find the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).
Constraints
* 1 \leq N \leq 10^4
* 1 \leq A \leq B \leq 36
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).
Examples
Input
20 2 5
Output
84
Input
10 1 2
Output
13
Input
100 4 16
Output
4554
|
N, A, B = map(int, input().split())
print(sum(i for i in range(1, N+1) if A <= sum(int(c) for c in str(i)) <= B))
|
{
"input": [
"10 1 2",
"20 2 5",
"100 4 16",
"10 1 0",
"20 2 6",
"100 4 12",
"20 3 6",
"100 5 12",
"20 1 6",
"37 2 6",
"101 3 12",
"37 1 6",
"37 1 9",
"37 1 18",
"001 1 12",
"37 1 2",
"37 1 3",
"4 1 6",
"101 -1 6",
"6 -2 6",
"5 -3 10",
"011 2 20",
"011 4 20",
"100 4 40",
"110 4 34",
"101 0 154",
"111 1 181",
"110 1 41",
"100 1 41",
"111 2 10",
"101 2 10",
"101 2 19",
"011 -1 110",
"36 -2 1",
"111 0 001",
"17 -2 2",
"21 0 4",
"21 0 6",
"21 0 10",
"21 0 8",
"2 0 8",
"2 2 2",
"3 0 4",
"6 2 3",
"6 2 5",
"10 2 4",
"010 3 100",
"10 0 4",
"10 1 6",
"110 2 100",
"100 2 100",
"101 1 011",
"101 1 010",
"100 1 010",
"100 2 010",
"110 3 010",
"110 3 110",
"110 6 110",
"110 5 110",
"100 3 010",
"100 3 011",
"100 1 011",
"110 1 011",
"111 1 011",
"100 2 011",
"100 5 011",
"4 4 6",
"100 10 011",
"110 2 010",
"101 3 111",
"101 6 111",
"110 4 011",
"010 8 010",
"010 5 010",
"010 6 010",
"5 1 0",
"5 0 0",
"101 5 12",
"2 0 0",
"2 0 -1",
"001 3 12",
"3 0 -1",
"001 6 12",
"3 0 0",
"0 0 0",
"001 0 12",
"0 0 1",
"001 0 13",
"0 1 1",
"37 0 6",
"001 0 3",
"0 1 0",
"001 0 6",
"0 2 0",
"4 0 6",
"001 -1 6",
"-1 2 0",
"4 -1 6",
"-1 3 0",
"4 -2 6",
"001 -2 6",
"0 3 0",
"001 -2 9"
],
"output": [
"13",
"84",
"4554",
"0\n",
"105\n",
"3146\n",
"72\n",
"3036\n",
"116\n",
"321\n",
"3212\n",
"332\n",
"590\n",
"703\n",
"1\n",
"44\n",
"110\n",
"10\n",
"817\n",
"21\n",
"15\n",
"55\n",
"39\n",
"4840\n",
"5582\n",
"5151\n",
"6216\n",
"6105\n",
"5050\n",
"3465\n",
"2400\n",
"5040\n",
"66\n",
"11\n",
"111\n",
"24\n",
"97\n",
"137\n",
"231\n",
"185\n",
"3\n",
"2\n",
"6\n",
"5\n",
"14\n",
"9\n",
"42\n",
"20\n",
"31\n",
"5994\n",
"4939\n",
"2995\n",
"2511\n",
"2410\n",
"2299\n",
"3110\n",
"5750\n",
"5100\n",
"5369\n",
"2266\n",
"2750\n",
"2894\n",
"3949\n",
"4060\n",
"2783\n",
"2574\n",
"4\n",
"979\n",
"3354\n",
"4906\n",
"4565\n",
"3426\n",
"17\n",
"35\n",
"30\n",
"0\n",
"0\n",
"3036\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"332\n",
"1\n",
"0\n",
"1\n",
"0\n",
"10\n",
"1\n",
"0\n",
"10\n",
"0\n",
"10\n",
"1\n",
"0\n",
"1\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Find the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).
Constraints
* 1 \leq N \leq 10^4
* 1 \leq A \leq B \leq 36
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).
Examples
Input
20 2 5
Output
84
Input
10 1 2
Output
13
Input
100 4 16
Output
4554
### Input:
10 1 2
### Output:
13
### Input:
20 2 5
### Output:
84
### Code:
N, A, B = map(int, input().split())
print(sum(i for i in range(1, N+1) if A <= sum(int(c) for c in str(i)) <= B))
|
p03643 AtCoder Beginner Contest 068 - ABCxxx_28461
|
This contest, AtCoder Beginner Contest, is abbreviated as ABC.
When we refer to a specific round of ABC, a three-digit number is appended after ABC. For example, ABC680 is the 680th round of ABC.
What is the abbreviation for the N-th round of ABC? Write a program to output the answer.
Constraints
* 100 ≤ N ≤ 999
Input
Input is given from Standard Input in the following format:
N
Output
Print the abbreviation for the N-th round of ABC.
Examples
Input
100
Output
ABC100
Input
425
Output
ABC425
Input
999
Output
ABC999
|
S = input()
print("ABC"+S)
|
{
"input": [
"999",
"425",
"100",
"1530",
"820",
"110",
"2825",
"293",
"5621",
"258",
"238",
"411",
"87",
"789",
"33",
"415",
"36",
"542",
"34",
"205",
"52",
"294",
"74",
"105",
"97",
"186",
"183",
"292",
"403",
"518",
"365",
"18",
"7",
"3",
"4",
"8",
"15",
"9",
"0",
"-1",
"1",
"2",
"6",
"-2",
"-4",
"-3",
"-7",
"-5",
"-8",
"-6",
"5",
"26",
"22",
"29",
"20",
"50",
"37",
"66",
"51",
"-9",
"-12",
"-21",
"-11",
"-20",
"11",
"21",
"-13",
"14",
"-14",
"-17",
"-10",
"-16",
"-25",
"-45",
"-72",
"-75",
"10",
"19",
"13",
"-18",
"-36",
"-52",
"-58",
"-95",
"-70",
"-22",
"-40",
"-68",
"-28",
"-51",
"-42",
"-24",
"-41",
"-55",
"-84",
"-105",
"-136",
"-215",
"-111",
"-104",
"-53",
"-56",
"17"
],
"output": [
"ABC999",
"ABC425",
"ABC100",
"ABC1530\n",
"ABC820\n",
"ABC110\n",
"ABC2825\n",
"ABC293\n",
"ABC5621\n",
"ABC258\n",
"ABC238\n",
"ABC411\n",
"ABC87\n",
"ABC789\n",
"ABC33\n",
"ABC415\n",
"ABC36\n",
"ABC542\n",
"ABC34\n",
"ABC205\n",
"ABC52\n",
"ABC294\n",
"ABC74\n",
"ABC105\n",
"ABC97\n",
"ABC186\n",
"ABC183\n",
"ABC292\n",
"ABC403\n",
"ABC518\n",
"ABC365\n",
"ABC18\n",
"ABC7\n",
"ABC3\n",
"ABC4\n",
"ABC8\n",
"ABC15\n",
"ABC9\n",
"ABC0\n",
"ABC-1\n",
"ABC1\n",
"ABC2\n",
"ABC6\n",
"ABC-2\n",
"ABC-4\n",
"ABC-3\n",
"ABC-7\n",
"ABC-5\n",
"ABC-8\n",
"ABC-6\n",
"ABC5\n",
"ABC26\n",
"ABC22\n",
"ABC29\n",
"ABC20\n",
"ABC50\n",
"ABC37\n",
"ABC66\n",
"ABC51\n",
"ABC-9\n",
"ABC-12\n",
"ABC-21\n",
"ABC-11\n",
"ABC-20\n",
"ABC11\n",
"ABC21\n",
"ABC-13\n",
"ABC14\n",
"ABC-14\n",
"ABC-17\n",
"ABC-10\n",
"ABC-16\n",
"ABC-25\n",
"ABC-45\n",
"ABC-72\n",
"ABC-75\n",
"ABC10\n",
"ABC19\n",
"ABC13\n",
"ABC-18\n",
"ABC-36\n",
"ABC-52\n",
"ABC-58\n",
"ABC-95\n",
"ABC-70\n",
"ABC-22\n",
"ABC-40\n",
"ABC-68\n",
"ABC-28\n",
"ABC-51\n",
"ABC-42\n",
"ABC-24\n",
"ABC-41\n",
"ABC-55\n",
"ABC-84\n",
"ABC-105\n",
"ABC-136\n",
"ABC-215\n",
"ABC-111\n",
"ABC-104\n",
"ABC-53\n",
"ABC-56\n",
"ABC17\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This contest, AtCoder Beginner Contest, is abbreviated as ABC.
When we refer to a specific round of ABC, a three-digit number is appended after ABC. For example, ABC680 is the 680th round of ABC.
What is the abbreviation for the N-th round of ABC? Write a program to output the answer.
Constraints
* 100 ≤ N ≤ 999
Input
Input is given from Standard Input in the following format:
N
Output
Print the abbreviation for the N-th round of ABC.
Examples
Input
100
Output
ABC100
Input
425
Output
ABC425
Input
999
Output
ABC999
### Input:
999
### Output:
ABC999
### Input:
425
### Output:
ABC425
### Code:
S = input()
print("ABC"+S)
|
p03801 AtCoder Regular Contest 069 - Frequency_28465
|
Snuke loves constructing integer sequences.
There are N piles of stones, numbered 1 through N. The pile numbered i consists of a_i stones.
Snuke will construct an integer sequence s of length Σa_i, as follows:
1. Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.
2. Select a pile with one or more stones remaining, and remove a stone from that pile.
3. If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.
We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?
Constraints
* 1 ≤ N ≤ 10^{5}
* 1 ≤ a_i ≤ 10^{9}
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{N}
Output
Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.
Examples
Input
2
1 2
Output
2
1
Input
10
1 2 1 3 2 4 2 5 8 1
Output
10
7
0
4
0
3
0
2
3
0
|
N = int(input())
As = list(map(int, input().split()))
sorted_iAs = sorted(map(tuple, enumerate(As)), key = lambda t: (t[1], t[0]), reverse = True)
#if As = 1 2 1 3 2 4 2 5 8 1
#then sorted_iAs is:
# i | 8 7 5 3 6 4 1 9 2 0
# A | 8 5 4 3 2 2 2 1 1 1
#I'll look at:
# x x x x x x
#where the next A decreases (or doesn't exist).
ans = [0] * N
youngest_index = 10 ** 9
for index, (original_index, A) in enumerate(sorted_iAs):
youngest_index = min(original_index, youngest_index)
if index == N - 1:
ans[youngest_index] += A * (index + 1)
elif sorted_iAs[index + 1][1] < A:
next_A = sorted_iAs[index + 1][1]
ans[youngest_index] += (A - next_A) * (index + 1)
print(*ans, sep = '\n')
|
{
"input": [
"2\n1 2",
"10\n1 2 1 3 2 4 2 5 8 1",
"10\n1 2 2 3 2 4 2 5 8 1",
"10\n1 3 2 3 2 4 2 5 8 1",
"10\n1 3 2 3 2 4 4 5 8 1",
"2\n1 0",
"10\n1 2 1 3 2 4 1 5 8 1",
"10\n1 2 1 3 2 4 2 5 8 0",
"10\n1 3 2 4 2 4 2 5 8 1",
"10\n1 3 2 6 2 4 4 5 8 1",
"2\n1 1",
"10\n1 2 1 3 2 4 1 5 8 0",
"10\n1 2 0 3 2 4 2 5 8 0",
"10\n1 3 0 4 2 4 2 5 8 1",
"10\n1 3 2 6 2 4 4 5 4 1",
"10\n1 2 1 3 2 4 1 5 12 0",
"10\n2 2 0 3 2 4 2 5 8 0",
"10\n1 3 0 4 2 2 2 5 8 1",
"10\n1 3 2 6 3 4 4 5 4 1",
"10\n2 2 0 3 0 4 2 5 8 0",
"10\n1 3 2 6 3 4 4 6 4 1",
"10\n4 2 0 3 0 4 2 5 8 0",
"10\n1 3 1 6 3 4 4 6 4 1",
"10\n4 2 0 3 0 4 2 5 12 0",
"10\n1 3 1 6 3 4 6 6 4 1",
"10\n4 2 0 3 1 4 2 5 12 0",
"10\n2 3 1 6 3 4 6 6 4 1",
"10\n4 4 0 3 1 4 2 5 12 0",
"10\n2 3 1 6 3 4 6 3 4 1",
"10\n1 4 0 3 1 4 2 5 12 0",
"10\n2 3 1 6 3 4 1 3 4 1",
"10\n1 4 0 3 1 4 4 5 12 0",
"10\n2 3 1 6 3 4 1 3 4 0",
"10\n2 3 1 7 3 4 1 3 4 0",
"10\n1 4 0 1 1 4 4 6 12 0",
"10\n2 3 1 7 5 4 1 3 4 0",
"10\n1 4 0 1 1 4 4 6 12 1",
"10\n2 3 1 7 2 4 1 3 4 0",
"10\n1 4 0 1 1 4 4 0 12 1",
"10\n2 3 1 7 3 4 1 3 2 0",
"10\n1 4 0 1 1 4 4 0 22 1",
"10\n2 3 1 7 1 4 1 3 2 0",
"10\n1 3 0 1 1 4 4 0 22 1",
"10\n2 1 1 7 1 4 1 3 2 0",
"10\n1 3 0 0 1 4 4 0 22 1",
"10\n2 1 1 7 1 4 1 3 4 0",
"10\n1 3 0 0 1 4 4 0 35 1",
"10\n4 1 1 7 1 4 1 3 4 0",
"10\n1 3 0 0 2 4 4 0 35 1",
"10\n4 1 1 3 1 4 1 3 4 0",
"10\n2 3 0 0 2 4 4 0 35 1",
"10\n4 1 1 3 1 4 1 6 4 0",
"10\n4 1 1 3 1 4 1 8 4 0",
"10\n4 1 1 3 1 4 0 8 4 0",
"10\n4 1 1 3 1 3 0 8 4 0",
"10\n4 1 1 3 1 3 0 7 4 0",
"10\n4 1 1 3 1 3 0 7 4 1",
"10\n4 1 1 3 2 3 0 7 4 1",
"10\n4 1 1 6 2 3 0 7 4 1",
"10\n4 1 1 6 2 3 0 7 1 1",
"10\n4 1 1 6 4 3 0 7 1 1",
"10\n2 1 1 6 4 3 0 7 1 1",
"10\n2 1 1 9 4 3 0 7 1 1",
"10\n2 1 1 17 4 3 0 7 1 1",
"10\n2 1 1 17 4 2 0 7 1 1",
"2\n2 1",
"10\n1 2 2 5 2 4 2 5 8 1",
"10\n1 2 2 3 2 4 2 0 8 1",
"10\n1 1 2 3 2 4 2 5 8 1",
"10\n1 3 2 3 2 4 4 5 7 1",
"10\n1 2 1 3 1 4 1 5 8 1",
"10\n1 2 1 5 2 4 2 5 8 0",
"10\n1 3 2 6 2 8 4 5 8 1",
"10\n1 2 0 3 2 4 2 5 10 0",
"10\n1 3 0 4 2 4 0 5 8 1",
"10\n1 3 2 6 2 4 4 2 4 1",
"10\n1 2 1 3 2 4 1 5 15 0",
"10\n2 2 0 3 4 4 2 5 8 0",
"10\n1 3 0 4 2 2 2 5 8 0",
"10\n1 3 3 6 3 4 4 5 4 1",
"10\n2 2 0 3 0 1 2 5 8 0",
"10\n1 3 2 6 3 0 4 6 4 1",
"10\n4 2 0 3 0 4 2 3 8 0",
"10\n1 3 1 6 3 4 6 6 7 1",
"10\n4 2 0 3 1 7 2 5 12 0",
"10\n3 3 1 6 3 4 6 6 4 1",
"10\n1 0 0 3 1 4 2 5 12 0",
"10\n2 3 1 8 3 4 1 3 4 1",
"10\n1 4 1 3 1 4 4 5 12 0",
"10\n2 3 1 6 5 4 1 3 4 0",
"10\n1 4 0 1 1 2 4 5 12 0",
"10\n2 3 1 7 1 4 1 3 4 0",
"10\n1 4 0 1 2 4 4 6 12 0",
"10\n2 3 1 9 5 4 1 3 4 0",
"10\n1 2 0 1 1 4 4 6 12 1",
"10\n2 3 1 7 2 4 1 6 4 0",
"10\n1 4 0 2 1 4 4 0 12 1",
"10\n2 3 1 7 6 4 1 3 2 0",
"10\n1 4 0 1 1 4 4 0 25 1",
"10\n3 3 1 7 1 4 1 3 2 0",
"10\n1 0 0 1 1 4 4 0 22 1",
"10\n2 0 1 7 1 4 1 3 2 0"
],
"output": [
"2\n1",
"10\n7\n0\n4\n0\n3\n0\n2\n3\n0",
"10\n8\n0\n4\n0\n3\n0\n2\n3\n0\n",
"10\n13\n0\n0\n0\n3\n0\n2\n3\n0\n",
"10\n14\n0\n0\n0\n4\n0\n2\n3\n0\n",
"1\n0\n",
"10\n6\n0\n4\n0\n3\n0\n2\n3\n0\n",
"9\n7\n0\n4\n0\n3\n0\n2\n3\n0\n",
"10\n13\n0\n4\n0\n0\n0\n2\n3\n0\n",
"10\n14\n0\n10\n0\n0\n0\n0\n2\n0\n",
"2\n0\n",
"9\n6\n0\n4\n0\n3\n0\n2\n3\n0\n",
"8\n7\n0\n4\n0\n3\n0\n2\n3\n0\n",
"9\n12\n0\n4\n0\n0\n0\n2\n3\n0\n",
"10\n14\n0\n8\n0\n0\n0\n0\n0\n0\n",
"9\n6\n0\n4\n0\n3\n0\n2\n7\n0\n",
"16\n0\n0\n4\n0\n3\n0\n2\n3\n0\n",
"9\n11\n0\n3\n0\n0\n0\n2\n3\n0\n",
"10\n15\n0\n8\n0\n0\n0\n0\n0\n0\n",
"14\n0\n0\n4\n0\n3\n0\n2\n3\n0\n",
"10\n15\n0\n9\n0\n0\n0\n0\n0\n0\n",
"23\n0\n0\n0\n0\n0\n0\n2\n3\n0\n",
"10\n14\n0\n9\n0\n0\n0\n0\n0\n0\n",
"23\n0\n0\n0\n0\n0\n0\n2\n7\n0\n",
"10\n14\n0\n11\n0\n0\n0\n0\n0\n0\n",
"24\n0\n0\n0\n0\n0\n0\n2\n7\n0\n",
"18\n7\n0\n11\n0\n0\n0\n0\n0\n0\n",
"26\n0\n0\n0\n0\n0\n0\n2\n7\n0\n",
"18\n7\n0\n8\n0\n0\n0\n0\n0\n0\n",
"8\n15\n0\n0\n0\n0\n0\n2\n7\n0\n",
"17\n6\n0\n5\n0\n0\n0\n0\n0\n0\n",
"8\n17\n0\n0\n0\n0\n0\n2\n7\n0\n",
"16\n6\n0\n5\n0\n0\n0\n0\n0\n0\n",
"16\n6\n0\n6\n0\n0\n0\n0\n0\n0\n",
"8\n15\n0\n0\n0\n0\n0\n4\n6\n0\n",
"16\n6\n0\n8\n0\n0\n0\n0\n0\n0\n",
"9\n15\n0\n0\n0\n0\n0\n4\n6\n0\n",
"16\n5\n0\n6\n0\n0\n0\n0\n0\n0\n",
"8\n12\n0\n0\n0\n0\n0\n0\n8\n0\n",
"16\n5\n0\n5\n0\n0\n0\n0\n0\n0\n",
"8\n12\n0\n0\n0\n0\n0\n0\n18\n0\n",
"15\n4\n0\n5\n0\n0\n0\n0\n0\n0\n",
"8\n8\n0\n0\n0\n3\n0\n0\n18\n0\n",
"14\n0\n0\n8\n0\n0\n0\n0\n0\n0\n",
"7\n8\n0\n0\n0\n3\n0\n0\n18\n0\n",
"14\n0\n0\n10\n0\n0\n0\n0\n0\n0\n",
"7\n8\n0\n0\n0\n3\n0\n0\n31\n0\n",
"23\n0\n0\n3\n0\n0\n0\n0\n0\n0\n",
"7\n9\n0\n0\n0\n3\n0\n0\n31\n0\n",
"22\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"13\n4\n0\n0\n0\n3\n0\n0\n31\n0\n",
"23\n0\n0\n0\n0\n0\n0\n2\n0\n0\n",
"23\n0\n0\n0\n0\n0\n0\n4\n0\n0\n",
"22\n0\n0\n0\n0\n0\n0\n4\n0\n0\n",
"21\n0\n0\n0\n0\n0\n0\n4\n0\n0\n",
"21\n0\n0\n0\n0\n0\n0\n3\n0\n0\n",
"22\n0\n0\n0\n0\n0\n0\n3\n0\n0\n",
"23\n0\n0\n0\n0\n0\n0\n3\n0\n0\n",
"24\n0\n0\n4\n0\n0\n0\n1\n0\n0\n",
"21\n0\n0\n4\n0\n0\n0\n1\n0\n0\n",
"23\n0\n0\n4\n0\n0\n0\n1\n0\n0\n",
"14\n0\n0\n11\n0\n0\n0\n1\n0\n0\n",
"14\n0\n0\n15\n0\n0\n0\n0\n0\n0\n",
"14\n0\n0\n23\n0\n0\n0\n0\n0\n0\n",
"14\n0\n0\n22\n0\n0\n0\n0\n0\n0\n",
"3\n0\n",
"10\n8\n0\n11\n0\n0\n0\n0\n3\n0\n",
"9\n7\n0\n3\n0\n2\n0\n0\n4\n0\n",
"10\n0\n7\n4\n0\n3\n0\n2\n3\n0\n",
"10\n14\n0\n0\n0\n4\n0\n2\n2\n0\n",
"10\n5\n0\n4\n0\n3\n0\n2\n3\n0\n",
"9\n7\n0\n11\n0\n0\n0\n0\n3\n0\n",
"10\n14\n0\n12\n0\n4\n0\n0\n0\n0\n",
"8\n7\n0\n4\n0\n3\n0\n2\n5\n0\n",
"8\n11\n0\n4\n0\n0\n0\n2\n3\n0\n",
"10\n13\n0\n6\n0\n0\n0\n0\n0\n0\n",
"9\n6\n0\n4\n0\n3\n0\n2\n10\n0\n",
"16\n0\n0\n5\n4\n0\n0\n2\n3\n0\n",
"8\n11\n0\n3\n0\n0\n0\n2\n3\n0\n",
"10\n16\n0\n8\n0\n0\n0\n0\n0\n0\n",
"13\n0\n0\n3\n0\n0\n0\n4\n3\n0\n",
"9\n13\n0\n8\n0\n0\n0\n0\n0\n0\n",
"22\n0\n0\n0\n0\n0\n0\n0\n4\n0\n",
"10\n14\n0\n13\n0\n0\n0\n0\n1\n0\n",
"24\n0\n0\n0\n0\n7\n0\n0\n5\n0\n",
"26\n0\n0\n11\n0\n0\n0\n0\n0\n0\n",
"7\n0\n0\n9\n0\n3\n0\n2\n7\n0\n",
"17\n6\n0\n7\n0\n0\n0\n0\n0\n0\n",
"9\n17\n0\n0\n0\n0\n0\n2\n7\n0\n",
"16\n6\n0\n7\n0\n0\n0\n0\n0\n0\n",
"8\n13\n0\n0\n0\n0\n0\n2\n7\n0\n",
"15\n5\n0\n6\n0\n0\n0\n0\n0\n0\n",
"8\n16\n0\n0\n0\n0\n0\n4\n6\n0\n",
"16\n6\n0\n10\n0\n0\n0\n0\n0\n0\n",
"9\n5\n0\n0\n0\n8\n0\n4\n6\n0\n",
"16\n5\n0\n9\n0\n0\n0\n0\n0\n0\n",
"8\n13\n0\n0\n0\n0\n0\n0\n8\n0\n",
"16\n5\n0\n8\n0\n0\n0\n0\n0\n0\n",
"8\n12\n0\n0\n0\n0\n0\n0\n21\n0\n",
"20\n0\n0\n5\n0\n0\n0\n0\n0\n0\n",
"7\n0\n0\n0\n0\n9\n0\n0\n18\n0\n",
"13\n0\n0\n8\n0\n0\n0\n0\n0\n0\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Snuke loves constructing integer sequences.
There are N piles of stones, numbered 1 through N. The pile numbered i consists of a_i stones.
Snuke will construct an integer sequence s of length Σa_i, as follows:
1. Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.
2. Select a pile with one or more stones remaining, and remove a stone from that pile.
3. If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.
We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?
Constraints
* 1 ≤ N ≤ 10^{5}
* 1 ≤ a_i ≤ 10^{9}
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{N}
Output
Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.
Examples
Input
2
1 2
Output
2
1
Input
10
1 2 1 3 2 4 2 5 8 1
Output
10
7
0
4
0
3
0
2
3
0
### Input:
2
1 2
### Output:
2
1
### Input:
10
1 2 1 3 2 4 2 5 8 1
### Output:
10
7
0
4
0
3
0
2
3
0
### Code:
N = int(input())
As = list(map(int, input().split()))
sorted_iAs = sorted(map(tuple, enumerate(As)), key = lambda t: (t[1], t[0]), reverse = True)
#if As = 1 2 1 3 2 4 2 5 8 1
#then sorted_iAs is:
# i | 8 7 5 3 6 4 1 9 2 0
# A | 8 5 4 3 2 2 2 1 1 1
#I'll look at:
# x x x x x x
#where the next A decreases (or doesn't exist).
ans = [0] * N
youngest_index = 10 ** 9
for index, (original_index, A) in enumerate(sorted_iAs):
youngest_index = min(original_index, youngest_index)
if index == N - 1:
ans[youngest_index] += A * (index + 1)
elif sorted_iAs[index + 1][1] < A:
next_A = sorted_iAs[index + 1][1]
ans[youngest_index] += (A - next_A) * (index + 1)
print(*ans, sep = '\n')
|
p00058 Orthogonal_28471
|
Read the coordinates of four different points on the plane, $ A (x_A, y_A) $, $ B (x_B, y_B) $, $ C (x_C, y_C) $, $ D (x_D, y_D) $, and straight line $ Create a program that outputs YES if AB $ and $ CD $ are orthogonal, and NO if they are not orthogonal. Here, "straight line" does not mean a line segment. Please refer to the figure below.
<image>
Input
Given multiple datasets. The format of each dataset is as follows.
$ x_A $ $ y_A $ $ x_B $ $ y_B $ $ x_C $ $ y_C $ $ x_D $ $ y_D $
$ x_A $, $ y_A $, $ x_B $, $ y_B $, $ x_C $, $ y_C $, $ x_D $, $ y_D $ are each -100 or more and 100 or less, and each value has a maximum of 5 digits after the decimal point. It is given as a real number including the number of.
The number of datasets does not exceed 100.
Output
Print YES or NO on one line for each dataset.
Example
Input
1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0
0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0
10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1
2.5 3.5 2.5 4.5 -3.3 -2.3 6.8 -2.3
Output
YES
NO
NO
YES
|
E = 10 ** -10
while True:
try:
xa, ya, xb, yb, xc, yc, xd, yd = map(float, input().split())
vabx, vaby = xb - xa, yb - ya
vcdx, vcdy = xd - xc, yd - yc
print("YES" if abs(vabx * vcdx + vaby * vcdy) < E else "NO")
except EOFError:
break
|
{
"input": [
"1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1\n2.5 3.5 2.5 4.5 -3.3 -2.3 6.8 -2.3",
"1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1\n2.5 3.5 2.5 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1\n3.455765838159193 3.5 2.5 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.0 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.0 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.4 5.2 6.8 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.4 5.2 6.8 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.4 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.092069677518794 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.2573677918714536 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.8174052507112806 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.2573677918714536 0.0 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.8174052507112806 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.0 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 1.8174052507112806 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 2.7766810766941656 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.5 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 2.7766810766941656 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.619279674149135 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -3.3 -2.3 6.8 -2.3",
"1.1938897485878988 2.7766810766941656 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.619279674149135 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 6.8 -2.3",
"1.1938897485878988 2.7766810766941656 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.619279674149135 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.0 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.619279674149135 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.619279674149135 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.0 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.2573677918714536 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -1.0\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -2.3 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.2 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -2.7189684746319136 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.3 2.1\n3.455765838159193 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.3 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.8123599485681215\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.6642008537722819 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.0 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.2069759298987606 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -1.7443863994674067 -1.2069759298987606 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -2.3",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.397538069721222 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 9.847987038656276 4.710391994583779 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 10.198924225205158 4.710391994583779 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.372545531941309 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.0 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"1.8204197209176585 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 3.7751909492984854 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.9884906966617272 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.1\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.6636008820578361 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.120315016839786 10.198924225205158 5.43738398075114 2.2844136274411446\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.6636008820578361 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.0 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.253479905647363 10.198924225205158 5.43738398075114 2.2844136274411446\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.6636008820578361 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.253479905647363 10.198924225205158 5.43738398075114 2.2844136274411446\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.6636008820578361 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.253479905647363 10.198924225205158 5.43738398075114 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 -0.6636008820578361 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 4.5928356826705 5.856722994178996 7.253479905647363 10.198924225205158 5.43738398075114 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.43738398075114 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.019111227858457314 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 0.8244635358245298 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -1.2069759298987606 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n4.583819304911643 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.0 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.13627377190391943 -1.0 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.6768252188131545 -1.0 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.6335053841034837",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.6768252188131545 -1.0 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.198924225205158 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.572069181554971 2.108763540719617 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.6768252188131545 -1.0 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.572069181554971 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.6768252188131545 -1.0 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.572069181554971 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.362334246917769 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.572069181554971 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n0.33054630677481556 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.572069181554971 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n1.292600536093688 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n1.292600536093688 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.6050613562174583\n1.5534006201248949 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.5534006201248949 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.7780078213948262 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.5534006201248949 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 5.324353001023156 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.5534006201248949 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.856722994178996 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.948853982866238 7.253479905647363 10.276227638334333 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 2.9848733378165186\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.0 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.422784202670174 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 2.572891727497494 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.04462365608480212 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 -0.22171423146006675 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 1.4207962394266105 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 0.6074422665679717 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 2.6723870681351944 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 0.6074422665679717 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 0.6074422665679717 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 5.821756655420878 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.3668013051677885\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 2.73593633965123 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 7.520157928820052 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 0.6768252188131545 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.0 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 2.7766810766941656 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 5.948853982866238 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 -0.38995022061991524\n1.9707706293063516 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 -0.38995022061991524\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.8777038152148869 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 6.573611160966758 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 6.870138129492446 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.162929927730617 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.162929927730617 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.5505524332407266",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.0\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.223429369416744 3.2263123324526175 3.173877408196737 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.223429369416744 3.2263123324526175 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.1119363853635456 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.223429369416744 3.2263123324526175 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.8203952761369226 3.2263123324526175 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.8203952761369226 4.153021285774258 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 3.4549756324749468 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"2.8203952761369226 4.153021285774258 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 4.375348294881063 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"3.338679167476614 4.153021285774258 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.384790875835813\n5.2351081056511815 3.5 4.375348294881063 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"3.338679167476614 4.153021285774258 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.0 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.581486646065169\n5.2351081056511815 3.5 4.375348294881063 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698",
"3.338679167476614 4.153021285774258 3.5962681645685493 3.0562783924178016 0.7824583380395241 0.6535611152381731 1.4307644766957708 0.2352661769827814\n2.6749426974072605 2.336361124342693 3.280415305064114 1.6735605571901062 -0.04476814775527138 2.2725919391555047 3.1294550602222495 2.8167160930096795\n10.965699022496894 7.088941795100844 5.436579099525304 6.657003460325214 7.253479905647363 11.267395003577702 7.30410294155307 3.581486646065169\n5.2351081056511815 3.5 4.375348294881063 6.509817789034612 0.4984898582781403 1.3568956579426947 8.029579677120136 -1.1734526367791698"
],
"output": [
"YES\nNO\nNO\nYES",
"YES\nNO\nNO\nYES\n",
"YES\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Read the coordinates of four different points on the plane, $ A (x_A, y_A) $, $ B (x_B, y_B) $, $ C (x_C, y_C) $, $ D (x_D, y_D) $, and straight line $ Create a program that outputs YES if AB $ and $ CD $ are orthogonal, and NO if they are not orthogonal. Here, "straight line" does not mean a line segment. Please refer to the figure below.
<image>
Input
Given multiple datasets. The format of each dataset is as follows.
$ x_A $ $ y_A $ $ x_B $ $ y_B $ $ x_C $ $ y_C $ $ x_D $ $ y_D $
$ x_A $, $ y_A $, $ x_B $, $ y_B $, $ x_C $, $ y_C $, $ x_D $, $ y_D $ are each -100 or more and 100 or less, and each value has a maximum of 5 digits after the decimal point. It is given as a real number including the number of.
The number of datasets does not exceed 100.
Output
Print YES or NO on one line for each dataset.
Example
Input
1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0
0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0
10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1
2.5 3.5 2.5 4.5 -3.3 -2.3 6.8 -2.3
Output
YES
NO
NO
YES
### Input:
1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0
0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0
10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1
2.5 3.5 2.5 4.5 -3.3 -2.3 6.8 -2.3
### Output:
YES
NO
NO
YES
### Input:
1.0 1.0 2.0 2.0 0.0 0.0 1.0 -1.0
0.0 0.0 2.0 0.0 -1.0 2.0 2.0 2.0
10.0 6.0 3.4 5.2 6.8 9.5 4.3 2.1
2.5 3.5 2.5 5.324353001023156 -3.3 -2.3 6.8 -2.3
### Output:
YES
NO
NO
YES
### Code:
E = 10 ** -10
while True:
try:
xa, ya, xb, yb, xc, yc, xd, yd = map(float, input().split())
vabx, vaby = xb - xa, yb - ya
vcdx, vcdy = xd - xc, yd - yc
print("YES" if abs(vabx * vcdx + vaby * vcdy) < E else "NO")
except EOFError:
break
|
p00189 Convenient Location_28475
|
Mr. A, who will graduate next spring, decided to move when he got a job. The company that finds a job has offices in several towns, and the offices that go to work differ depending on the day. So Mr. A decided to live in a town where he had a short time to go to any office.
So you decided to find the most convenient town to live in to help Mr. A.
<image>
Towns are numbered starting with 0 and there is a road between towns. Commuting time is fixed for each road. If Mr. A lives in a town, the commuting time to the office in his town is 0. At this time, consider the total commuting time to all towns. For example, if the layout of towns and roads is as shown in the figure above and Mr. A lives in town 1, the commuting time to each town will be
Town 0 to 80
0 to town 1
Up to town 2 20
Up to town 3 70
Town 4 to 90
And the sum is 260.
Enter the number of roads and information on all roads, calculate the total commuting time when living in each town, and output the number of the town that minimizes it and the total commuting time at that time. Create a program. However, if there are multiple towns with the smallest total commuting time, please output the number of the smallest town and the total commuting time at that time. The total number of towns is 10 or less, the total number of roads is 45 or less, all roads can move in both directions, and commuting time does not change depending on the direction. We also assume that there are routes from any town to all other towns.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
a1 b1 c1
a2 b2 c2
::
an bn cn
The number of roads n (1 ≤ n ≤ 45) is given on the first line. The following n lines give information on the i-th way. ai, bi (0 ≤ ai, bi ≤ 9) is the number of the town to which the i-th road connects, and ci (0 ≤ ci ≤ 100) is the commute time for that road.
Output
For each data set, the town number that minimizes the total commuting time and the total commuting time at that time are output on one line separated by blanks.
Example
Input
6
0 1 80
1 2 20
0 2 60
2 3 50
3 4 60
1 4 90
2
0 1 1
1 2 1
0
Output
2 240
1 2
|
INF = 10 ** 10
while True:
n = int(input())
if n == 0:
break
costs = [[INF] * 10 for _ in range(10)]
for i in range(10):
costs[i][i] = 0
city = set()
for _ in range(n):
a, b, c = map(int, input().split())
city = city | {a, b}
costs[a][b] = c
costs[b][a] = c
city = sorted(list(city))
for k in range(10):
for i in range(10):
for j in range(10):
costs[i][j] = min(costs[i][j], costs[i][k] + costs[k][j])
min_total = INF
best_city = -1
for fr in city:
total = 0
for to in city:
total += costs[fr][to]
if total < min_total:
min_total = total
best_city = fr
print(best_city, min_total)
|
{
"input": [
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 0 1\n0",
"6\n0 1 80\n1 2 28\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 0 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n2 3 50\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n2 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n3 2 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 0 80\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 14\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n2 4 66\n1 4 90\n2\n0 1 1\n1 0 1\n0",
"6\n0 1 50\n1 2 20\n0 2 60\n1 2 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 66\n0 4 90\n2\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n0 1 20\n0 2 60\n2 3 50\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n2 4 66\n1 4 90\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n1 2 20\n0 1 60\n2 2 50\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n0 3 50\n2 4 66\n1 4 90\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n0 2 20\n0 1 60\n2 2 50\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n0 2 20\n0 1 60\n2 3 50\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n0 2 20\n0 1 34\n2 3 50\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n1 2 37\n0 1 34\n2 3 50\n3 4 14\n1 3 90\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 37\n0 1 57\n2 3 50\n3 4 14\n1 1 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 37\n0 1 57\n2 3 50\n3 4 14\n1 0 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 20\n0 2 60\n2 1 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n0 4 90\n2\n0 2 1\n1 2 1\n0",
"6\n0 1 80\n1 4 20\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 28\n0 2 60\n2 2 50\n3 4 77\n1 4 90\n2\n0 1 1\n1 0 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n2 3 62\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 0 80\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 80\n0 2 20\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n0 3 20\n0 2 60\n2 3 50\n5 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 2 50\n3 4 66\n0 4 90\n0\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n0 1 20\n0 2 60\n2 5 50\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n2 3 50\n2 4 66\n1 4 90\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n2 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n0 3 50\n2 0 66\n1 4 90\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n0 2 20\n0 1 90\n2 2 50\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n1 2 60\n0 3 50\n2 4 66\n1 4 87\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n0 2 20\n0 1 60\n2 1 50\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 1\n1",
"6\n0 1 80\n0 2 20\n0 1 60\n2 2 50\n3 4 3\n1 4 90\n0\n0 1 1\n1 3 1\n1",
"6\n0 0 80\n0 2 20\n0 1 34\n2 3 88\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 50\n4 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 39\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 50\n3 4 14\n1 3 35\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 37\n0 1 34\n2 3 31\n3 4 14\n1 3 90\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 62\n0 1 34\n2 3 50\n3 4 14\n1 3 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 37\n0 1 57\n2 3 50\n3 4 20\n1 1 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 0 20\n0 2 60\n2 3 50\n3 0 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n0 2 20\n0 2 60\n2 3 50\n3 4 66\n0 4 90\n2\n0 2 1\n1 2 1\n0",
"6\n0 0 99\n1 2 20\n0 2 60\n2 3 50\n3 4 66\n1 4 90\n2\n0 2 1\n1 2 1\n0",
"6\n0 1 80\n1 3 23\n0 2 60\n2 3 62\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n1 4 82\n3 4 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 55\n0 2 20\n0 2 60\n2 2 50\n3 4 66\n1 4 90\n2\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n0 4 20\n0 2 60\n2 3 50\n5 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n2 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n0 2 1\n0",
"6\n0 1 50\n1 2 20\n1 2 60\n1 2 22\n3 4 66\n0 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 3 20\n1 2 60\n0 3 50\n2 4 66\n1 4 87\n2\n0 1 1\n2 0 1\n0",
"6\n0 1 80\n0 2 22\n0 1 34\n2 3 50\n3 4 14\n1 4 90\n0\n0 0 1\n0 3 1\n1",
"6\n0 0 80\n0 2 20\n0 1 34\n2 0 88\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 39\n3 4 3\n1 4 90\n0\n0 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 50\n2 4 14\n1 3 90\n0\n0 0 1\n2 3 1\n2",
"6\n0 1 80\n1 2 26\n0 1 34\n2 3 31\n3 4 14\n1 3 90\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 0 20\n0 2 60\n2 3 50\n3 0 60\n1 3 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 113\n1 4 20\n0 2 60\n2 2 47\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n1 0 80\n1 4 20\n0 2 60\n2 3 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 80\n0 4 20\n0 2 60\n2 3 99\n5 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 0 107\n1 2 20\n0 2 60\n2 3 10\n0 4 66\n1 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 80\n1 2 20\n0 2 60\n2 1 17\n3 4 14\n1 4 90\n0\n0 1 1\n1 2 0\n0",
"6\n0 1 80\n1 2 35\n0 2 60\n0 2 50\n3 4 66\n0 4 90\n0\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n1 3 20\n0 2 60\n0 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n0 2 1\n0",
"6\n0 1 80\n1 3 20\n1 2 60\n0 3 50\n2 4 20\n1 4 87\n2\n0 1 1\n2 0 1\n0",
"6\n0 0 80\n0 2 20\n0 1 13\n2 0 88\n3 4 14\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n0 2 37\n0 1 57\n2 3 54\n3 4 14\n1 0 90\n0\n0 0 2\n1 3 1\n2",
"6\n0 1 80\n1 0 20\n0 2 60\n2 3 50\n3 0 60\n1 0 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 113\n1 4 20\n0 2 60\n2 2 47\n3 4 66\n1 4 90\n2\n0 1 1\n1 2 2\n0",
"6\n0 1 80\n1 3 23\n0 2 117\n2 3 23\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n0 1 80\n1 3 20\n0 3 60\n0 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n0 2 1\n0",
"6\n0 1 80\n1 3 20\n1 2 60\n0 3 50\n2 4 20\n1 4 87\n2\n0 1 0\n2 0 1\n0",
"6\n0 2 80\n1 2 20\n0 1 37\n2 3 50\n4 4 15\n1 4 90\n0\n0 0 1\n1 3 1\n1",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 39\n2 4 3\n1 4 90\n0\n-1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 2 20\n0 1 64\n2 4 93\n3 4 14\n1 3 35\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 47\n1 2 37\n0 1 34\n2 3 50\n3 4 4\n1 1 90\n0\n1 0 1\n1 3 0\n2",
"6\n0 1 80\n0 2 9\n0 1 57\n2 3 54\n3 4 14\n1 0 90\n0\n0 0 2\n1 3 1\n2",
"6\n0 1 80\n1 0 20\n0 2 60\n2 3 50\n3 0 60\n1 0 90\n0\n0 1 1\n1 2 1\n0",
"6\n0 1 113\n1 4 20\n0 2 60\n2 2 47\n3 4 21\n1 4 90\n2\n0 1 1\n1 2 2\n0",
"6\n0 1 80\n1 3 23\n0 2 117\n1 3 23\n3 4 60\n1 4 90\n2\n0 1 1\n1 2 1\n0",
"6\n1 0 80\n1 4 35\n0 2 44\n2 3 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 55\n0 2 20\n0 2 60\n2 3 50\n0 2 66\n1 4 90\n2\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n1 1 35\n0 2 60\n0 2 3\n3 4 66\n0 4 90\n0\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n1 3 22\n0 3 60\n0 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n0 2 1\n0",
"6\n0 1 80\n1 2 20\n0 1 34\n2 3 25\n2 4 3\n1 4 90\n0\n-1 0 1\n1 3 1\n2",
"6\n0 1 80\n1 3 20\n0 1 64\n2 4 93\n3 4 14\n1 3 35\n0\n1 0 1\n1 3 1\n2",
"6\n0 1 47\n1 2 37\n0 1 34\n2 3 50\n3 4 2\n1 1 90\n0\n1 0 1\n1 3 0\n2",
"6\n0 1 113\n1 4 20\n0 2 60\n2 0 47\n3 4 21\n1 4 90\n2\n0 1 1\n1 2 2\n0",
"6\n1 0 80\n1 4 35\n0 2 44\n2 2 50\n3 4 66\n0 4 90\n2\n0 1 1\n1 1 1\n0",
"6\n0 1 55\n0 2 20\n0 2 60\n2 3 50\n0 2 84\n1 4 90\n2\n0 1 2\n1 0 1\n0",
"6\n0 1 80\n1 1 22\n0 3 60\n0 4 50\n3 2 66\n0 4 165\n2\n0 1 1\n0 2 1\n0",
"6\n0 2 80\n1 2 20\n0 1 37\n4 3 50\n4 1 15\n1 4 90\n0\n0 0 1\n1 3 1\n1"
],
"output": [
"2 240\n1 2",
"2 240\n1 2\n",
"2 246\n1 2\n",
"0 386\n1 2\n",
"1 346\n1 2\n",
"1 346\n0 1\n",
"1 354\n0 1\n",
"3 230\n1 2\n",
"2 196\n1 2\n",
"2 296\n1 2\n",
"2 240\n0 1\n",
"1 294\n1 2\n",
"2 196\n0 1\n",
"0 356\n1 2\n",
"1 294\n",
"0 386\n0 1\n",
"0 300\n1 2\n",
"2 196\n0 2\n",
"1 274\n",
"2 256\n0 2\n",
"1 334\n",
"2 214\n",
"2 188\n",
"2 222\n",
"2 245\n",
"2 278\n",
"1 376\n1 2\n",
"2 246\n2 2\n",
"1 466\n1 2\n",
"1 365\n0 1\n",
"3 242\n1 2\n",
"2 246\n0 1\n",
"1 466\n0 1\n",
"0 560\n1 2\n",
"0 386\n",
"0 470\n1 2\n",
"2 246\n0 2\n",
"2 262\n1 2\n",
"2 312\n0 2\n",
"1 394\n",
"1 357\n0 2\n",
"1 304\n",
"1 323\n",
"2 264\n",
"1 214\n",
"2 166\n",
"1 138\n",
"2 184\n",
"2 272\n",
"2 251\n",
"0 250\n1 2\n",
"0 340\n2 2\n",
"2 240\n2 2\n",
"3 248\n1 2\n",
"1 330\n1 2\n",
"1 416\n0 1\n",
"0 350\n1 2\n",
"2 262\n0 2\n",
"0 368\n1 2\n",
"1 237\n0 2\n",
"2 192\n",
"1 350\n",
"2 155\n",
"2 138\n",
"2 162\n",
"0 140\n1 2\n",
"1 532\n1 2\n",
"4 292\n0 1\n",
"0 399\n1 2\n",
"2 200\n0 1\n",
"1 288\n",
"0 376\n",
"0 405\n0 2\n",
"1 230\n0 2\n",
"1 308\n",
"2 286\n",
"0 210\n1 2\n",
"1 532\n1 3\n",
"3 209\n1 2\n",
"3 371\n0 2\n",
"1 230\n0 1\n",
"1 217\n",
"2 116\n",
"1 168\n",
"2 212\n",
"2 230\n",
"0 210\n",
"1 487\n1 3\n",
"1 383\n1 2\n",
"4 307\n0 1\n",
"0 382\n0 1\n",
"0 329\n",
"3 373\n0 2\n",
"2 102\n",
"3 255\n",
"2 210\n",
"1 474\n1 3\n",
"4 325\n0 1\n",
"0 418\n0 1\n",
"0 431\n0 2\n",
"1 287\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Mr. A, who will graduate next spring, decided to move when he got a job. The company that finds a job has offices in several towns, and the offices that go to work differ depending on the day. So Mr. A decided to live in a town where he had a short time to go to any office.
So you decided to find the most convenient town to live in to help Mr. A.
<image>
Towns are numbered starting with 0 and there is a road between towns. Commuting time is fixed for each road. If Mr. A lives in a town, the commuting time to the office in his town is 0. At this time, consider the total commuting time to all towns. For example, if the layout of towns and roads is as shown in the figure above and Mr. A lives in town 1, the commuting time to each town will be
Town 0 to 80
0 to town 1
Up to town 2 20
Up to town 3 70
Town 4 to 90
And the sum is 260.
Enter the number of roads and information on all roads, calculate the total commuting time when living in each town, and output the number of the town that minimizes it and the total commuting time at that time. Create a program. However, if there are multiple towns with the smallest total commuting time, please output the number of the smallest town and the total commuting time at that time. The total number of towns is 10 or less, the total number of roads is 45 or less, all roads can move in both directions, and commuting time does not change depending on the direction. We also assume that there are routes from any town to all other towns.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
a1 b1 c1
a2 b2 c2
::
an bn cn
The number of roads n (1 ≤ n ≤ 45) is given on the first line. The following n lines give information on the i-th way. ai, bi (0 ≤ ai, bi ≤ 9) is the number of the town to which the i-th road connects, and ci (0 ≤ ci ≤ 100) is the commute time for that road.
Output
For each data set, the town number that minimizes the total commuting time and the total commuting time at that time are output on one line separated by blanks.
Example
Input
6
0 1 80
1 2 20
0 2 60
2 3 50
3 4 60
1 4 90
2
0 1 1
1 2 1
0
Output
2 240
1 2
### Input:
6
0 1 80
1 2 20
0 2 60
2 3 50
3 4 60
1 4 90
2
0 1 1
1 2 1
0
### Output:
2 240
1 2
### Input:
6
0 1 80
1 2 20
0 2 60
2 3 50
3 4 66
1 4 90
2
0 1 1
1 2 1
0
### Output:
2 240
1 2
### Code:
INF = 10 ** 10
while True:
n = int(input())
if n == 0:
break
costs = [[INF] * 10 for _ in range(10)]
for i in range(10):
costs[i][i] = 0
city = set()
for _ in range(n):
a, b, c = map(int, input().split())
city = city | {a, b}
costs[a][b] = c
costs[b][a] = c
city = sorted(list(city))
for k in range(10):
for i in range(10):
for j in range(10):
costs[i][j] = min(costs[i][j], costs[i][k] + costs[k][j])
min_total = INF
best_city = -1
for fr in city:
total = 0
for to in city:
total += costs[fr][to]
if total < min_total:
min_total = total
best_city = fr
print(best_city, min_total)
|
p00344 Cyclic Sugoroku_28478
|
Yuki made a sugoroku so that everyone can play at the children's association event. In this sugoroku, squares are lined up in a ring, and each square has an integer of 1 or more written on it.
The player chooses a square as a starting point and places his piece. Advance the pieces clockwise by the number written on the square. Advance the pieces clockwise again by the number written on the stopped square. Repeat this, and when the piece stops on the square selected as the starting point, it is "Agari".
In reality, depending on how you choose the squares, it may never be "finished". Yuki is trying to count the number of squares that can reach the "Agari" in this sugoroku.
Create a program that inputs sugoroku information and reports the number of squares that can reach "Agari".
Input
The input is given in the following format.
N
a1 a2 ... aN
The number N (1 ≤ N ≤ 100000) of all the cells contained in the sugoroku is given in the first line. On the second line, the number ai (1 ≤ ai ≤ 109) written in each cell is given in turn clockwise.
Output
The number of squares that can reach "Agari" is output in one line.
Examples
Input
3
1 1 1
Output
3
Input
3
1 1 2
Output
2
Input
8
2 3 7 3 3 3 4 4
Output
6
|
import sys
sys.setrecursionlimit(1000000)
def dfs(x, order, edges, visited):
visited[x] = True
for e in edges[x]:
if not visited[e]:
dfs(e, order, edges, visited)
order.append(x)
def dfs_rev(x, rev_edges, visited):
visited[x] = True
ret = 0
for e in rev_edges[x]:
if not visited[e]:
ret += 1
ret += dfs_rev(e, rev_edges, visited)
return ret
n = int(input())
alst = list(map(int, input().split()))
edges = [[] for _ in range(n)]
rev_edges = [[] for _ in range(n)]
for i in range(n):
edges[i].append((i + alst[i]) % n)
rev_edges[(i + alst[i]) % n].append(i)
order = []
visited = [False] * n
for i in range(n):
if not visited[i]:
dfs(i, order, edges, visited)
order.reverse()
visited = [False] * n
cycles = 0
for i in order:
if not visited[i]:
a = dfs_rev(i, rev_edges, visited)
if a > 0 or i in rev_edges[i]:
a += 1
cycles += a
print(cycles)
|
{
"input": [
"3\n1 1 1",
"8\n2 3 7 3 3 3 4 4",
"3\n1 1 2",
"3\n2 1 1",
"8\n2 3 7 3 3 1 4 4",
"3\n1 1 3",
"3\n1 2 3",
"8\n2 4 4 0 3 4 4 4",
"8\n0 3 6 0 5 4 4 4",
"8\n0 3 5 1 6 0 0 4",
"8\n1 1 1 2 11 1 -2 1",
"3\n2 1 0",
"8\n2 3 4 3 3 1 4 4",
"3\n1 1 0",
"8\n2 3 4 0 3 1 4 4",
"3\n1 2 1",
"3\n2 2 1",
"8\n2 3 4 0 3 2 4 4",
"3\n1 2 0",
"3\n4 2 1",
"8\n2 4 4 0 3 2 4 4",
"3\n0 2 0",
"3\n4 2 0",
"3\n1 4 0",
"8\n2 4 6 0 3 4 4 4",
"3\n0 4 0",
"8\n2 4 6 0 5 4 4 4",
"3\n0 3 0",
"8\n2 4 6 0 5 4 5 4",
"3\n0 1 0",
"8\n2 3 6 0 5 4 5 4",
"3\n1 3 0",
"8\n2 3 6 0 5 4 4 4",
"3\n1 3 -1",
"3\n1 5 -1",
"8\n0 3 6 1 5 4 4 4",
"3\n0 5 -1",
"8\n0 3 5 1 5 4 4 4",
"3\n0 5 0",
"8\n0 3 5 1 6 4 4 4",
"3\n0 5 1",
"8\n0 3 5 1 6 0 4 4",
"3\n1 5 1",
"3\n0 2 1",
"8\n0 3 1 1 6 0 0 4",
"8\n0 3 1 2 6 0 0 4",
"8\n0 1 1 2 6 0 0 4",
"8\n0 1 1 2 6 0 0 6",
"8\n0 1 0 2 6 0 0 6",
"8\n0 1 0 2 6 0 0 12",
"8\n1 1 0 2 6 0 0 12",
"8\n1 0 0 2 6 0 0 12",
"8\n1 0 1 2 6 0 0 12",
"8\n1 0 1 2 6 0 1 12",
"8\n1 0 1 2 6 0 1 8",
"8\n1 0 1 2 6 0 0 8",
"8\n1 0 1 2 10 0 0 8",
"8\n1 0 1 2 10 1 0 8",
"8\n1 0 1 2 14 1 0 8",
"8\n1 0 1 2 17 1 0 8",
"8\n1 0 1 2 17 1 0 2",
"8\n1 0 1 2 17 1 0 1",
"8\n2 0 1 2 17 1 0 1",
"8\n2 0 1 2 1 1 0 1",
"8\n2 1 1 2 1 1 0 1",
"8\n2 1 1 2 1 2 0 1",
"8\n2 1 1 2 1 2 -1 1",
"8\n2 0 1 2 1 2 -1 1",
"8\n2 0 1 2 1 4 -1 1",
"8\n3 0 1 2 1 4 -1 1",
"8\n3 0 1 2 1 2 -1 1",
"8\n3 0 1 4 1 4 -1 1",
"8\n1 0 1 2 1 4 -1 1",
"8\n1 0 1 2 1 4 -1 0",
"8\n0 0 1 2 1 4 -1 0",
"8\n0 0 1 4 1 4 -1 0",
"8\n0 0 2 4 1 4 -1 0",
"8\n1 0 2 4 1 4 -1 0",
"8\n1 0 2 0 1 4 -1 0",
"8\n1 0 3 0 1 4 -1 0",
"8\n2 0 3 0 1 4 -1 0",
"8\n2 -1 3 0 1 4 -1 0",
"8\n2 -1 3 -1 1 4 -1 0",
"8\n3 -1 3 -1 1 4 -1 0",
"8\n3 -1 3 -1 2 4 -1 0",
"8\n3 -1 3 -1 0 4 -1 0",
"8\n3 -1 3 -1 0 4 -1 1",
"8\n3 -1 3 0 0 4 -1 1",
"3\n0 0 0",
"8\n2 3 7 3 3 3 2 4",
"3\n1 1 5",
"3\n4 1 1",
"8\n2 2 7 3 3 1 4 4",
"3\n2 1 3",
"3\n2 2 0",
"8\n2 3 4 3 3 1 8 4",
"3\n1 2 5",
"3\n2 2 -1",
"8\n2 3 4 0 3 1 4 3",
"3\n1 4 1",
"3\n2 2 2",
"8\n2 3 4 0 3 2 4 3",
"3\n1 2 -1"
],
"output": [
"3",
"6",
"2",
"2\n",
"6\n",
"1\n",
"3\n",
"5\n",
"4\n",
"7\n",
"8\n",
"1\n",
"2\n",
"1\n",
"3\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n",
"5\n",
"2\n",
"5\n",
"3\n",
"5\n",
"2\n",
"5\n",
"2\n",
"5\n",
"1\n",
"2\n",
"3\n",
"1\n",
"3\n",
"2\n",
"5\n",
"1\n",
"6\n",
"2\n",
"1\n",
"6\n",
"3\n",
"3\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"3\n",
"2\n",
"3\n",
"4\n",
"4\n",
"3\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"6\n",
"5\n",
"6\n",
"1\n",
"1\n",
"5\n",
"4\n",
"1\n",
"2\n",
"3\n",
"3\n",
"3\n",
"2\n",
"3\n",
"3\n",
"3\n",
"6\n",
"5\n",
"6\n",
"6\n",
"7\n",
"6\n",
"2\n",
"3\n",
"7\n",
"2\n",
"3\n",
"4\n",
"1\n",
"1\n",
"1\n",
"2\n",
"3\n",
"3\n",
"3\n",
"3\n",
"3\n",
"2\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Yuki made a sugoroku so that everyone can play at the children's association event. In this sugoroku, squares are lined up in a ring, and each square has an integer of 1 or more written on it.
The player chooses a square as a starting point and places his piece. Advance the pieces clockwise by the number written on the square. Advance the pieces clockwise again by the number written on the stopped square. Repeat this, and when the piece stops on the square selected as the starting point, it is "Agari".
In reality, depending on how you choose the squares, it may never be "finished". Yuki is trying to count the number of squares that can reach the "Agari" in this sugoroku.
Create a program that inputs sugoroku information and reports the number of squares that can reach "Agari".
Input
The input is given in the following format.
N
a1 a2 ... aN
The number N (1 ≤ N ≤ 100000) of all the cells contained in the sugoroku is given in the first line. On the second line, the number ai (1 ≤ ai ≤ 109) written in each cell is given in turn clockwise.
Output
The number of squares that can reach "Agari" is output in one line.
Examples
Input
3
1 1 1
Output
3
Input
3
1 1 2
Output
2
Input
8
2 3 7 3 3 3 4 4
Output
6
### Input:
3
1 1 1
### Output:
3
### Input:
8
2 3 7 3 3 3 4 4
### Output:
6
### Code:
import sys
sys.setrecursionlimit(1000000)
def dfs(x, order, edges, visited):
visited[x] = True
for e in edges[x]:
if not visited[e]:
dfs(e, order, edges, visited)
order.append(x)
def dfs_rev(x, rev_edges, visited):
visited[x] = True
ret = 0
for e in rev_edges[x]:
if not visited[e]:
ret += 1
ret += dfs_rev(e, rev_edges, visited)
return ret
n = int(input())
alst = list(map(int, input().split()))
edges = [[] for _ in range(n)]
rev_edges = [[] for _ in range(n)]
for i in range(n):
edges[i].append((i + alst[i]) % n)
rev_edges[(i + alst[i]) % n].append(i)
order = []
visited = [False] * n
for i in range(n):
if not visited[i]:
dfs(i, order, edges, visited)
order.reverse()
visited = [False] * n
cycles = 0
for i in order:
if not visited[i]:
a = dfs_rev(i, rev_edges, visited)
if a > 0 or i in rev_edges[i]:
a += 1
cycles += a
print(cycles)
|
p00843 Bingo_28485
|
A Bingo game is played by one gamemaster and several players. At the beginning of a game, each player is given a card with M × M numbers in a matrix (See Figure 10).
<image>
As the game proceeds, the gamemaster announces a series of numbers one by one. Each player punches a hole in his card on the announced number, if any.
When at least one 'Bingo' is made on the card, the player wins and leaves the game. The 'Bingo' means that all the M numbers in a line are punched vertically, horizontally or diagonally (See Figure 11).
<image>
The gamemaster continues announcing numbers until all the players make a Bingo.
In the ordinary Bingo games, the gamemaster chooses numbers by a random process and has no control on them. But in this problem the gamemaster knows all the cards at the beginning of the game and controls the game by choosing the number sequence to be announced at his will.
Specifically, he controls the game to satisfy the following condition.
Cardi makes a Bingo no later than Cardj, for i < j. (*)
Figure 12 shows an example of how a game proceeds. The gamemaster cannot announce '5' before '16', because Card4 makes a Bingo before Card2 and Card3, violating the condition (*).
Your job is to write a program which finds the minimum length of such sequence of numbers for the given cards.
Input
The input consists of multiple datasets. The format of each dataset is as follows.
<image>
All data items are integers. P is the number of the cards, namely the number of the players. M is the number of rows and the number of columns of the matrix on each card. Nkij means the number written at the position (i, j) on the k-th card. If (i, j) ≠ (p, q), then Nkij ≠ Nkpq. The parameters P, M, and N satisfy the conditions 2 ≤ P ≤ 4, 3 ≤ M ≤ 4, and 0 ≤ Nkij ≤ 99.
The end of the input is indicated by a line containing two zeros separated by a space. It is not a dataset.
Output
For each dataset, output the minimum length of the sequence of numbers which satisfy the condition (*). Output a zero if there are no such sequences. Output for each dataset must be printed on a separate line.
Example
Input
4 3
10 25 11 20 6 2 1 15 23
5 21 3 12 23 17 7 26 2
8 18 4 22 13 27 16 5 11
19 9 24 2 11 5 14 28 16
4 3
12 13 20 24 28 32 15 16 17
12 13 21 25 29 33 16 17 18
12 13 22 26 30 34 17 18 15
12 13 23 27 31 35 18 15 16
4 3
11 12 13 14 15 16 17 18 19
21 22 23 24 25 26 27 28 29
31 32 33 34 35 36 37 38 39
41 42 43 44 45 46 47 48 49
4 4
2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36
22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29
26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5
36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2
0 0
Output
5
4
12
0
|
def solve():
from itertools import product
from sys import stdin
f_i = stdin
while True:
P, M = map(int, f_i.readline().split())
if P == 0:
break
bingo = []
for i in range(P):
b = []
card = list(map(int, f_i.readline().split()))
d1 = [] # diagonally
d2 = [] # diagonally
for i in range(M):
b.append(card[i::M]) # vertically
b.append(card[i*M:i*M+M]) # horizontally
d1.append(card[i*M+i])
d2.append(card[(M-1)*(i+1)])
b += [d1, d2]
bingo.append(set(frozenset(b_i) for b_i in b))
if P == 2:
ans = min(len(t1 | t2) for t1, t2 in product(*bingo))
elif P == 3:
ans = P * M + 1
c0, c1, c2 = bingo
for b0 in c0:
if b0 in c2:
for b1 in c1:
if b1.intersection(b0):
break
else:
continue
for b1 in c1:
b01 = b0.union(b1)
last = set(b for b in c2 if b.issubset(b01))
if last:
if not b1.intersection(*last):
continue
for b2 in c2:
tmp = len(b2.union(b01))
if tmp < ans:
ans = tmp
if ans == P * M + 1:
ans = 0
else:
ans = P * M + 1
c0, c1, c2, c3 = bingo
for b0 in c0:
if b0 in c2:
for b1 in c1:
if b1.intersection(b0):
break
else:
continue
if b0 in c3:
for b1, b2 in product(c1, c2):
if b0.intersection(b1, b2):
break
else:
continue
for b1 in c1:
b01 = b0.union(b1)
third = set(b2 for b2 in c2 if b2.issubset(b01))
if third:
if not b1.intersection(*third):
continue
last = set(b3 for b3 in c3 if b3.issubset(b01))
if last:
if not b1.intersection(*last):
continue
if third and last:
if not b1.intersection(*third, *last):
continue
if not third and last:
for b2, b3 in product(c2, last):
if b1.intersection(b2, b3):
break
else:
continue
for b2 in c2:
b012 = b0.union(b1, b2)
last = set(b for b in c3 if b.issubset(b012))
if last:
last_num = b2.intersection(*last)
if not last_num:
continue
first = set(b for b in c0 if b.issubset(b012))
if first.issubset(last):
sec = set(b for b in c1 if b.issubset(b012))
if not last_num.intersection(*sec):
continue
for b3 in c3:
tmp = len(b012.union(b3))
if tmp < ans:
ans = tmp
if ans == P * M + 1:
ans = 0
print(ans)
solve()
|
{
"input": [
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 3 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 15\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n11 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 23\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 26 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 17 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 4 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 10 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 52 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 6 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 17 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 3 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 26 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 26 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 9 24 13 36\n22 18 27 26 36 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 6 3\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 17 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n24 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 47 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 20 16\n4 3\n11 12 13 14 15 16 17 34 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 26 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 17 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 9 24 13 36\n22 18 27 26 36 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 19 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 43 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 6 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 0 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 1 32 9 32 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 49 17 18 15\n9 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 71 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 12 23 17 7 3 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n20 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 20 38 39\n41 42 43 44 45 46 47 48 23\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 15 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 26 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 43 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 17 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 9 24 13 36\n22 18 27 26 36 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 36 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 27 1 12 13 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 2 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 26 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 32 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 1 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 1 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 7 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 35 24 1 32 9 32 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 49 17 18 15\n9 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 71 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 3 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 26 33 34 35 36 37 15 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 5 24 13 36\n22 18 27 26 35 28 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 22 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 14 23 15 21 9 6 2\n0 0",
"4 3\n10 25 0 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 6 3\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 8 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 23 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n48 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 52 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n24 9 24 2 11 2 0 28 16\n4 3\n12 13 20 24 46 32 15 16 17\n12 13 21 36 29 47 16 17 18\n12 13 22 26 96 34 17 18 15\n12 13 23 27 31 35 18 20 16\n4 3\n11 12 13 14 15 16 17 34 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 15 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 27 1 12 13 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 2 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 26 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 32 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 1 20 26 16 5 32 14 29\n26 7 21 48 27 3 38 14 1 28 20 32 22 0 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 7 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 26 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 43 31 35 18 15 2\n4 3\n11 12 13 14 15 8 17 18 19\n21 22 23 24 25 17 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 22 25 4 9 24 13 36\n22 18 27 26 36 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 36 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 8 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 38 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 29 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 6 43 44 45 46 47 48 49\n4 4\n2 6 9 21 6 23 17 31 33 12 25 4 8 24 13 36\n20 18 27 26 35 28 5 7 2 20 38 16 5 32 14 29\n26 7 21 29 25 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n7 18 4 22 13 27 16 5 11\n24 9 3 2 11 2 0 28 16\n4 3\n12 13 20 24 46 32 15 16 17\n12 13 21 36 29 47 29 17 18\n12 13 22 26 96 34 17 18 15\n12 13 23 27 31 35 18 20 16\n4 3\n11 12 13 16 15 16 17 34 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 15 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 3 13 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 26 33 34 35 36 37 15 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 5 24 9 36\n22 18 27 13 35 4 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 22 3 38 20 18 31 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 14 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 9 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 17 24 28 32 15 16 19\n12 13 21 27 29 49 16 17 18\n9 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 10\n4 3\n11 12 13 14 15 16 17 18 19\n9 22 23 24 25 26 27 28 29\n31 32 57 34 39 36 37 23 39\n78 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 30 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 32 11 5\n36 13 37 8 4 28 12 14 39 17 28 15 21 9 6 1\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 3 13 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 26 33 34 35 36 37 15 39\n41 42 43 44 45 46 41 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 5 24 9 36\n22 18 27 13 35 4 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 22 3 38 20 18 31 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 14 23 15 21 9 6 2\n0 0",
"4 3\n13 25 11 20 6 2 1 9 23\n5 21 3 12 23 17 13 26 2\n13 18 4 22 13 27 16 8 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 37 32 15 16 17\n12 13 5 25 29 33 16 17 18\n12 13 22 37 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n2 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 52 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 14 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 35\n26 7 16 2 27 3 38 14 18 28 20 15 40 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 3\n0 0",
"4 3\n13 25 11 20 6 2 1 9 23\n5 21 3 12 23 17 13 26 2\n13 18 4 22 13 27 16 8 11\n19 9 24 2 11 5 14 28 18\n4 3\n12 13 20 24 37 32 15 16 17\n12 13 5 25 29 33 16 17 18\n12 13 22 37 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 29 18 19\n2 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 52 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 14 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 35\n26 7 16 2 27 3 38 14 18 28 20 15 40 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 3\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 23 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 6\n19 9 24 2 11 5 0 28 16\n4 3\n23 22 12 24 40 32 15 16 17\n12 13 34 25 58 33 16 17 15\n12 13 22 26 51 34 19 18 15\n12 13 23 2 31 36 18 15 16\n4 3\n11 12 9 14 3 16 17 18 19\n21 22 10 3 30 26 27 28 29\n31 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 8 17 31 43 12 25 4 8 24 13 36\n22 18 3 26 35 28 3 7 2 20 38 16 6 32 14 29\n26 8 21 29 27 3 38 14 18 48 1 32 22 35 11 5\n36 13 5 8 4 25 0 33 31 22 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 1 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 3 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 15\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 22\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 33\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n11 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 23 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 26 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 1\n2 6 9 21 15 23 17 31 43 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 6 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 0 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 0 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 12 23 17 7 3 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 20 38 39\n41 42 43 44 45 46 47 48 23\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 15 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 17 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 21 23 17 7 3 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n20 12 13 14 15 16 17 18 19\n21 12 23 24 25 26 27 28 29\n31 32 33 34 35 36 20 38 39\n41 42 43 44 45 46 47 48 23\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 15 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 0 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 6 3\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 8 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 23 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n48 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 21\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 52 11 5\n36 13 37 8 4 25 12 33 31 17 23 6 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 27 1 12 13 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 2 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 10\n12 26 23 27 31 35 18 15 16\n4 3\n7 12 13 14 15 16 17 18 19\n21 32 23 24 25 26 27 28 29\n31 32 57 34 48 36 21 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 1 20 26 16 5 32 14 29\n26 7 21 48 27 3 38 14 1 28 20 32 22 0 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 8 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 38 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 29 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 6 43 44 45 46 47 48 49\n4 3\n2 6 9 21 6 23 17 31 33 12 25 4 8 24 13 36\n20 18 27 26 35 28 5 7 2 20 38 16 5 32 14 29\n26 7 21 29 25 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 9 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 17 24 28 32 15 16 19\n12 13 21 27 29 49 16 17 18\n9 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 10\n4 3\n11 12 13 14 15 16 17 9 19\n9 22 23 24 25 26 27 28 29\n31 32 57 34 39 36 37 23 39\n78 42 43 61 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 30 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 32 11 5\n36 13 37 8 4 28 12 14 39 17 28 15 21 9 6 1\n0 0",
"4 3\n13 25 11 20 6 2 1 9 23\n5 21 3 12 23 17 13 26 2\n13 18 4 22 13 27 16 8 11\n19 9 24 2 11 5 14 28 18\n4 3\n12 13 20 24 37 32 15 16 17\n12 13 5 25 29 33 16 17 18\n12 13 22 37 30 34 17 18 15\n12 13 23 18 31 35 18 15 16\n4 3\n11 12 13 14 15 16 29 18 19\n2 22 23 24 25 26 27 41 29\n31 32 33 34 35 36 52 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 14 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 35\n26 7 16 2 27 3 38 14 18 28 20 15 40 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 3\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 6\n19 9 24 2 11 5 0 28 16\n4 3\n12 22 12 24 40 32 15 16 17\n12 13 34 25 58 33 16 17 15\n12 13 22 26 51 34 19 18 15\n12 13 23 27 31 36 18 15 16\n4 3\n11 12 9 14 15 16 21 18 19\n21 22 10 3 30 26 27 28 29\n31 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 8 17 31 43 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 6 32 14 29\n26 8 21 29 27 3 38 14 18 48 1 32 22 35 11 5\n36 13 5 8 4 25 0 33 31 22 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 24\n12 4 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 10 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 52 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 1",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 9 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 29 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 6 43 44 45 46 47 48 49\n4 4\n2 6 9 21 6 23 17 31 33 12 25 4 8 24 13 36\n20 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 54 3 38 14 18 39 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n7 18 4 22 13 27 16 5 11\n24 9 3 2 0 2 0 28 16\n4 3\n12 13 20 24 46 32 15 16 17\n12 13 21 36 29 47 29 17 18\n12 13 22 26 96 34 17 18 15\n12 13 23 27 31 35 18 30 16\n4 3\n11 12 13 16 15 16 17 34 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 15 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 9 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 19 16\n4 3\n12 13 17 24 28 32 15 16 19\n12 13 21 27 29 49 16 17 18\n9 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 23 10\n4 3\n11 12 13 14 15 16 17 18 19\n9 22 23 24 25 26 27 28 29\n31 8 57 34 39 36 37 23 39\n78 42 43 61 45 8 47 63 49\n4 4\n2 6 9 21 15 23 29 30 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 32 11 5\n36 13 37 8 4 28 12 14 39 17 28 15 21 9 6 1\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 2 20 23 17 7 26 2\n8 18 4 22 13 27 16 5 12\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 19 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 15 18 15\n12 13 23 27 31 35 3 13 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 21 24 25 26 27 28 34\n31 26 33 34 35 36 37 15 39\n41 42 43 44 45 46 41 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 5 24 9 36\n22 18 27 13 35 4 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 22 3 38 20 18 31 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 14 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 28 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 36 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 25 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 22\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 56 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 2\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 44 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 13\n5 21 1 12 23 17 7 25 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 9 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 23\n0 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 6 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 28 27 31 35 23 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 17 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 12 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n0 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 3 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 24 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 0 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n2 25 11 20 6 2 1 15 13\n5 21 1 21 23 17 7 3 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n20 12 13 14 15 16 17 18 19\n21 12 23 24 25 26 27 28 29\n31 32 33 34 35 36 20 38 39\n41 42 43 44 45 46 47 48 23\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 21 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 15 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 7 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 39 35 18 5 16\n4 3\n11 12 13 24 29 16 17 18 19\n21 22 23 24 25 26 27 28 29\n6 32 33 26 48 36 37 38 39\n41 6 43 44 45 46 47 48 49\n4 4\n2 6 9 21 6 23 17 31 33 12 25 4 8 24 13 36\n20 18 27 26 35 28 5 7 2 20 38 16 5 32 14 29\n26 7 21 29 54 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 20 23 17 7 26 2\n8 18 4 12 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 19 17\n12 13 21 25 29 33 16 17 18\n12 13 22 24 30 34 15 18 15\n12 13 23 27 31 35 3 13 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 21 24 25 26 27 28 34\n31 26 33 34 35 36 37 15 39\n41 42 43 44 45 46 41 25 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 5 24 9 36\n22 18 27 13 35 4 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 22 3 38 20 18 31 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 15 14 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 1 3 1 15 23\n5 23 1 12 23 17 7 26 2\n8 27 4 22 13 27 16 5 6\n19 9 24 2 11 5 0 28 16\n4 3\n23 22 12 24 40 32 15 16 17\n12 13 34 25 58 33 16 17 15\n12 13 22 26 51 34 19 18 15\n12 13 23 2 31 36 18 15 16\n4 3\n11 12 9 14 15 16 17 18 19\n21 22 10 3 30 26 27 28 29\n31 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 8 17 31 43 12 25 4 8 24 13 36\n22 18 3 26 35 28 3 7 2 20 38 16 6 32 14 29\n26 8 21 29 27 3 38 14 18 48 1 32 22 35 11 5\n36 13 5 8 4 25 0 33 31 22 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 21 6 2 1 15 23\n5 23 1 12 23 17 7 26 2\n8 18 4 22 13 27 8 5 6\n19 9 24 2 11 5 0 28 16\n4 3\n23 22 12 24 40 32 15 16 17\n12 13 34 25 58 33 16 17 15\n12 13 22 26 51 34 19 18 15\n12 13 23 2 31 36 18 15 16\n4 3\n11 12 9 1 3 16 17 18 19\n21 6 10 3 30 26 27 28 29\n9 32 33 34 48 36 44 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 8 17 31 43 12 25 4 8 24 13 36\n22 18 3 26 35 28 3 14 2 20 38 16 6 32 14 29\n26 8 21 29 27 3 38 14 18 48 1 32 22 35 11 5\n36 13 5 8 4 25 0 33 31 22 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 3 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 37 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 6 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 3 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 10 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 43 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 26 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 73 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 5 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 24 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n24 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 3 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 1\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 1 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 71 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 2 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 15\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 9 16 17\n12 13 21 27 29 33 16 17 18\n12 13 22 26 51 51 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 57 34 48 36 37 38 39\n41 42 43 44 45 46 47 63 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 48 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 28 12 14 39 17 23 15 21 9 6 2\n0 0",
"4 3\n13 25 11 20 6 2 1 15 23\n5 21 3 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 37 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 5 7 11 20 38 16 6 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 4 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 10 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 43 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 0 33 31 17 23 15 21 9 6 2\n0 0",
"4 3\n10 25 11 20 6 2 1 15 23\n5 21 1 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 0 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 51 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n11 32 33 26 48 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 2 20 38 16 5 32 14 29\n26 7 21 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 37 8 4 25 12 14 31 17 23 15 21 9 6 2\n0 0"
],
"output": [
"5\n4\n12\n0",
"5\n4\n12\n0\n",
"5\n4\n11\n0\n",
"5\n4\n11\n9\n",
"5\n4\n11\n8\n",
"5\n4\n12\n8\n",
"5\n5\n12\n8\n",
"6\n5\n12\n8\n",
"6\n4\n12\n0\n",
"5\n5\n12\n0\n",
"5\n4\n10\n8\n",
"6\n4\n11\n0\n",
"5\n6\n12\n0\n",
"5\n4\n10\n9\n",
"5\n4\n12\n9\n",
"7\n4\n10\n9\n",
"5\n5\n11\n0\n",
"5\n6\n12\n9\n",
"8\n4\n10\n9\n",
"5\n4\n9\n8\n",
"5\n5\n11\n8\n",
"5\n6\n11\n9\n",
"5\n5\n11\n9\n",
"5\n6\n12\n8\n",
"6\n4\n10\n0\n",
"5\n6\n11\n7\n",
"6\n5\n11\n8\n",
"6\n6\n12\n8\n",
"5\n5\n10\n9\n",
"8\n4\n11\n9\n",
"7\n5\n11\n8\n",
"6\n5\n11\n9\n",
"6\n6\n11\n7\n",
"5\n5\n9\n8\n",
"7\n6\n11\n8\n",
"5\n6\n10\n9\n",
"5\n6\n11\n8\n",
"5\n6\n9\n9\n",
"6\n4\n12\n8\n",
"6\n4\n11\n8\n",
"6\n5\n10\n9\n",
"7\n4\n11\n8\n",
"7\n5\n12\n8\n",
"6\n5\n12\n0\n",
"5\n5\n10\n8\n",
"5\n4\n10\n0\n",
"5\n4\n11\n4\n",
"5\n4\n9\n9\n",
"6\n4\n11\n9\n",
"6\n4\n9\n0\n",
"8\n4\n11\n8\n",
"6\n6\n11\n9\n",
"5\n5\n9\n9\n",
"5\n6\n10\n8\n",
"6\n4\n10\n8\n",
"6\n5\n10\n8\n",
"5\n5\n12\n9\n",
"6\n4\n9\n8\n",
"6\n6\n11\n8\n",
"5\n7\n10\n9\n",
"6\n6\n9\n9\n",
"6\n4\n10\n9\n",
"6\n5\n12\n9\n",
"6\n4\n12\n",
"7\n5\n10\n9\n",
"5\n",
"6\n4\n9\n9\n",
"6\n5\n9\n8\n",
"5\n6\n9\n8\n",
"7\n5\n11\n9\n",
"6\n5\n9\n9\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n11\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n5\n12\n8\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"6\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n11\n9\n",
"5\n4\n11\n9\n",
"5\n4\n11\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n4\n12\n8\n",
"5\n5\n12\n8\n",
"5\n5\n12\n8\n",
"6\n5\n12\n8\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n12\n0\n",
"5\n4\n11\n9\n",
"5\n4\n10\n8\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A Bingo game is played by one gamemaster and several players. At the beginning of a game, each player is given a card with M × M numbers in a matrix (See Figure 10).
<image>
As the game proceeds, the gamemaster announces a series of numbers one by one. Each player punches a hole in his card on the announced number, if any.
When at least one 'Bingo' is made on the card, the player wins and leaves the game. The 'Bingo' means that all the M numbers in a line are punched vertically, horizontally or diagonally (See Figure 11).
<image>
The gamemaster continues announcing numbers until all the players make a Bingo.
In the ordinary Bingo games, the gamemaster chooses numbers by a random process and has no control on them. But in this problem the gamemaster knows all the cards at the beginning of the game and controls the game by choosing the number sequence to be announced at his will.
Specifically, he controls the game to satisfy the following condition.
Cardi makes a Bingo no later than Cardj, for i < j. (*)
Figure 12 shows an example of how a game proceeds. The gamemaster cannot announce '5' before '16', because Card4 makes a Bingo before Card2 and Card3, violating the condition (*).
Your job is to write a program which finds the minimum length of such sequence of numbers for the given cards.
Input
The input consists of multiple datasets. The format of each dataset is as follows.
<image>
All data items are integers. P is the number of the cards, namely the number of the players. M is the number of rows and the number of columns of the matrix on each card. Nkij means the number written at the position (i, j) on the k-th card. If (i, j) ≠ (p, q), then Nkij ≠ Nkpq. The parameters P, M, and N satisfy the conditions 2 ≤ P ≤ 4, 3 ≤ M ≤ 4, and 0 ≤ Nkij ≤ 99.
The end of the input is indicated by a line containing two zeros separated by a space. It is not a dataset.
Output
For each dataset, output the minimum length of the sequence of numbers which satisfy the condition (*). Output a zero if there are no such sequences. Output for each dataset must be printed on a separate line.
Example
Input
4 3
10 25 11 20 6 2 1 15 23
5 21 3 12 23 17 7 26 2
8 18 4 22 13 27 16 5 11
19 9 24 2 11 5 14 28 16
4 3
12 13 20 24 28 32 15 16 17
12 13 21 25 29 33 16 17 18
12 13 22 26 30 34 17 18 15
12 13 23 27 31 35 18 15 16
4 3
11 12 13 14 15 16 17 18 19
21 22 23 24 25 26 27 28 29
31 32 33 34 35 36 37 38 39
41 42 43 44 45 46 47 48 49
4 4
2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36
22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29
26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5
36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2
0 0
Output
5
4
12
0
### Input:
4 3
10 25 11 20 6 2 1 15 23
5 21 3 12 23 17 7 26 2
8 18 4 22 13 27 16 5 11
19 9 24 2 11 5 14 28 16
4 3
12 13 20 24 28 32 15 16 17
12 13 21 25 29 33 16 17 18
12 13 22 26 30 34 17 18 15
12 13 23 27 31 35 18 15 16
4 3
11 12 13 14 15 16 17 18 19
21 22 23 24 25 26 27 28 29
31 32 33 34 35 36 37 38 39
41 42 43 44 45 46 47 48 49
4 4
2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36
22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29
26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5
36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2
0 0
### Output:
5
4
12
0
### Input:
4 3
10 25 11 20 6 2 1 15 23
5 21 1 12 23 17 7 26 2
8 18 4 22 13 27 16 5 11
19 9 24 2 11 5 14 28 16
4 3
12 13 20 24 28 32 15 16 17
12 13 21 25 29 33 16 17 18
12 13 22 26 30 34 17 18 15
12 13 23 27 31 35 18 15 16
4 3
11 12 13 14 15 16 17 18 19
21 22 23 24 25 26 27 28 29
31 32 33 34 35 36 37 38 39
41 42 43 44 45 46 47 48 49
4 4
2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36
22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29
26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5
36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2
0 0
### Output:
5
4
12
0
### Code:
def solve():
from itertools import product
from sys import stdin
f_i = stdin
while True:
P, M = map(int, f_i.readline().split())
if P == 0:
break
bingo = []
for i in range(P):
b = []
card = list(map(int, f_i.readline().split()))
d1 = [] # diagonally
d2 = [] # diagonally
for i in range(M):
b.append(card[i::M]) # vertically
b.append(card[i*M:i*M+M]) # horizontally
d1.append(card[i*M+i])
d2.append(card[(M-1)*(i+1)])
b += [d1, d2]
bingo.append(set(frozenset(b_i) for b_i in b))
if P == 2:
ans = min(len(t1 | t2) for t1, t2 in product(*bingo))
elif P == 3:
ans = P * M + 1
c0, c1, c2 = bingo
for b0 in c0:
if b0 in c2:
for b1 in c1:
if b1.intersection(b0):
break
else:
continue
for b1 in c1:
b01 = b0.union(b1)
last = set(b for b in c2 if b.issubset(b01))
if last:
if not b1.intersection(*last):
continue
for b2 in c2:
tmp = len(b2.union(b01))
if tmp < ans:
ans = tmp
if ans == P * M + 1:
ans = 0
else:
ans = P * M + 1
c0, c1, c2, c3 = bingo
for b0 in c0:
if b0 in c2:
for b1 in c1:
if b1.intersection(b0):
break
else:
continue
if b0 in c3:
for b1, b2 in product(c1, c2):
if b0.intersection(b1, b2):
break
else:
continue
for b1 in c1:
b01 = b0.union(b1)
third = set(b2 for b2 in c2 if b2.issubset(b01))
if third:
if not b1.intersection(*third):
continue
last = set(b3 for b3 in c3 if b3.issubset(b01))
if last:
if not b1.intersection(*last):
continue
if third and last:
if not b1.intersection(*third, *last):
continue
if not third and last:
for b2, b3 in product(c2, last):
if b1.intersection(b2, b3):
break
else:
continue
for b2 in c2:
b012 = b0.union(b1, b2)
last = set(b for b in c3 if b.issubset(b012))
if last:
last_num = b2.intersection(*last)
if not last_num:
continue
first = set(b for b in c0 if b.issubset(b012))
if first.issubset(last):
sec = set(b for b in c1 if b.issubset(b012))
if not last_num.intersection(*sec):
continue
for b3 in c3:
tmp = len(b012.union(b3))
if tmp < ans:
ans = tmp
if ans == P * M + 1:
ans = 0
print(ans)
solve()
|
p01107 Go around the Labyrinth_28488
|
Go around the Labyrinth
Explorer Taro got a floor plan of a labyrinth. The floor of this labyrinth is in the form of a two-dimensional grid. Each of the cells on the floor plan corresponds to a room and is indicated whether it can be entered or not. The labyrinth has only one entrance located at the northwest corner, which is upper left on the floor plan. There is a treasure chest in each of the rooms at other three corners, southwest, southeast, and northeast. To get a treasure chest, Taro must move onto the room where the treasure chest is placed.
Taro starts from the entrance room and repeats moving to one of the enterable adjacent rooms in the four directions, north, south, east, or west. He wants to collect all the three treasure chests and come back to the entrance room. A bad news for Taro is that, the labyrinth is quite dilapidated and even for its enterable rooms except for the entrance room, floors are so fragile that, once passed over, it will collapse and the room becomes not enterable. Determine whether it is possible to collect all the treasure chests and return to the entrance.
Input
The input consists of at most 100 datasets, each in the following format.
N M
c1,1...c1,M
...
cN,1...cN,M
The first line contains N, which is the number of rooms in the north-south direction, and M, which is the number of rooms in the east-west direction. N and M are integers satisfying 2 ≤ N ≤ 50 and 2 ≤ M ≤ 50. Each of the following N lines contains a string of length M. The j-th character ci,j of the i-th string represents the state of the room (i,j), i-th from the northernmost and j-th from the westernmost; the character is the period ('`.`') if the room is enterable and the number sign ('`#`') if the room is not enterable. The entrance is located at (1,1), and the treasure chests are placed at (N,1), (N,M) and (1,M). All of these four rooms are enterable. Taro cannot go outside the given N × M rooms.
The end of the input is indicated by a line containing two zeros.
Output
For each dataset, output `YES` if it is possible to collect all the treasure chests and return to the entrance room, and otherwise, output `NO` in a single line.
Sample Input
3 3
...
.#.
...
5 5
..#..
.....
....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
.....
..#..
4 4
....
....
..##
..#.
0 0
Output for the Sample Input
YES
NO
YES
NO
NO
Example
Input
3 3
...
.#.
...
5 5
..#..
.....
#....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
.....
..#..
4 4
....
....
..##
..#.
0 0
Output
YES
NO
YES
NO
NO
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import copy
def rdp_connect() -> bool:
global n, m, c
n, m = map(int, input().split())
if n == m == 0:
return False
c = [list(input()) for _ in range(n)]
return True
def rdp_check() -> bool:
DY = (0, 1, 0, -1)
DX = (1, 0, -1, 0)
def refresh(d: int, x1: int, y1: int, x2: int, y2: int) -> bool:
global c
st = copy.deepcopy(c)
y, x = y1, x1
flag = True
while flag or not ((y, x) == (y1, x1) or (y, x) == (y2, x2)):
st[y][x] = '#'
for _ in range(4):
fy, fx = y + DY[d], x + DX[d]
ly, lx = y + DY[(d + 3) % 4], x + DX[(d + 3) % 4]
if 0 <= ly < n and 0 <= lx < m and c[ly][lx] == '.':
y, x = ly, lx
d = (d + 3) % 4
flag = False
break
elif 0 <= fy < n and 0 <= fx < m and c[fy][fx] == '.':
y, x = fy, fx
flag = False
break
d = (d + 1) % 4
if flag:
return d, False
st[y1][x1] = '.'
c = st
return d, (y, x) == (y2, x2)
d, flag = refresh(0, 0, 0, m - 1, 0)
if not flag:
return False
d, flag = refresh(d, m - 1, 0, m - 1, n - 1)
if not flag:
return False
d, flag = refresh(d, m - 1, n - 1, 0, n - 1)
if not flag:
return False
return refresh(d, 0, n - 1, 0, 0)[1]
if __name__ == '__main__':
while rdp_connect():
if rdp_check():
print('YES')
else:
print('NO')
|
{
"input": [
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n../..\n.....\n3 8\n..#.....\n........\n..#.....\n3 5\n..#..\n....-\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n...#.\n.....\n.....\n3 8\n.....#..\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n....-\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n....-\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n./...\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n..##\n-.#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n../..\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n....-\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#.-\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n..##\n-.#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....$..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n./#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....$..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n....-\n..#..\n4 4\n....\n....\n..##\n./#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.0...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n....-\n..#..\n4 4\n.../\n....\n..##\n./#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.-...\n..#..\n4 4\n....\n....\n##..\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#.-\n.....\n#....\n.....\n.../.\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n..##\n-.#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n....-\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n-....\n-.#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n./...\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n.-#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##.-\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#.-\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n...-.\n..#..\n4 4\n....\n....\n..##\n-.#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.0...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##.-\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n/....\n#....\n../..\n.....\n3 8\n..#.....\n........\n..#.....\n3 5\n..#..\n....-\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n....#\n....-\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n./...\n#....\n.....\n./...\n3 8\n..#.....\n........\n.....#..\n3 5\n.-#..\n.....\n..#..\n4 4\n....\n....\n..$#\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#.-\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n...-.\n.#...\n4 4\n....\n....\n..##\n-.#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.-...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n.....#..\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.-...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n..-.\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n...-.\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n..-.\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-/#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-/#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-/#$\n.#..\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n##..\n..#,\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.-...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n.-..\n....\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.-...\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n..-.\n..##\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n...-.\n3 8\n..#.....\n........\n.....$..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n..-.\n##..\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n$#/-\n..#.\n0 0",
"3 3\n...\n.\".\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-/#$\n.#..\n0 0",
"3 3\n...\n.\".\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n./#$\n.#..\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n-....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#.../\n.....\n.....\n3 8\n.....#..\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n....#\n.....\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n-.#$\n..#.\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n#\"..\n..#,\n0 0",
"3 3\n...\n.\".\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n./#$\n.#..\n0 0",
"3 3\n...\n.\".\n...\n5 5\n..#..\n.....\n#....\n...-.\n.....\n3 8\n.....#/.\n........\n.....#..\n3 5\n..#..\n-....\n..#..\n4 4\n....\n....\n$#/.\n.#..\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..#$\n..#-\n0 0",
"3 3\n...\n.#.\n...\n5 5\n..#..\n-....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..#$\n..#.\n0 0"
],
"output": [
"YES\nNO\nYES\nNO\nNO",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nYES\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Go around the Labyrinth
Explorer Taro got a floor plan of a labyrinth. The floor of this labyrinth is in the form of a two-dimensional grid. Each of the cells on the floor plan corresponds to a room and is indicated whether it can be entered or not. The labyrinth has only one entrance located at the northwest corner, which is upper left on the floor plan. There is a treasure chest in each of the rooms at other three corners, southwest, southeast, and northeast. To get a treasure chest, Taro must move onto the room where the treasure chest is placed.
Taro starts from the entrance room and repeats moving to one of the enterable adjacent rooms in the four directions, north, south, east, or west. He wants to collect all the three treasure chests and come back to the entrance room. A bad news for Taro is that, the labyrinth is quite dilapidated and even for its enterable rooms except for the entrance room, floors are so fragile that, once passed over, it will collapse and the room becomes not enterable. Determine whether it is possible to collect all the treasure chests and return to the entrance.
Input
The input consists of at most 100 datasets, each in the following format.
N M
c1,1...c1,M
...
cN,1...cN,M
The first line contains N, which is the number of rooms in the north-south direction, and M, which is the number of rooms in the east-west direction. N and M are integers satisfying 2 ≤ N ≤ 50 and 2 ≤ M ≤ 50. Each of the following N lines contains a string of length M. The j-th character ci,j of the i-th string represents the state of the room (i,j), i-th from the northernmost and j-th from the westernmost; the character is the period ('`.`') if the room is enterable and the number sign ('`#`') if the room is not enterable. The entrance is located at (1,1), and the treasure chests are placed at (N,1), (N,M) and (1,M). All of these four rooms are enterable. Taro cannot go outside the given N × M rooms.
The end of the input is indicated by a line containing two zeros.
Output
For each dataset, output `YES` if it is possible to collect all the treasure chests and return to the entrance room, and otherwise, output `NO` in a single line.
Sample Input
3 3
...
.#.
...
5 5
..#..
.....
....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
.....
..#..
4 4
....
....
..##
..#.
0 0
Output for the Sample Input
YES
NO
YES
NO
NO
Example
Input
3 3
...
.#.
...
5 5
..#..
.....
#....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
.....
..#..
4 4
....
....
..##
..#.
0 0
Output
YES
NO
YES
NO
NO
### Input:
3 3
...
.#.
...
5 5
..#..
.....
#....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
.....
..#..
4 4
....
....
..##
..#.
0 0
### Output:
YES
NO
YES
NO
NO
### Input:
3 3
...
.#.
...
5 5
..#..
.....
#....
.....
.....
3 8
..#.....
........
.....#..
3 5
..#..
-....
..#..
4 4
....
....
..##
..#.
0 0
### Output:
YES
NO
YES
NO
NO
### Code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import copy
def rdp_connect() -> bool:
global n, m, c
n, m = map(int, input().split())
if n == m == 0:
return False
c = [list(input()) for _ in range(n)]
return True
def rdp_check() -> bool:
DY = (0, 1, 0, -1)
DX = (1, 0, -1, 0)
def refresh(d: int, x1: int, y1: int, x2: int, y2: int) -> bool:
global c
st = copy.deepcopy(c)
y, x = y1, x1
flag = True
while flag or not ((y, x) == (y1, x1) or (y, x) == (y2, x2)):
st[y][x] = '#'
for _ in range(4):
fy, fx = y + DY[d], x + DX[d]
ly, lx = y + DY[(d + 3) % 4], x + DX[(d + 3) % 4]
if 0 <= ly < n and 0 <= lx < m and c[ly][lx] == '.':
y, x = ly, lx
d = (d + 3) % 4
flag = False
break
elif 0 <= fy < n and 0 <= fx < m and c[fy][fx] == '.':
y, x = fy, fx
flag = False
break
d = (d + 1) % 4
if flag:
return d, False
st[y1][x1] = '.'
c = st
return d, (y, x) == (y2, x2)
d, flag = refresh(0, 0, 0, m - 1, 0)
if not flag:
return False
d, flag = refresh(d, m - 1, 0, m - 1, n - 1)
if not flag:
return False
d, flag = refresh(d, m - 1, n - 1, 0, n - 1)
if not flag:
return False
return refresh(d, 0, n - 1, 0, 0)[1]
if __name__ == '__main__':
while rdp_connect():
if rdp_check():
print('YES')
else:
print('NO')
|
p01560 Enumeration_28493
|
Given n integers a1, a2,…, an and n integers p1, p2,…, pn, integer m. The operation of selecting the kth integer ak with a probability of pk [%] is performed for each k (1 ≤ k ≤ n), and 0 or more and n or less integers are selected. Find the expected number of integers between 1 and m that are divisible by at least one of the selected integers.
Constraints
* 1 ≤ n ≤ 20
* 1 ≤ m ≤ 1018
* 1 ≤ ak ≤ 1018 (1 ≤ k ≤ n)
* 1 ≤ pk ≤ 99 (1 ≤ k ≤ n)
Input
The input is given in the following format.
> n m
> a1 a2… an
> p1 p2… pn
>
Output
Print the solution to the problem on one line. The output must not have an absolute or relative error of more than 0.0000001 (= 10-7).
Examples
Input
2 15
3 5
50 50
Output
3.75
Input
4 100
2 3 5 7
80 60 40 20
Output
57.352
Input
4 210
2 3 5 7
80 60 40 20
Output
119.9136
|
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n,m = LI()
a = LI()
p = [c / 100.0 for c in LI()]
d = collections.defaultdict(lambda: 1.0)
e = collections.defaultdict(lambda: 1)
r = 0
for k in range(1,1<<n):
t = [i for i in range(n) if k & (1 << i)]
l = k & (k-1)
d[k] = d[l] * p[t[0]]
e[k] = e[l] * a[t[0]] // fractions.gcd(a[t[0]], e[l])
o = m // e[k]
if len(t) % 2 == 1:
r += o * d[k]
else:
r -= o * d[k]
return '{:0.8f}'.format(r)
print(main())
|
{
"input": [
"2 15\n3 5\n50 50",
"4 100\n2 3 5 7\n80 60 40 20",
"4 210\n2 3 5 7\n80 60 40 20",
"2 15\n3 5\n50 72",
"4 100\n1 3 5 7\n80 60 40 20",
"4 210\n2 2 5 7\n80 60 40 20",
"2 15\n3 5\n32 72",
"4 100\n1 3 8 7\n80 60 40 20",
"2 210\n2 2 5 7\n80 60 40 20",
"2 15\n3 5\n32 64",
"4 100\n1 3 14 7\n80 60 40 20",
"2 115\n2 2 5 7\n80 60 40 20",
"2 7\n3 5\n32 64",
"0 100\n1 3 14 7\n80 60 40 20",
"2 115\n3 2 5 7\n80 60 40 20",
"2 115\n3 2 5 12\n80 60 40 20",
"2 115\n2 2 5 12\n80 60 40 20",
"2 115\n2 2 0 12\n80 60 40 20",
"2 115\n2 2 -1 12\n91 60 40 20",
"2 2\n2 2 -1 12\n91 60 40 20",
"2 2\n2 2 -2 12\n91 60 40 20",
"1 2\n2 2 -2 12\n45 60 40 41",
"2 15\n1 5\n50 50",
"4 100\n1 3 5 7\n80 60 40 40",
"4 210\n2 2 5 7\n80 14 40 20",
"2 15\n3 5\n52 72",
"4 100\n1 3 1 7\n80 60 40 20",
"2 210\n3 2 5 7\n80 60 40 20",
"2 15\n3 5\n32 51",
"4 100\n1 3 14 1\n80 60 40 20",
"2 7\n3 5\n32 78",
"2 115\n5 2 5 7\n80 60 40 20",
"3 115\n3 2 5 12\n80 60 40 20",
"1 100\n1 3 14 7\n80 60 40 79",
"2 16\n2 2 0 12\n80 60 40 20",
"2 115\n2 2 0 13\n91 60 40 20",
"2 2\n1 2 -2 12\n23 60 40 20",
"2 2\n2 2 -2 7\n45 60 40 20",
"2 15\n1 7\n50 50",
"2 15\n3 5\n52 57",
"4 100\n1 3 1 7\n80 39 40 20",
"4 101\n1 3 14 1\n80 60 40 20",
"2 196\n2 2 5 7\n80 25 40 20",
"2 115\n5 2 10 7\n80 60 40 20",
"2 187\n2 2 5 12\n80 46 40 20",
"2 26\n2 2 0 12\n80 60 40 20",
"2 115\n2 2 -1 24\n91 60 40 23",
"2 15\n1 7\n59 50",
"4 100\n1 3 5 13\n80 60 40 19",
"2 15\n3 1\n52 57",
"4 100\n1 3 2 7\n80 39 40 20",
"4 111\n1 3 14 1\n80 60 40 20",
"1 196\n2 2 5 7\n80 25 40 20",
"2 7\n3 5\n3 78",
"2 115\n5 2 10 4\n80 60 40 20",
"2 187\n1 2 5 12\n80 46 40 20",
"2 15\n1 7\n59 64",
"4 100\n1 5 5 13\n80 60 40 19",
"2 15\n3 1\n52 78",
"2 7\n2 5\n3 78",
"2 204\n1 2 5 12\n80 46 40 20",
"2 115\n2 4 0 13\n91 118 40 32",
"2 115\n2 2 -1 17\n91 43 40 23",
"2 15\n2 7\n59 64",
"4 100\n1 5 5 13\n80 16 40 19",
"1 15\n3 1\n52 78",
"2 12\n2 5\n3 78",
"3 115\n3 2 5 12\n80 55 55 2",
"2 204\n1 2 3 12\n80 46 40 20",
"2 26\n3 2 0 24\n29 60 40 20",
"2 115\n3 2 -1 17\n91 43 40 23",
"2 2\n1 2 -2 3\n23 60 84 20",
"1 2\n2 4 -3 12\n45 126 40 34",
"4 100\n2 5 5 13\n80 16 40 19",
"2 12\n2 5\n3 130",
"2 115\n5 2 10 1\n80 98 40 12",
"3 207\n3 2 5 12\n80 55 55 2",
"4 100\n2 5 10 13\n80 16 40 19",
"2 12\n2 5\n3 241",
"2 115\n6 2 10 1\n80 98 40 12",
"2 115\n1 6 0 13\n162 118 40 32",
"2 115\n3 2 -2 17\n91 66 40 23",
"4 100\n2 5 10 13\n80 28 40 19",
"1 11\n3 1\n13 29",
"2 12\n4 5\n3 241",
"3 38\n3 2 5 12\n80 55 55 3",
"4 100\n3 5 10 13\n80 28 40 19",
"2 21\n4 5\n3 241",
"2 115\n3 2 10 1\n80 98 79 12",
"3 38\n3 4 5 12\n80 55 55 3",
"2 104\n3 2 -2 17\n25 66 40 23",
"2 2\n1 2 -2 6\n23 17 84 49",
"4 100\n3 6 10 13\n80 28 40 19",
"2 21\n4 5\n6 241",
"3 12\n3 4 5 12\n80 55 55 3",
"2 2\n1 2 -4 6\n23 17 84 49",
"4 100\n3 6 10 13\n160 28 40 19",
"2 115\n2 7 0 13\n162 76 40 7",
"4 100\n3 6 3 13\n160 28 40 19",
"2 115\n2 7 0 16\n162 76 40 7",
"4 100\n3 6 3 26\n160 28 40 19",
"1 010\n2 3 18 7\n70 60 40 10",
"3 115\n3 2 10 1\n121 33 79 11"
],
"output": [
"3.75",
"57.352",
"119.9136",
"4.300000000\n",
"85.704000000\n",
"108.652800000\n",
"3.529600000\n",
"85.176000000\n",
"12.232500000\n",
"3.315200000\n",
"84.795200000\n",
"6.640500000\n",
"1.280000000\n",
"0.000000000\n",
"5.823500000\n",
"8.626000000\n",
"9.348000000\n",
"6.840000000\n",
"6.338400000\n",
"0.111200000\n",
"0.102400000\n",
"0.020000000\n",
"8.250000000\n",
"86.136000000\n",
"100.019520000\n",
"4.385600000\n",
"90.654400000\n",
"10.727500000\n",
"2.966800000\n",
"87.539200000\n",
"1.420000000\n",
"5.101500000\n",
"56.524800000\n",
"3.000000000\n",
"0.960000000\n",
"7.410000000\n",
"0.082400000\n",
"0.051400000\n",
"8.000000000\n",
"4.013600000\n",
"89.842960000\n",
"88.379200000\n",
"11.417000000\n",
"6.213000000\n",
"15.252000000\n",
"1.560000000\n",
"13.246800000\n",
"9.260000000\n",
"85.477200000\n",
"9.668000000\n",
"86.472880000\n",
"97.163200000\n",
"1.960000000\n",
"0.840000000\n",
"4.536000000\n",
"19.952000000\n",
"9.374800000\n",
"83.277120000\n",
"12.272000000\n",
"0.870000000\n",
"21.828000000\n",
"3.640000000\n",
"9.216900000\n",
"5.032400000\n",
"82.231152000\n",
"0.050000000\n",
"1.716600000\n",
"55.842400000\n",
"17.992800000\n",
"3.120000000\n",
"9.342300000\n",
"-0.009400000\n",
"0.040000000\n",
"46.731760000\n",
"2.741000000\n",
"2.859000000\n",
"100.624800000\n",
"43.435600000\n",
"4.927700000\n",
"2.451000000\n",
"2.470000000\n",
"8.994600000\n",
"44.756800000\n",
"0.030000000\n",
"4.910000000\n",
"18.514800000\n",
"33.817600000\n",
"9.717700000\n",
"4.351000000\n",
"11.630000000\n",
"8.217800000\n",
"0.021200000\n",
"31.284160000\n",
"9.795400000\n",
"3.884000000\n",
"-0.017600000\n",
"53.147520000\n",
"2.080000000\n",
"44.099552000\n",
"2.560000000\n",
"43.597952000\n",
"0.150000000\n",
"68.359879000\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Given n integers a1, a2,…, an and n integers p1, p2,…, pn, integer m. The operation of selecting the kth integer ak with a probability of pk [%] is performed for each k (1 ≤ k ≤ n), and 0 or more and n or less integers are selected. Find the expected number of integers between 1 and m that are divisible by at least one of the selected integers.
Constraints
* 1 ≤ n ≤ 20
* 1 ≤ m ≤ 1018
* 1 ≤ ak ≤ 1018 (1 ≤ k ≤ n)
* 1 ≤ pk ≤ 99 (1 ≤ k ≤ n)
Input
The input is given in the following format.
> n m
> a1 a2… an
> p1 p2… pn
>
Output
Print the solution to the problem on one line. The output must not have an absolute or relative error of more than 0.0000001 (= 10-7).
Examples
Input
2 15
3 5
50 50
Output
3.75
Input
4 100
2 3 5 7
80 60 40 20
Output
57.352
Input
4 210
2 3 5 7
80 60 40 20
Output
119.9136
### Input:
2 15
3 5
50 50
### Output:
3.75
### Input:
4 100
2 3 5 7
80 60 40 20
### Output:
57.352
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n,m = LI()
a = LI()
p = [c / 100.0 for c in LI()]
d = collections.defaultdict(lambda: 1.0)
e = collections.defaultdict(lambda: 1)
r = 0
for k in range(1,1<<n):
t = [i for i in range(n) if k & (1 << i)]
l = k & (k-1)
d[k] = d[l] * p[t[0]]
e[k] = e[l] * a[t[0]] // fractions.gcd(a[t[0]], e[l])
o = m // e[k]
if len(t) % 2 == 1:
r += o * d[k]
else:
r -= o * d[k]
return '{:0.8f}'.format(r)
print(main())
|
p01722 Fast Division_28497
|
Ikta loves fast programs. Recently, I'm trying to speed up the division program. However, it doesn't get much faster, so I thought it would be better to make it faster only for "common sense and typical" inputs. The problem Ikta is trying to solve is as follows.
For a given non-negative integer n, divide p (n) − 1-digit positive integer 11 ... 1 by p (n) in decimal notation. However, p (n) represents the smallest prime number larger than 22 {... 2} (n 2). Let p (0) = 2.
Your job is to complete the program faster than Ikta.
Input
The input is given in the following format.
n
Given the non-negative integer n of the input in question.
Constraints
Each variable being input satisfies the following constraints.
* 0 ≤ n <1000
Output
Print the solution to the problem on one line.
Examples
Input
0
Output
1
Input
1
Output
2
Input
2
Output
1
|
# p(n) = 2^^n より大きい最小の素数 (ただし^^はクヌースの二重矢印記号) と定義したとき、
# x = (10^(p(n)-1)-1)/9 (mod p(n)) を求めよ
# 「フェルマーの小定理」
# pが素数ならば、a^p == a (mod p(n))
# とくに、aとpが互いに素 (gcd(a,p)=1) のとき
# a^p * a^-1 == a * a^-1 (mod p(n))
# a^(p-1) == 1 (mod p)
#
# 9とp(n)が互いに素ならば
# x * 9^-1 = 10^(p(n)-1)-1 (mod p(n))
# 10とp(n)が互いに素ならば
# 10^(p(n)-1) = 1 (mod p(n))
# ゆえに
# x * 9^-1 = 0 (mod p(n))
# p(n)は素数であるから、p(n)>10のとき9とp(n)および10とp(n)は互いに素でありx=0
n = int(input())
if n == 0:
# 1 mod 2
print(1)
elif n == 1:
# 11 mod 3
print(2)
elif n == 2:
# 111 mod 5
print(1)
else:
print(0)
|
{
"input": [
"0",
"1",
"2",
"3",
"001",
"000",
"6",
"4",
"10",
"5",
"7",
"17",
"11",
"12",
"18",
"9",
"35",
"15",
"8",
"29",
"14",
"41",
"27",
"62",
"30",
"25",
"42",
"58",
"21",
"83",
"98",
"178",
"209",
"375",
"51",
"79",
"65",
"28",
"16",
"22",
"20",
"36",
"13",
"43",
"45",
"26",
"56",
"38",
"39",
"24",
"61",
"37",
"112",
"32",
"34",
"67",
"76",
"143",
"93",
"277",
"164",
"177",
"50",
"127",
"44",
"84",
"19",
"31",
"63",
"53",
"49",
"48",
"57",
"198",
"52",
"40",
"81",
"126",
"152",
"104",
"388",
"69",
"89",
"99",
"71",
"66",
"23",
"33",
"148",
"85",
"86",
"82",
"60",
"90",
"135",
"46",
"102",
"186",
"205",
"134",
"75",
"119",
"97"
],
"output": [
"1",
"2",
"1",
"0\n",
"2\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ikta loves fast programs. Recently, I'm trying to speed up the division program. However, it doesn't get much faster, so I thought it would be better to make it faster only for "common sense and typical" inputs. The problem Ikta is trying to solve is as follows.
For a given non-negative integer n, divide p (n) − 1-digit positive integer 11 ... 1 by p (n) in decimal notation. However, p (n) represents the smallest prime number larger than 22 {... 2} (n 2). Let p (0) = 2.
Your job is to complete the program faster than Ikta.
Input
The input is given in the following format.
n
Given the non-negative integer n of the input in question.
Constraints
Each variable being input satisfies the following constraints.
* 0 ≤ n <1000
Output
Print the solution to the problem on one line.
Examples
Input
0
Output
1
Input
1
Output
2
Input
2
Output
1
### Input:
0
### Output:
1
### Input:
1
### Output:
2
### Code:
# p(n) = 2^^n より大きい最小の素数 (ただし^^はクヌースの二重矢印記号) と定義したとき、
# x = (10^(p(n)-1)-1)/9 (mod p(n)) を求めよ
# 「フェルマーの小定理」
# pが素数ならば、a^p == a (mod p(n))
# とくに、aとpが互いに素 (gcd(a,p)=1) のとき
# a^p * a^-1 == a * a^-1 (mod p(n))
# a^(p-1) == 1 (mod p)
#
# 9とp(n)が互いに素ならば
# x * 9^-1 = 10^(p(n)-1)-1 (mod p(n))
# 10とp(n)が互いに素ならば
# 10^(p(n)-1) = 1 (mod p(n))
# ゆえに
# x * 9^-1 = 0 (mod p(n))
# p(n)は素数であるから、p(n)>10のとき9とp(n)および10とp(n)は互いに素でありx=0
n = int(input())
if n == 0:
# 1 mod 2
print(1)
elif n == 1:
# 11 mod 3
print(2)
elif n == 2:
# 111 mod 5
print(1)
else:
print(0)
|
p01995 Palindromic Subsequences_28501
|
G: Palindromic Subsequences
problem
Given a string S consisting only of lowercase letters, find out how many subsequences of this string S are not necessarily continuous and are palindromes.
Here, a subsequence that is not necessarily continuous with S is an arbitrary selection of one or more characters | S | characters or less from the original character string S (the position of each character to be selected may be discontinuous), and they are used. Refers to a character string created by concatenating the characters in the original order. Note that an empty string is not allowed as a subsequence in this issue.
Also, if the string X is a palindrome, it means that the original string X and the inverted X string X'are equal.
Also note that even if the same palindrome is generated as a result of different subsequence arrangements, it will not be counted twice. For example, if S = `acpc`, both the subsequence consisting of only the second character and the subsequence consisting of only the fourth character are palindromes` c`, but this cannot be repeated multiple times, only once in total. I will count it.
The answer can be very large, so print the remainder divided by 1,000,000,007.
Input format
S
Constraint
* 1 \ leq | S | \ leq 2,000
* S contains only lowercase letters
Output format
* Output the remainder of the answer divided by 1,000,000,007 on one line.
Input example 1
acpc
Output example 1
Five
There are five types of subsequences of the string `acpc` that are not necessarily continuous and are palindromes:` a`, `c`,` cc`, `cpc`, and` p`. Note that we count the number of substring types.
Input example 2
z
Output example 2
1
The only subsequence that meets the condition is `z`. Note that an empty string is not allowed as a subsequence.
Input example 3
madokamagica
Output example 3
28
Example
Input
acpc
Output
5
|
def main():
from bisect import bisect_left as bl
from bisect import bisect_right as br
s=input()
alpha="abcdefghijklmnopqrstuvwxyz"
l=len(s)
alpha2={j:i for i,j in enumerate(alpha)}
memo=[[] for _ in [0]*26]
mod=10**9+7
for i in range(l):
memo[alpha2[s[i]]].append(i)
dp=[[0]*(l+1) for _ in range(l+1)]
dp[0][l]=1
ans=0
for i in range(l):
for j in range(i+1,l+1):
p=dp[i][j]
if p==0:
continue
for k in range(26):
x=bl(memo[k],i)
y=br(memo[k],j-1)-1
if x>y:
continue
ans+=p
if x<y:
mx,my=memo[k][x],memo[k][y]
dp[mx+1][my]=(dp[mx+1][my]+p)%mod
ans=ans%mod
ans=(ans+sum([sum([i for i in j])%mod for j in dp])+mod-1)%mod
print(ans)
if __name__=='__main__':
main()
|
{
"input": [
"acpc",
"ccpa",
"cnbc",
"emec",
"ccoa",
"aocc",
"pcca",
"ccao",
"pcda",
"ccbo",
"qcda",
"ccbn",
"qbda",
"adbq",
"dnbc",
"dobc",
"dobd",
"cobd",
"dboc",
"cbod",
"cboe",
"eobc",
"cobe",
"boce",
"bode",
"edob",
"edoc",
"code",
"coee",
"ocde",
"edco",
"edcn",
"ednc",
"denc",
"deoc",
"demc",
"medc",
"cdem",
"cdme",
"emdc",
"cdle",
"cdlf",
"cclf",
"cblf",
"calf",
"flac",
"cakf",
"fakc",
"kafc",
"cfak",
"fcak",
"fack",
"facj",
"afcj",
"cpca",
"ccap",
"acoc",
"ancc",
"pbca",
"ccbp",
"qcdb",
"nbcc",
"pbda",
"cbnc",
"abdq",
"bncc",
"adbr",
"dnac",
"dcbo",
"docd",
"cnbd",
"eboc",
"cbpd",
"cbne",
"eoac",
"coae",
"bedo",
"fdob",
"ednb",
"eeoc",
"cpde",
"ceeo",
"ocdd",
"ecco",
"ncde",
"endc",
"cned",
"coed",
"cmed",
"ccem",
"edcm",
"cdmf",
"edmc",
"emce",
"cdke",
"celf",
"ccfl",
"bclf",
"cflb",
"fcal",
"cafk"
],
"output": [
"5",
"4\n",
"6\n",
"5\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"6\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"5\n",
"4\n",
"5\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"6\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"6\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"6\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
G: Palindromic Subsequences
problem
Given a string S consisting only of lowercase letters, find out how many subsequences of this string S are not necessarily continuous and are palindromes.
Here, a subsequence that is not necessarily continuous with S is an arbitrary selection of one or more characters | S | characters or less from the original character string S (the position of each character to be selected may be discontinuous), and they are used. Refers to a character string created by concatenating the characters in the original order. Note that an empty string is not allowed as a subsequence in this issue.
Also, if the string X is a palindrome, it means that the original string X and the inverted X string X'are equal.
Also note that even if the same palindrome is generated as a result of different subsequence arrangements, it will not be counted twice. For example, if S = `acpc`, both the subsequence consisting of only the second character and the subsequence consisting of only the fourth character are palindromes` c`, but this cannot be repeated multiple times, only once in total. I will count it.
The answer can be very large, so print the remainder divided by 1,000,000,007.
Input format
S
Constraint
* 1 \ leq | S | \ leq 2,000
* S contains only lowercase letters
Output format
* Output the remainder of the answer divided by 1,000,000,007 on one line.
Input example 1
acpc
Output example 1
Five
There are five types of subsequences of the string `acpc` that are not necessarily continuous and are palindromes:` a`, `c`,` cc`, `cpc`, and` p`. Note that we count the number of substring types.
Input example 2
z
Output example 2
1
The only subsequence that meets the condition is `z`. Note that an empty string is not allowed as a subsequence.
Input example 3
madokamagica
Output example 3
28
Example
Input
acpc
Output
5
### Input:
acpc
### Output:
5
### Input:
ccpa
### Output:
4
### Code:
def main():
from bisect import bisect_left as bl
from bisect import bisect_right as br
s=input()
alpha="abcdefghijklmnopqrstuvwxyz"
l=len(s)
alpha2={j:i for i,j in enumerate(alpha)}
memo=[[] for _ in [0]*26]
mod=10**9+7
for i in range(l):
memo[alpha2[s[i]]].append(i)
dp=[[0]*(l+1) for _ in range(l+1)]
dp[0][l]=1
ans=0
for i in range(l):
for j in range(i+1,l+1):
p=dp[i][j]
if p==0:
continue
for k in range(26):
x=bl(memo[k],i)
y=br(memo[k],j-1)-1
if x>y:
continue
ans+=p
if x<y:
mx,my=memo[k][x],memo[k][y]
dp[mx+1][my]=(dp[mx+1][my]+p)%mod
ans=ans%mod
ans=(ans+sum([sum([i for i in j])%mod for j in dp])+mod-1)%mod
print(ans)
if __name__=='__main__':
main()
|
p02141 Donut Hole_28504
|
Problem
You brought a flat, holeless donut with a $ W $ horizontal $ H $ vertical $ H $ rectangle for ACPC.
Place this donut on the $ 2 $ dimension plane coordinate $ (0,0) $ with the center of the donut so that the side of length H and the $ y $ axis are parallel.
On the ACPC $ 1 $ day you ate a donut that was in the range of $ w $ vertical $ h $ centered on the coordinates ($ x $, $ y $).
If you want to eat the same amount on the $ 2 $ and $ 3 $ days, divide the donut by a straight line passing through the coordinates $ (0,0) $, and the sum of the donut areas in the area on one side of the straight line is on the other side I want it to be equal to the sum of the donut areas in the area of.
Find one slope of such a straight line.
Constraints
The input satisfies the following conditions.
* $ 1 \ lt h \ lt H \ lt 10 ^ 6 $
* $ 1 \ lt w \ lt W \ lt 10 ^ 6 $
* $ 1 \ le y \ le (h / 2 + H-1)-H / 2 $
* $ 1 \ le x \ le (w / 2 + W-1)-W / 2 $
* $ W $, $ H $, $ w $, $ h $ are even numbers
Input
The input is given in the following format.
$ W $ $ H $ $ w $ $ h $ $ x $ $ y $
Output
Output the slope of a straight line in one line. If the absolute error or relative error is $ 10 ^ {-6} $ or less, the answer is correct.
Examples
Input
6000 5000 20 10 400 300
Output
0.75
Input
10 10 8 8 8 8
Output
1
|
def inpl(): return list(map(int, input().split()))
W, H, w, h, x, y = inpl()
a = (min(W//2 , x + w//2) + max(-W//2, x-w//2))
b = (min(H//2 , y + h//2) + max(-H//2, y-h//2))
print(b/a)
|
{
"input": [
"6000 5000 20 10 400 300",
"10 10 8 8 8 8",
"6000 5000 20 2 400 300",
"6000 5000 20 2 400 204",
"6000 5000 20 2 499 204",
"274 5000 28 1 499 204",
"274 4268 28 0 499 209",
"274 8140 32 0 499 209",
"274 14753 32 0 499 132",
"6000 5000 20 10 400 575",
"16 16 8 8 8 8",
"16 18 8 8 8 8",
"6000 5000 20 2 400 228",
"6000 5000 20 2 998 204",
"2096 5000 28 2 697 204",
"2096 5000 28 1 499 225",
"344 5000 28 0 499 204",
"274 4268 28 0 499 186",
"274 4268 28 0 250 209",
"274 8140 32 0 499 173",
"6000 5000 20 10 71 575",
"16 8 8 8 8 8",
"9396 5000 49 2 42 204",
"2096 5000 28 1 794 225",
"274 914 28 1 499 282",
"486 5000 28 0 499 204",
"274 4268 52 0 499 186",
"274 5991 28 0 827 209",
"274 14753 32 1 499 418",
"274 21473 32 0 499 249",
"7828 5000 20 0 671 300",
"6000 5000 40 2 499 359",
"274 914 2 1 499 282",
"486 5000 28 0 499 131",
"274 4268 30 0 499 186",
"274 318 32 0 499 173",
"274 21473 26 0 499 249",
"16 16 0 8 8 5",
"9396 5000 58 2 42 288",
"6000 5000 40 2 972 359",
"2096 5000 45 3 495 204",
"486 5000 28 0 181 131",
"274 21473 20 0 499 249",
"7828 5000 20 -1 1069 300",
"7075 7635 20 0 400 383",
"6000 5000 40 2 1342 359",
"2096 5000 45 3 124 204",
"7828 5000 20 -1 646 300",
"7075 7635 20 0 400 677",
"7599 5000 20 14 998 118",
"16 16 -1 8 8 7",
"7828 5000 20 -1 438 300",
"7075 7635 20 0 400 1301",
"13365 5000 91 2 42 564",
"373 5000 6 0 181 32",
"274 53635 32 0 499 785",
"274 5918 20 1 690 249",
"16 16 -1 8 4 7",
"7828 5000 20 -1 438 464",
"8336 5000 29 2 2651 359",
"274 5918 20 1 690 471",
"956 8792 0 7 71 966",
"16 22 -1 8 4 7",
"7599 6795 20 9 1330 118",
"8336 5000 29 2 1938 359",
"274 5918 20 1 690 869",
"1581 7635 20 1 650 1301",
"7599 6795 20 9 1330 236",
"709 9203 6 0 181 23",
"274 5918 20 1 690 1139",
"543 8792 0 7 71 1168",
"228 2947 46 2 124 204",
"8336 5000 4 3 1449 359",
"7828 10252 13 -1 292 464",
"8336 5000 4 3 1132 359",
"328 76 46 2 124 204",
"7828 10252 13 -1 574 464",
"8454 6795 25 9 1330 258",
"328 130 46 2 124 204",
"8336 5000 4 2 1132 686",
"42 130 46 2 124 204",
"8336 5000 4 2 1132 190",
"42 130 46 4 124 204",
"42 130 46 6 124 204",
"9740 10252 20 0 388 464",
"4583 5000 4 2 1132 278",
"42 130 46 6 241 204",
"4583 5000 4 2 1258 278",
"42 130 46 6 241 240",
"4583 5000 4 2 1137 278",
"4997 2843 22 12 1330 391",
"4583 5000 4 2 1137 472",
"8327 8725 5 0 1871 472",
"3092 6443 5 0 23 464",
"5498 8725 5 0 1871 244",
"5498 8725 5 0 359 244",
"616 11394 7 0 23 484",
"6305 10729 5 1 359 484",
"108 11394 7 0 23 535",
"6305 10729 7 1 312 484",
"135 11394 8 1 7 535",
"6305 1450 6 1 180 484"
],
"output": [
"0.75",
"1",
"0.7500000000\n",
"0.5100000000\n",
"0.4088176353\n",
"0.6559485531\n",
"0.6720257235\n",
"0.6741935484\n",
"0.4258064516\n",
"1.4375000000\n",
"1.0000000000\n",
"1.0833333333\n",
"0.5700000000\n",
"0.2044088176\n",
"0.2926829268\n",
"0.4509018036\n",
"0.6210045662\n",
"0.5980707395\n",
"1.1206434316\n",
"0.5580645161\n",
"8.0985915493\n",
"0.6666666667\n",
"4.8571428571\n",
"0.2833753149\n",
"0.9067524116\n",
"0.5604395604\n",
"0.6098360656\n",
"0.4400000000\n",
"1.3483870968\n",
"0.8032258065\n",
"0.4470938897\n",
"0.7194388778\n",
"0.8881889764\n",
"0.3598901099\n",
"0.5990338164\n",
"0.5354838710\n",
"0.7993579454\n",
"0.5625000000\n",
"6.8571428571\n",
"0.3693415638\n",
"0.4121212121\n",
"0.7237569061\n",
"0.7955271565\n",
"0.2806361085\n",
"0.9575000000\n",
"0.2675111773\n",
"1.6451612903\n",
"0.4643962848\n",
"1.6925000000\n",
"0.1182364729\n",
"0.6875000000\n",
"0.6849315068\n",
"3.2525000000\n",
"13.4285714286\n",
"0.1767955801\n",
"2.5322580645\n",
"0.6095471236\n",
"1.3750000000\n",
"1.0593607306\n",
"0.1354205960\n",
"1.1529987760\n",
"13.6056338028\n",
"1.7500000000\n",
"0.0887218045\n",
"0.1852425181\n",
"2.1272949816\n",
"2.0015384615\n",
"0.1774436090\n",
"0.1270718232\n",
"2.7882496940\n",
"16.4507042254\n",
"1.8976744186\n",
"0.2477570738\n",
"1.5890410959\n",
"0.3171378092\n",
"0.9717741935\n",
"0.8083623693\n",
"0.1939849624\n",
"1.0806451613\n",
"0.6060070671\n",
"2.1967213115\n",
"0.1678445230\n",
"2.1885245902\n",
"2.1803278689\n",
"1.1958762887\n",
"0.2455830389\n",
"1.1129707113\n",
"0.2209856916\n",
"1.2635983264\n",
"0.2445030783\n",
"0.2939849624\n",
"0.4151275286\n",
"0.2522715126\n",
"20.1739130435\n",
"0.1304115446\n",
"0.6796657382\n",
"21.0434782609\n",
"1.3481894150\n",
"23.2608695652\n",
"1.5512820513\n",
"76.4285714286\n",
"2.6888888889\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem
You brought a flat, holeless donut with a $ W $ horizontal $ H $ vertical $ H $ rectangle for ACPC.
Place this donut on the $ 2 $ dimension plane coordinate $ (0,0) $ with the center of the donut so that the side of length H and the $ y $ axis are parallel.
On the ACPC $ 1 $ day you ate a donut that was in the range of $ w $ vertical $ h $ centered on the coordinates ($ x $, $ y $).
If you want to eat the same amount on the $ 2 $ and $ 3 $ days, divide the donut by a straight line passing through the coordinates $ (0,0) $, and the sum of the donut areas in the area on one side of the straight line is on the other side I want it to be equal to the sum of the donut areas in the area of.
Find one slope of such a straight line.
Constraints
The input satisfies the following conditions.
* $ 1 \ lt h \ lt H \ lt 10 ^ 6 $
* $ 1 \ lt w \ lt W \ lt 10 ^ 6 $
* $ 1 \ le y \ le (h / 2 + H-1)-H / 2 $
* $ 1 \ le x \ le (w / 2 + W-1)-W / 2 $
* $ W $, $ H $, $ w $, $ h $ are even numbers
Input
The input is given in the following format.
$ W $ $ H $ $ w $ $ h $ $ x $ $ y $
Output
Output the slope of a straight line in one line. If the absolute error or relative error is $ 10 ^ {-6} $ or less, the answer is correct.
Examples
Input
6000 5000 20 10 400 300
Output
0.75
Input
10 10 8 8 8 8
Output
1
### Input:
6000 5000 20 10 400 300
### Output:
0.75
### Input:
10 10 8 8 8 8
### Output:
1
### Code:
def inpl(): return list(map(int, input().split()))
W, H, w, h, x, y = inpl()
a = (min(W//2 , x + w//2) + max(-W//2, x-w//2))
b = (min(H//2 , y + h//2) + max(-H//2, y-h//2))
print(b/a)
|
p02282 Reconstruction of a Tree_28507
|
Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.
Constraints
* $1 \leq n \leq 40$
Input
In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.
In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.
In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.
Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.
Output
Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.
Examples
Input
5
1 2 3 4 5
3 2 4 1 5
Output
3 4 2 5 1
Input
4
1 2 3 4
1 2 3 4
Output
4 3 2 1
|
class BinaryTree:
class Node:
def __init__(self, nid, left, right):
self.id = nid
self.left = left
self.right = right
def has_left(self):
return self.left is not None
def has_right(self):
return self.right is not None
def __str__(self):
return str(self.id)
@classmethod
def create(cls, ids):
nodes = {}
def find(n, li):
for e1, e2, e3 in li:
if e1 == n:
return (e2, e3)
raise ValueError()
def _create(nid):
if nid in nodes:
return nodes[nid]
if nid == -1:
return None
lid, rid = find(nid, ids)
if lid == -1 and rid == -1:
right = None
left = None
elif lid == -1:
right = _create(rid)
left = None
elif lid == -1:
right = None
left = _create(lid)
else:
right = _create(rid)
left = _create(lid)
nodes[nid] = cls.Node(nid, left, right)
return nodes[nid]
def _root(nodeids):
for nid in [n[0] for n in nodeids]:
if all([lid != nid and rid != nid for _, lid, rid in nodeids]):
return nid
root = _create(_root(ids))
return cls(root)
def __init__(self, root):
self.root = root
def preorder(self):
def _preorder(node):
yield node
if node.has_left():
yield from _preorder(node.left)
if node.has_right():
yield from _preorder(node.right)
yield from _preorder(self.root)
def inorder(self):
def _inorder(node):
if node.has_left():
yield from _inorder(node.left)
yield node
if node.has_right():
yield from _inorder(node.right)
yield from _inorder(self.root)
def postorder(self):
def _postorder(node):
if node.has_left():
yield from _postorder(node.left)
if node.has_right():
yield from _postorder(node.right)
yield node
yield from _postorder(self.root)
def reconstruct(preorder, inorder):
"""Reconstruct a binary tree from preorder list
and inorder list of the tree.
>>> tree = reconstruct([1, 2, 3, 4, 5], [3, 2, 4, 1, 5])
>>> print(" ".join([str(node) for node in tree.postorder()]))
3 4 2 5 1
"""
def _first(li):
if len(li) > 0:
return li[0]
else:
return -1
def _reconstruct(_pre, _in):
assert(len(_pre) == len(_in))
if len(_pre) == 0:
return []
if len(_pre) == 1:
return [[_pre[0], -1, -1]]
root, *pre = _pre
i = _in.index(root)
in1, in2 = _in[:i], _in[i+1:]
pre1, pre2 = _pre[1:i+1], _pre[i+1:]
return ([[root, _first(pre1), _first(pre2)]] +
_reconstruct(pre1, in1) +
_reconstruct(pre2, in2))
return BinaryTree.create(_reconstruct(preorder, inorder))
def run():
_ = int(input())
preorder = [int(i) for i in input().split()]
inorder = [int(i) for i in input().split()]
tree = reconstruct(preorder, inorder)
print(" ".join([str(n) for n in tree.postorder()]))
if __name__ == '__main__':
run()
|
{
"input": [
"5\n1 2 3 4 5\n3 2 4 1 5",
"4\n1 2 3 4\n1 2 3 4",
"4\n1 2 3 4\n2 1 3 4",
"4\n2 1 3 4\n2 1 3 4",
"4\n2 1 3 4\n3 1 2 4",
"5\n1 2 3 4 5\n1 2 4 3 5",
"4\n2 1 3 4\n1 2 3 4",
"5\n1 3 2 4 5\n3 2 4 1 5",
"4\n1 4 3 2\n1 2 3 4",
"5\n1 2 3 4 5\n3 4 2 1 5",
"4\n1 2 3 4\n1 2 4 3",
"4\n2 1 3 4\n2 1 4 3",
"4\n1 2 3 4\n2 1 3 4",
"4\n1 2 4 3\n2 1 3 4",
"4\n1 2 3 4\n2 1 4 3"
],
"output": [
"3 4 2 5 1",
"4 3 2 1",
"2 4 3 1\n",
"4 3 1 2\n",
"3 1 4 2\n",
"4 5 3 2 1\n",
"1 4 3 2\n",
"4 2 3 5 1\n",
"2 3 4 1\n",
"4 3 2 5 1\n",
"4 3 2 1\n",
"4 3 1 2\n",
"2 4 3 1\n",
"2 3 4 1\n",
"2 4 3 1\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.
Constraints
* $1 \leq n \leq 40$
Input
In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.
In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.
In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.
Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.
Output
Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.
Examples
Input
5
1 2 3 4 5
3 2 4 1 5
Output
3 4 2 5 1
Input
4
1 2 3 4
1 2 3 4
Output
4 3 2 1
### Input:
5
1 2 3 4 5
3 2 4 1 5
### Output:
3 4 2 5 1
### Input:
4
1 2 3 4
1 2 3 4
### Output:
4 3 2 1
### Code:
class BinaryTree:
class Node:
def __init__(self, nid, left, right):
self.id = nid
self.left = left
self.right = right
def has_left(self):
return self.left is not None
def has_right(self):
return self.right is not None
def __str__(self):
return str(self.id)
@classmethod
def create(cls, ids):
nodes = {}
def find(n, li):
for e1, e2, e3 in li:
if e1 == n:
return (e2, e3)
raise ValueError()
def _create(nid):
if nid in nodes:
return nodes[nid]
if nid == -1:
return None
lid, rid = find(nid, ids)
if lid == -1 and rid == -1:
right = None
left = None
elif lid == -1:
right = _create(rid)
left = None
elif lid == -1:
right = None
left = _create(lid)
else:
right = _create(rid)
left = _create(lid)
nodes[nid] = cls.Node(nid, left, right)
return nodes[nid]
def _root(nodeids):
for nid in [n[0] for n in nodeids]:
if all([lid != nid and rid != nid for _, lid, rid in nodeids]):
return nid
root = _create(_root(ids))
return cls(root)
def __init__(self, root):
self.root = root
def preorder(self):
def _preorder(node):
yield node
if node.has_left():
yield from _preorder(node.left)
if node.has_right():
yield from _preorder(node.right)
yield from _preorder(self.root)
def inorder(self):
def _inorder(node):
if node.has_left():
yield from _inorder(node.left)
yield node
if node.has_right():
yield from _inorder(node.right)
yield from _inorder(self.root)
def postorder(self):
def _postorder(node):
if node.has_left():
yield from _postorder(node.left)
if node.has_right():
yield from _postorder(node.right)
yield node
yield from _postorder(self.root)
def reconstruct(preorder, inorder):
"""Reconstruct a binary tree from preorder list
and inorder list of the tree.
>>> tree = reconstruct([1, 2, 3, 4, 5], [3, 2, 4, 1, 5])
>>> print(" ".join([str(node) for node in tree.postorder()]))
3 4 2 5 1
"""
def _first(li):
if len(li) > 0:
return li[0]
else:
return -1
def _reconstruct(_pre, _in):
assert(len(_pre) == len(_in))
if len(_pre) == 0:
return []
if len(_pre) == 1:
return [[_pre[0], -1, -1]]
root, *pre = _pre
i = _in.index(root)
in1, in2 = _in[:i], _in[i+1:]
pre1, pre2 = _pre[1:i+1], _pre[i+1:]
return ([[root, _first(pre1), _first(pre2)]] +
_reconstruct(pre1, in1) +
_reconstruct(pre2, in2))
return BinaryTree.create(_reconstruct(preorder, inorder))
def run():
_ = int(input())
preorder = [int(i) for i in input().split()]
inorder = [int(i) for i in input().split()]
tree = reconstruct(preorder, inorder)
print(" ".join([str(n) for n in tree.postorder()]))
if __name__ == '__main__':
run()
|
p02429 Enumeration of Subsets III_28510
|
You are given a set $T$, which is a subset of $S$. The set $S$ consists of $0, 1, ... n-1$. Print all subsets of $T$. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 28$
* $0 \leq k \leq 18$
* $k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
0:
1: 0
4: 2
5: 0 2
|
n=int(input())
ind='0'+str(n)+'b'
t=list(map(int,input().split()))
k=t[0]
t.pop(0)
T=t
T.reverse()
ind='0'+str(k)+'b'
for i in range(2**k):
compare=[int(j) for j in format(i,ind)]
disp=[T[j] for j in range(k) if compare[j]==1]
disp.reverse()
if len(disp)==0:
print("0:")
else:
calc=[2**j for j in disp]
print(str(sum(calc))+":",end="")
print(" "+' '.join(map(str,disp)))
|
{
"input": [
"4\n2 0 2",
"4\n2 0 3",
"4\n2 1 2",
"4\n0 0 3",
"4\n2 0 1",
"4\n1 0 2",
"4\n1 1 0",
"4\n1 2 -2",
"4\n1 3 0",
"4\n2 1 3",
"4\n0 0 1",
"4\n0 1 3",
"4\n0 1 1",
"4\n0 1 5",
"4\n0 1 2",
"4\n0 2 1",
"4\n0 1 0",
"4\n0 2 0",
"4\n0 0 0",
"4\n0 3 0",
"4\n0 0 2",
"4\n0 4 0",
"4\n0 -1 3",
"4\n0 8 0",
"4\n0 -2 3",
"4\n0 6 0",
"4\n0 -2 0",
"4\n0 7 0",
"4\n0 -1 0",
"4\n0 2 3",
"4\n0 0 5",
"4\n0 -1 -1",
"4\n0 2 -1",
"4\n0 3 -1",
"4\n0 -3 3",
"4\n0 6 -1",
"4\n1 0 1",
"4\n0 -2 -1",
"4\n0 0 6",
"4\n1 0 0",
"4\n0 3 -2",
"4\n0 -3 6",
"4\n0 1 -1",
"4\n1 0 6",
"4\n0 2 -2",
"4\n0 0 9",
"4\n1 0 9",
"4\n0 2 -4",
"4\n1 0 16",
"4\n0 2 -5",
"4\n0 2 -9",
"4\n1 2 -4",
"4\n1 1 -4",
"4\n1 1 -6",
"4\n1 1 -12",
"4\n1 2 -12",
"4\n1 2 -24",
"4\n1 2 -30",
"4\n0 2 -30",
"4\n0 2 -28",
"4\n0 2 -49",
"4\n0 2 -62",
"4\n1 0 3",
"4\n0 0 4",
"4\n1 1 2",
"4\n0 1 4",
"4\n1 2 1",
"4\n1 2 0",
"4\n0 5 -1",
"4\n0 2 2",
"4\n0 4 -1",
"4\n0 8 -1",
"4\n0 7 1",
"4\n1 0 4",
"4\n1 1 1",
"4\n1 0 -1",
"4\n0 -4 -1",
"4\n0 0 -2",
"4\n0 4 -2",
"4\n1 3 -2",
"4\n0 -3 0",
"4\n1 2 -1",
"4\n1 2 -6",
"4\n1 1 16",
"4\n0 1 -5",
"4\n0 0 -9",
"4\n1 3 -4",
"4\n0 1 -12",
"4\n0 2 -12",
"4\n1 2 -44",
"4\n0 2 -3",
"4\n0 2 -6",
"4\n0 3 -49",
"4\n0 2 -91",
"4\n1 1 3",
"4\n0 0 10",
"4\n0 1 7",
"4\n0 5 0",
"4\n1 2 2",
"4\n0 3 1",
"4\n1 0 7"
],
"output": [
"0:\n1: 0\n4: 2\n5: 0 2",
"0:\n1: 0\n8: 3\n9: 0 3\n",
"0:\n2: 1\n4: 2\n6: 1 2\n",
"0:\n",
"0:\n1: 0\n2: 1\n3: 0 1\n",
"0:\n1: 0\n",
"0:\n2: 1\n",
"0:\n4: 2\n",
"0:\n8: 3\n",
"0:\n2: 1\n8: 3\n10: 1 3\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n",
"0:\n4: 2\n",
"0:\n2: 1\n",
"0:\n2: 1\n",
"0:\n2: 1\n",
"0:\n4: 2\n",
"0:\n4: 2\n",
"0:\n4: 2\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n",
"0:\n2: 1\n",
"0:\n",
"0:\n4: 2\n",
"0:\n4: 2\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n1: 0\n",
"0:\n2: 1\n",
"0:\n1: 0\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n8: 3\n",
"0:\n",
"0:\n4: 2\n",
"0:\n4: 2\n",
"0:\n2: 1\n",
"0:\n",
"0:\n",
"0:\n8: 3\n",
"0:\n",
"0:\n",
"0:\n4: 2\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n2: 1\n",
"0:\n",
"0:\n",
"0:\n",
"0:\n4: 2\n",
"0:\n",
"0:\n1: 0\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a set $T$, which is a subset of $S$. The set $S$ consists of $0, 1, ... n-1$. Print all subsets of $T$. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 28$
* $0 \leq k \leq 18$
* $k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
0:
1: 0
4: 2
5: 0 2
### Input:
4
2 0 2
### Output:
0:
1: 0
4: 2
5: 0 2
### Input:
4
2 0 3
### Output:
0:
1: 0
8: 3
9: 0 3
### Code:
n=int(input())
ind='0'+str(n)+'b'
t=list(map(int,input().split()))
k=t[0]
t.pop(0)
T=t
T.reverse()
ind='0'+str(k)+'b'
for i in range(2**k):
compare=[int(j) for j in format(i,ind)]
disp=[T[j] for j in range(k) if compare[j]==1]
disp.reverse()
if len(disp)==0:
print("0:")
else:
calc=[2**j for j in disp]
print(str(sum(calc))+":",end="")
print(" "+' '.join(map(str,disp)))
|
1023_B. Pair of Toys_28520
|
Tanechka is shopping in the toy shop. There are exactly n toys in the shop for sale, the cost of the i-th toy is i burles. She wants to choose two toys in such a way that their total cost is k burles. How many ways to do that does she have?
Each toy appears in the shop exactly once. Pairs (a, b) and (b, a) are considered equal. Pairs (a, b), where a=b, are not allowed.
Input
The first line of the input contains two integers n, k (1 ≤ n, k ≤ 10^{14}) — the number of toys and the expected total cost of the pair of toys.
Output
Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is k burles.
Examples
Input
8 5
Output
2
Input
8 15
Output
1
Input
7 20
Output
0
Input
1000000000000 1000000000001
Output
500000000000
Note
In the first example Tanechka can choose the pair of toys (1, 4) or the pair of toys (2, 3).
In the second example Tanechka can choose only the pair of toys (7, 8).
In the third example choosing any pair of toys will lead to the total cost less than 20. So the answer is 0.
In the fourth example she can choose the following pairs: (1, 1000000000000), (2, 999999999999), (3, 999999999998), ..., (500000000000, 500000000001). The number of such pairs is exactly 500000000000.
|
n,k = [int(x) for x in input().split()]
if k>n:
if k>=2*n:
print(0)
else:
print((2*n-k+1)//2)
else:
if k%2==0:
k-=1
print(k//2)
|
{
"input": [
"8 15\n",
"1000000000000 1000000000001\n",
"7 20\n",
"8 5\n",
"99999999999999 100000000000000\n",
"100000000000000 100000000000000\n",
"4 7\n",
"50000000000000 99999999999999\n",
"3 1\n",
"1 100000000000000\n",
"4 4\n",
"49999999999996 99999999999999\n",
"49999999999997 99999999999999\n",
"3 4\n",
"3 2\n",
"6 8\n",
"50000000000003 99999999999999\n",
"1 5\n",
"2 4\n",
"5 8\n",
"1010101010 1010101010\n",
"1 2\n",
"41 66\n",
"100000000000000 5\n",
"100000000000000 99999999999999\n",
"99999999999999 65536\n",
"100000000000000 11\n",
"50000000000000 100000000000000\n",
"3294967296 5\n",
"4 5\n",
"1 6\n",
"3 6\n",
"7 10\n",
"3 3\n",
"50000000000001 99999999999999\n",
"1 1\n",
"50000000000002 99999999999999\n",
"13324 13736\n",
"4 2\n",
"4827 5436\n",
"1 123456789\n",
"99999999999998 100000000000000\n",
"3 5\n",
"100000000000000 2\n",
"100000000000 100000000001\n",
"1 8\n",
"38 74\n",
"2 5\n",
"2 8\n",
"2 6\n",
"99999999999977 100000000000000\n",
"100000000000000 4\n",
"100000000000000 99999999999998\n",
"100000000000000 1023\n",
"49999999999998 100000000000000\n",
"100000000000000 1\n",
"4 6\n",
"2 2\n",
"4 8\n",
"100000000000 130000000000\n",
"50000000000001 100000000000000\n",
"4 1\n",
"4 3\n",
"123456789 1\n",
"1 7\n",
"8 14\n",
"2 3\n",
"100000000000 10000000000\n",
"998244353 19260817\n",
"49999999999998 99999999999999\n",
"7 14\n",
"8 16\n",
"100000000000000 6\n",
"1 4\n",
"49999999999997 100000000000000\n",
"99999999999999 99999999999998\n",
"100000000000 130000000001\n",
"50000000000003 100000000000000\n",
"49999999999999 99999999999999\n",
"7 8\n",
"99999999999996 100000000000000\n",
"50000000000002 100000000000000\n",
"2 7\n",
"44999999999177 100000000000000\n",
"49999999999996 100000000000000\n",
"69999999999177 100000000000000\n",
"99999999999997 100000000000000\n",
"2 1\n",
"100000000000000 3\n",
"3 8\n",
"3 7\n",
"99999999999999 99999999999997\n",
"49999999999999 100000000000000\n",
"59999999999177 100000000000000\n",
"1 3\n",
"100000000000000 100\n",
"100000000000 100000000000\n",
"99999999999999 99999999999999\n",
"99999999999999 100000000001000\n",
"100000000010000 100000000000000\n",
"4 11\n",
"50000000000000 59204469252435\n",
"6 3\n",
"1010101010 1011101010\n",
"41 63\n",
"100000000010000 5\n",
"156463135268026 65536\n",
"110000000000000 11\n",
"72209373991004 100000000000000\n",
"3294967296 10\n",
"68861863843081 99999999999999\n",
"13324 15178\n",
"100000000000 100000000011\n",
"99999999999977 100000000000100\n",
"100000000000001 99999999999998\n",
"7 7\n",
"100000000000 110546196252\n",
"100000000000 10000001000\n",
"825954239 19260817\n",
"99999999999999 164374093490300\n",
"100000010000 130000000001\n",
"49999999999999 14752772551252\n",
"92122820665616 100000000000000\n",
"92303240844096 100000000000000\n",
"59999999999177 100000000100000\n",
"100010000000000 100\n",
"100000000000 100000100000\n",
"99999999999999 103246683590518\n",
"1000000010000 1000000000001\n",
"105925489085800 100000000001000\n",
"50000000000000 59257435820612\n",
"93803127109369 150878756750858\n",
"1 110000000000000\n",
"45765460895346 99999999999999\n",
"2220334390216 99999999999999\n",
"8 4\n",
"50000000000003 150878756750858\n",
"1 14\n",
"5 2\n",
"5 16\n",
"100000100000000 99999999999999\n",
"4 12\n",
"1 10\n",
"3 9\n",
"7 2\n",
"7 5\n",
"981098184001 99999999999999\n",
"7 1\n",
"2108 5436\n",
"1 61960338\n",
"12283935172049 100000000000000\n",
"6 5\n",
"100000000000010 1\n",
"38 102\n",
"2 10\n",
"0 1\n",
"2 12\n",
"100000000001000 4\n",
"100001000000000 11\n",
"12550978948660 100000000000000\n",
"110000000000000 4\n",
"6 2\n",
"31121108554531 100000000000000\n",
"6 10\n",
"182480173 1\n",
"8 27\n",
"14360987829795 99999999999999\n",
"3 14\n",
"6 16\n",
"100000000000100 6\n",
"0 2\n",
"44604552259816 100000000000000\n",
"50000000000003 100000000001000\n",
"8 8\n",
"125933287682784 100000000000000\n",
"2 13\n",
"44999999999177 100001000000000\n",
"33733668057826 100000000000000\n",
"10042931378507 100000000000000\n",
"110000000000000 3\n",
"6 4\n",
"27808842428411 99999999999997\n",
"49999999999999 100010000000000\n",
"9 20\n",
"5 5\n",
"101000000010000 100000000000000\n",
"9 5\n",
"45765460895346 152657771153606\n",
"2220334390216 194335198485292\n",
"8 3\n",
"1 13\n",
"5 3\n",
"9 16\n"
],
"output": [
"1\n",
"500000000000\n",
"0\n",
"2\n",
"49999999999999\n",
"49999999999999\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"2\n",
"4\n",
"0\n",
"0\n",
"1\n",
"505050504\n",
"0\n",
"8\n",
"2\n",
"49999999999999\n",
"32767\n",
"5\n",
"0\n",
"2\n",
"2\n",
"0\n",
"0\n",
"2\n",
"1\n",
"2\n",
"0\n",
"3\n",
"6456\n",
"0\n",
"2109\n",
"0\n",
"49999999999998\n",
"1\n",
"0\n",
"50000000000\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"49999999999977\n",
"1\n",
"49999999999998\n",
"511\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"35000000000\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"1\n",
"4999999999\n",
"9630408\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"49999999999998\n",
"35000000000\n",
"3\n",
"0\n",
"3\n",
"49999999999996\n",
"2\n",
"0\n",
"0\n",
"0\n",
"19999999999177\n",
"49999999999997\n",
"0\n",
"1\n",
"0\n",
"0\n",
"49999999999998\n",
"0\n",
"9999999999177\n",
"0\n",
"49\n",
"49999999999\n",
"49999999999999\n",
"49999999999499\n",
"49999999999999\n",
"0\n",
"20397765373783\n",
"1\n",
"504550505\n",
"10\n",
"2\n",
"32767\n",
"5\n",
"22209373991004\n",
"4\n",
"18861863843082\n",
"5735\n",
"49999999995\n",
"49999999999927\n",
"49999999999998\n",
"3\n",
"44726901874\n",
"5000000499\n",
"9630408\n",
"17812953254849\n",
"35000010000\n",
"7376386275625\n",
"42122820665616\n",
"42303240844096\n",
"9999999949177\n",
"49\n",
"49999950000\n",
"48376658204740\n",
"500000000000\n",
"50000000000499\n",
"20371282089694\n",
"18363748733940\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"49999999999999\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"5\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"0\n",
"3\n",
"49999999999999\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"0\n",
"2\n",
"49999999999999\n",
"2\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Tanechka is shopping in the toy shop. There are exactly n toys in the shop for sale, the cost of the i-th toy is i burles. She wants to choose two toys in such a way that their total cost is k burles. How many ways to do that does she have?
Each toy appears in the shop exactly once. Pairs (a, b) and (b, a) are considered equal. Pairs (a, b), where a=b, are not allowed.
Input
The first line of the input contains two integers n, k (1 ≤ n, k ≤ 10^{14}) — the number of toys and the expected total cost of the pair of toys.
Output
Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is k burles.
Examples
Input
8 5
Output
2
Input
8 15
Output
1
Input
7 20
Output
0
Input
1000000000000 1000000000001
Output
500000000000
Note
In the first example Tanechka can choose the pair of toys (1, 4) or the pair of toys (2, 3).
In the second example Tanechka can choose only the pair of toys (7, 8).
In the third example choosing any pair of toys will lead to the total cost less than 20. So the answer is 0.
In the fourth example she can choose the following pairs: (1, 1000000000000), (2, 999999999999), (3, 999999999998), ..., (500000000000, 500000000001). The number of such pairs is exactly 500000000000.
### Input:
8 15
### Output:
1
### Input:
1000000000000 1000000000001
### Output:
500000000000
### Code:
n,k = [int(x) for x in input().split()]
if k>n:
if k>=2*n:
print(0)
else:
print((2*n-k+1)//2)
else:
if k%2==0:
k-=1
print(k//2)
|
1044_C. Optimal Polygon Perimeter_28524
|
You are given n points on the plane. The polygon formed from all the n points is strictly convex, that is, the polygon is convex, and there are no three collinear points (i.e. lying in the same straight line). The points are numbered from 1 to n, in clockwise order.
We define the distance between two points p_1 = (x_1, y_1) and p_2 = (x_2, y_2) as their Manhattan distance: $$$d(p_1, p_2) = |x_1 - x_2| + |y_1 - y_2|.$$$
Furthermore, we define the perimeter of a polygon, as the sum of Manhattan distances between all adjacent pairs of points on it; if the points on the polygon are ordered as p_1, p_2, …, p_k (k ≥ 3), then the perimeter of the polygon is d(p_1, p_2) + d(p_2, p_3) + … + d(p_k, p_1).
For some parameter k, let's consider all the polygons that can be formed from the given set of points, having any k vertices, such that the polygon is not self-intersecting. For each such polygon, let's consider its perimeter. Over all such perimeters, we define f(k) to be the maximal perimeter.
Please note, when checking whether a polygon is self-intersecting, that the edges of a polygon are still drawn as straight lines. For instance, in the following pictures:
<image>
In the middle polygon, the order of points (p_1, p_3, p_2, p_4) is not valid, since it is a self-intersecting polygon. The right polygon (whose edges resemble the Manhattan distance) has the same order and is not self-intersecting, but we consider edges as straight lines. The correct way to draw this polygon is (p_1, p_2, p_3, p_4), which is the left polygon.
Your task is to compute f(3), f(4), …, f(n). In other words, find the maximum possible perimeter for each possible number of points (i.e. 3 to n).
Input
The first line contains a single integer n (3 ≤ n ≤ 3⋅ 10^5) — the number of points.
Each of the next n lines contains two integers x_i and y_i (-10^8 ≤ x_i, y_i ≤ 10^8) — the coordinates of point p_i.
The set of points is guaranteed to be convex, all points are distinct, the points are ordered in clockwise order, and there will be no three collinear points.
Output
For each i (3≤ i≤ n), output f(i).
Examples
Input
4
2 4
4 3
3 0
1 3
Output
12 14
Input
3
0 0
0 2
2 0
Output
8
Note
In the first example, for f(3), we consider four possible polygons:
* (p_1, p_2, p_3), with perimeter 12.
* (p_1, p_2, p_4), with perimeter 8.
* (p_1, p_3, p_4), with perimeter 12.
* (p_2, p_3, p_4), with perimeter 12.
For f(4), there is only one option, taking all the given points. Its perimeter 14.
In the second example, there is only one possible polygon. Its perimeter is 8.
|
n = int(input())
north = -100000000
south = 100000000
east = -100000000
west = 100000000
ne = -200000000
nw = -200000000
se = -200000000
sw = -200000000
for i in range(n):
x,y = map(int,input().split())
north = max(north,y)
east = max(east,x)
south = min(south,y)
west = min(west,x)
ne = max(ne,x+y)
nw = max(nw,y-x)
se = max(se,x-y)
sw = max(sw,-1*x-y)
best = 2*(ne-south-west)
best = max(best,2*(nw-south+east))
best = max(best,2*(se+north-west))
best = max(best,2*(sw+north+east))
ans = str(best)
peri = 2*(north-south+east-west)
ans += (" "+str(peri))*(n-3)
print(ans)
|
{
"input": [
"4\n2 4\n4 3\n3 0\n1 3\n",
"3\n0 0\n0 2\n2 0\n",
"12\n-83240790 -33942371\n-83240805 -33942145\n-83240821 -33941752\n-83240424 -33941833\n-83240107 -33942105\n-83239958 -33942314\n-83239777 -33942699\n-83239762 -33942925\n-83239746 -33943318\n-83240143 -33943237\n-83240460 -33942965\n-83240609 -33942756\n",
"3\n51800836 -5590860\n51801759 -5590419\n51801320 -5590821\n",
"8\n0 3\n2 2\n3 0\n2 -2\n0 -3\n-2 -2\n-3 0\n-2 2\n",
"20\n-2967010 48581504\n-2967318 48581765\n-2967443 48581988\n-2967541 48582265\n-2967443 48582542\n-2967318 48582765\n-2967010 48583026\n-2966691 48583154\n-2966252 48583234\n-2965813 48583154\n-2965494 48583026\n-2965186 48582765\n-2965061 48582542\n-2964963 48582265\n-2965061 48581988\n-2965186 48581765\n-2965494 48581504\n-2965813 48581376\n-2966252 48581296\n-2966691 48581376\n",
"4\n-100000000 -100000000\n-100000000 100000000\n100000000 100000000\n100000000 -100000000\n",
"3\n77445196 95326351\n77444301 95326820\n77444705 95326693\n",
"4\n0 99999999\n0 100000000\n1 -99999999\n1 -100000000\n",
"4\n100000000 0\n0 -100000000\n-100000000 0\n0 100000000\n",
"4\n0 0\n10 10\n10 9\n1 0\n",
"3\n97972354 -510322\n97972814 -510361\n97972410 -510528\n",
"4\n12345678 99999999\n12345679 100000000\n12345680 99999999\n12345679 99999998\n",
"4\n-95989415 -89468419\n-95989014 -89468179\n-95989487 -89468626\n-95989888 -89468866\n",
"6\n-1000 1000\n-998 1001\n-996 1000\n-996 996\n-997 995\n-1001 997\n",
"10\n811055 21220458\n813063 21222323\n815154 21220369\n817067 21218367\n815214 21216534\n813198 21214685\n803185 21212343\n805063 21214436\n806971 21216475\n808966 21218448\n",
"3\n-99297393 80400183\n-99297475 80399631\n-99297428 80399972\n",
"12\n-83240790 -33942371\n-83240805 -33942145\n-83240821 -33941752\n-83240424 -33941833\n-83240107 -33942105\n-83239958 -33942314\n-83239777 -33942699\n-83239762 -33942925\n-83239746 -33943318\n-66971704 -33943237\n-83240460 -33942965\n-83240609 -33942756\n",
"3\n51800836 -1756836\n51801759 -5590419\n51801320 -5590821\n",
"8\n0 3\n2 2\n3 0\n2 -2\n0 -3\n-2 -2\n-3 1\n-2 2\n",
"4\n-100000000 -100000000\n-100000000 100000000\n100000000 101000000\n100000000 -100000000\n",
"3\n77445196 171582774\n77444301 95326820\n77444705 95326693\n",
"4\n0 111328374\n0 100000000\n1 -99999999\n1 -100000000\n",
"4\n100100000 0\n0 -100000000\n-100000000 0\n0 100000000\n",
"4\n0 0\n6 10\n10 9\n1 0\n",
"3\n97972354 -510322\n97972814 -510361\n3428786 -510528\n",
"4\n-95989415 -89468419\n-95989014 -89468179\n-95989487 -89468626\n-148841738 -89468866\n",
"10\n811055 21220458\n813063 21222323\n815154 21220369\n1558875 21218367\n815214 21216534\n813198 21214685\n803185 21212343\n805063 21214436\n806971 21216475\n808966 21218448\n",
"3\n-99297393 80400183\n-99297475 80399631\n-99297428 54604918\n",
"4\n3 4\n4 3\n3 0\n1 3\n",
"3\n0 0\n-1 2\n2 0\n",
"3\n51800836 -1756836\n51801759 -5590419\n4115806 -5590821\n",
"8\n0 3\n2 2\n3 0\n2 -2\n0 -3\n-2 -2\n-3 1\n-2 3\n",
"3\n89662205 171582774\n77444301 95326820\n77444705 95326693\n",
"4\n0 111328374\n0 100000000\n1 -99999999\n1 -73518429\n",
"4\n100100000 0\n0 -100000000\n-100000000 0\n0 100000100\n",
"4\n0 0\n6 10\n10 17\n1 0\n",
"3\n97972354 -510322\n97972814 -510361\n9107 -510528\n",
"4\n-95989415 -89468419\n-95989014 -89468179\n-95989487 -89468626\n-194052636 -89468866\n",
"3\n-99297393 80400183\n-196853177 80399631\n-99297428 54604918\n",
"4\n5 4\n4 3\n3 0\n1 3\n",
"3\n0 0\n-1 1\n2 0\n",
"3\n51800836 -1756836\n51801759 -6116854\n4115806 -5590821\n",
"4\n-100000000 -100000000\n-100000000 101100000\n100000000 101000000\n100000000 -100000000\n",
"3\n89662205 171582774\n77444301 174371428\n77444705 95326693\n",
"4\n100100000 0\n0 -165428644\n-100000000 0\n0 100000100\n",
"4\n0 -1\n6 10\n10 17\n1 0\n",
"3\n97972354 -510322\n97972814 -510361\n10937 -510528\n",
"4\n-95989415 -89468419\n-95989014 -89468179\n-33126318 -89468626\n-194052636 -89468866\n",
"3\n-46733155 80400183\n-196853177 80399631\n-99297428 54604918\n",
"4\n9 4\n4 3\n3 0\n1 3\n",
"3\n0 0\n-1 1\n4 0\n",
"3\n89662205 196980867\n77444301 174371428\n77444705 95326693\n",
"4\n0 111328374\n0 100000000\n0 -61141526\n1 -73518429\n",
"4\n100100000 0\n0 -165428644\n-100000000 0\n-1 100000100\n",
"3\n97972354 -510322\n97972814 -510361\n1989 -510528\n",
"3\n-64574641 80400183\n-196853177 80399631\n-99297428 54604918\n",
"3\n0 0\n-1 1\n4 -1\n",
"3\n89662205 385501139\n77444301 174371428\n77444705 95326693\n",
"4\n100100000 0\n0 -165428644\n-100000000 0\n-2 100000100\n",
"3\n97972354 -510322\n11104794 -510361\n1989 -510528\n",
"4\n-100000000 -100000000\n-100000000 101000000\n100000000 101000000\n100000000 -100000000\n",
"4\n0 111328374\n0 100000000\n0 -99999999\n1 -73518429\n",
"3\n45955541 -1756836\n51801759 -6116854\n4115806 -5590821\n",
"4\n-100000000 -100000000\n-100000000 101100000\n000000000 101000000\n100000000 -100000000\n",
"4\n0 -1\n6 5\n10 17\n1 0\n",
"4\n9 4\n4 3\n4 0\n1 3\n",
"3\n45955541 -1756836\n51801759 -6116854\n4115806 -4677823\n",
"4\n-100000000 -100000000\n-100000000 101100000\n000000000 001000000\n100000000 -100000000\n",
"4\n0 111328374\n0 100100000\n0 -61141526\n1 -73518429\n",
"4\n0 -1\n6 5\n10 17\n1 1\n",
"3\n-64574641 80400183\n-196853177 80399631\n-111339133 54604918\n"
],
"output": [
"12 14\n",
"8\n",
"5282 5282 5282 5282 5282 5282 5282 5282 5282 5282\n",
"2728\n",
"20 24 24 24 24 24\n",
"7648 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032 9032\n",
"800000000 800000000\n",
"2728\n",
"400000002 400000002\n",
"600000000 800000000\n",
"40 40\n",
"1332\n",
"6 8\n",
"3122 3122\n",
"20 22 22 22\n",
"47724 47724 47724 47724 47724 47724 47724 47724\n",
"1268\n",
"32541366 32541366 32541366 32541366 32541366 32541366 32541366 32541366 32541366 32541366 \n",
"7669816 \n",
"20 24 24 24 24 24 \n",
"802000000 802000000 \n",
"152513952 \n",
"422656750 422656750 \n",
"600200000 800200000 \n",
"40 40 \n",
"189088468 \n",
"105706822 105706822 \n",
"1531340 1531340 1531340 1531340 1531340 1531340 1531340 1531340 \n",
"51590694 \n",
"12 14 \n",
"10 \n",
"103039876 \n",
"22 24 24 24 24 24 \n",
"176947970 \n",
"422656748 422656748 \n",
"600200200 800200200 \n",
"54 54 \n",
"195927826 \n",
"196128618 196128618 \n",
"246702098 \n",
"16 16 \n",
"8 \n",
"104091942 \n",
"802200000 802200000 \n",
"182525278 \n",
"731057488 931057488 \n",
"56 56 \n",
"195924166 \n",
"321854010 321854010 \n",
"351830574 \n",
"24 24 \n",
"12 \n",
"227744156 \n",
"369693608 369693608 \n",
"731057490 931057488 \n",
"195942062 \n",
"316147602 \n",
"14 \n",
"604784700 \n",
"731057492 931057488 \n",
"195941142 \n",
"802000000 802000000 \n",
"422656748 422656748 \n",
"104091942 \n",
"802200000 802200000 \n",
"56 56 \n",
"24 24 \n",
"104091942 \n",
"802200000 802200000 \n",
"369693608 369693608 \n",
"56 56 \n",
"316147602 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given n points on the plane. The polygon formed from all the n points is strictly convex, that is, the polygon is convex, and there are no three collinear points (i.e. lying in the same straight line). The points are numbered from 1 to n, in clockwise order.
We define the distance between two points p_1 = (x_1, y_1) and p_2 = (x_2, y_2) as their Manhattan distance: $$$d(p_1, p_2) = |x_1 - x_2| + |y_1 - y_2|.$$$
Furthermore, we define the perimeter of a polygon, as the sum of Manhattan distances between all adjacent pairs of points on it; if the points on the polygon are ordered as p_1, p_2, …, p_k (k ≥ 3), then the perimeter of the polygon is d(p_1, p_2) + d(p_2, p_3) + … + d(p_k, p_1).
For some parameter k, let's consider all the polygons that can be formed from the given set of points, having any k vertices, such that the polygon is not self-intersecting. For each such polygon, let's consider its perimeter. Over all such perimeters, we define f(k) to be the maximal perimeter.
Please note, when checking whether a polygon is self-intersecting, that the edges of a polygon are still drawn as straight lines. For instance, in the following pictures:
<image>
In the middle polygon, the order of points (p_1, p_3, p_2, p_4) is not valid, since it is a self-intersecting polygon. The right polygon (whose edges resemble the Manhattan distance) has the same order and is not self-intersecting, but we consider edges as straight lines. The correct way to draw this polygon is (p_1, p_2, p_3, p_4), which is the left polygon.
Your task is to compute f(3), f(4), …, f(n). In other words, find the maximum possible perimeter for each possible number of points (i.e. 3 to n).
Input
The first line contains a single integer n (3 ≤ n ≤ 3⋅ 10^5) — the number of points.
Each of the next n lines contains two integers x_i and y_i (-10^8 ≤ x_i, y_i ≤ 10^8) — the coordinates of point p_i.
The set of points is guaranteed to be convex, all points are distinct, the points are ordered in clockwise order, and there will be no three collinear points.
Output
For each i (3≤ i≤ n), output f(i).
Examples
Input
4
2 4
4 3
3 0
1 3
Output
12 14
Input
3
0 0
0 2
2 0
Output
8
Note
In the first example, for f(3), we consider four possible polygons:
* (p_1, p_2, p_3), with perimeter 12.
* (p_1, p_2, p_4), with perimeter 8.
* (p_1, p_3, p_4), with perimeter 12.
* (p_2, p_3, p_4), with perimeter 12.
For f(4), there is only one option, taking all the given points. Its perimeter 14.
In the second example, there is only one possible polygon. Its perimeter is 8.
### Input:
4
2 4
4 3
3 0
1 3
### Output:
12 14
### Input:
3
0 0
0 2
2 0
### Output:
8
### Code:
n = int(input())
north = -100000000
south = 100000000
east = -100000000
west = 100000000
ne = -200000000
nw = -200000000
se = -200000000
sw = -200000000
for i in range(n):
x,y = map(int,input().split())
north = max(north,y)
east = max(east,x)
south = min(south,y)
west = min(west,x)
ne = max(ne,x+y)
nw = max(nw,y-x)
se = max(se,x-y)
sw = max(sw,-1*x-y)
best = 2*(ne-south-west)
best = max(best,2*(nw-south+east))
best = max(best,2*(se+north-west))
best = max(best,2*(sw+north+east))
ans = str(best)
peri = 2*(north-south+east-west)
ans += (" "+str(peri))*(n-3)
print(ans)
|
1067_B. Multihedgehog_28528
|
Someone give a strange birthday present to Ivan. It is hedgehog — connected undirected graph in which one vertex has degree at least 3 (we will call it center) and all other vertices has degree 1. Ivan thought that hedgehog is too boring and decided to make himself k-multihedgehog.
Let us define k-multihedgehog as follows:
* 1-multihedgehog is hedgehog: it has one vertex of degree at least 3 and some vertices of degree 1.
* For all k ≥ 2, k-multihedgehog is (k-1)-multihedgehog in which the following changes has been made for each vertex v with degree 1: let u be its only neighbor; remove vertex v, create a new hedgehog with center at vertex w and connect vertices u and w with an edge. New hedgehogs can differ from each other and the initial gift.
Thereby k-multihedgehog is a tree. Ivan made k-multihedgehog but he is not sure that he did not make any mistakes. That is why he asked you to check if his tree is indeed k-multihedgehog.
Input
First line of input contains 2 integers n, k (1 ≤ n ≤ 10^{5}, 1 ≤ k ≤ 10^{9}) — number of vertices and hedgehog parameter.
Next n-1 lines contains two integers u v (1 ≤ u, v ≤ n; u ≠ v) — indices of vertices connected by edge.
It is guaranteed that given graph is a tree.
Output
Print "Yes" (without quotes), if given graph is k-multihedgehog, and "No" (without quotes) otherwise.
Examples
Input
14 2
1 4
2 4
3 4
4 13
10 5
11 5
12 5
14 5
5 13
6 7
8 6
13 6
9 6
Output
Yes
Input
3 1
1 3
2 3
Output
No
Note
2-multihedgehog from the first example looks like this:
<image>
Its center is vertex 13. Hedgehogs created on last step are: [4 (center), 1, 2, 3], [6 (center), 7, 8, 9], [5 (center), 10, 11, 12, 13].
Tree from second example is not a hedgehog because degree of center should be at least 3.
|
from sys import stdin
from collections import deque
n, k = map(int, stdin.readline().split())
graph = [[] for _ in range(n)]
leaf = -1
for _ in range(n-1):
a,b = map(int,stdin.readline().split())
graph[a - 1].append(b - 1)
graph[b - 1].append(a - 1)
def bfs(G, s):
# la cola comienza con el vertice desde el cual hacemos bfs
Q = deque()
Q.append(s)
# al inicio todas las distancias comienzan en infinito, por las
# restricciones del problema ningun camino va a ser de ese tamanno
infinite = 10 ** 6
d = [infinite]*n
parent = [-1]*n
valid = True
# la distancia del vertice raiz es 0
d[s] = 0
while Q:
# visitamos u
u = Q.popleft()
not_visited_count = 0
# visitamos cada adyacente de u
for v in G[u]:
# si no lo hemos visitado, le ponemos distancia y
# lo agregamos a la cola para visitar sus adyacentes
if d[v] == infinite:
d[v] = d[u] + 1
parent[v] = u
Q.append(v)
not_visited_count += 1
if not_visited_count < 3 and d[u] != k:
valid = False
# retornamos el array d, que es el de las distancias del
# nodo s al resto de los nodos del grafo
return d, parent, valid
leaf = -1
for i,v in enumerate(graph):
if len(v) == 1:
leaf = i
break
d, parent, _ = bfs(graph,leaf)
center = -1
farthest_leaf = -1
path = 2*k
for i,level in enumerate(d):
if level == path:
farthest_leaf = i
break
if len(graph[farthest_leaf]) != 1 or farthest_leaf == -1:
print("NO")
exit()
for _ in range(k):
center = parent[farthest_leaf]
farthest_leaf = center
_, _, valid = bfs(graph,center)
if valid:
print("YES")
else:
print("NO")
|
{
"input": [
"3 1\n1 3\n2 3\n",
"14 2\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n6 7\n8 6\n13 6\n9 6\n",
"13 2\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n",
"14 3\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n6 7\n8 6\n13 6\n9 6\n",
"18 2\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n6 7\n8 6\n13 6\n9 6\n13 15\n15 16\n15 17\n15 18\n",
"25 2\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n3 8\n3 9\n3 10\n4 11\n4 12\n4 13\n4 14\n14 15\n14 16\n14 17\n4 18\n18 19\n18 20\n18 21\n1 22\n22 23\n22 24\n22 25\n",
"22 2\n1 4\n2 4\n3 4\n5 8\n6 8\n7 8\n9 12\n10 12\n11 12\n13 16\n14 16\n15 16\n17 20\n18 20\n19 20\n4 21\n8 21\n12 21\n4 22\n16 22\n20 22\n",
"33 2\n3 13\n17 3\n2 6\n5 33\n4 18\n1 2\n31 5\n4 19\n3 16\n1 3\n9 2\n10 3\n5 1\n5 28\n21 4\n7 2\n1 4\n5 24\n30 5\n14 3\n3 11\n27 5\n8 2\n22 4\n12 3\n20 4\n26 5\n4 23\n32 5\n25 5\n15 3\n29 5\n",
"16 2\n1 12\n2 12\n3 12\n4 13\n5 13\n6 13\n7 16\n8 16\n9 15\n10 15\n11 15\n12 14\n13 14\n16 14\n15 14\n",
"8 2\n8 2\n2 5\n5 1\n7 2\n2 4\n3 5\n5 6\n",
"5 1\n4 1\n3 1\n5 1\n1 2\n",
"1 1\n",
"13 2\n7 5\n10 11\n5 12\n1 2\n10 7\n2 6\n10 4\n9 5\n13 10\n2 8\n3 10\n2 7\n",
"2 1\n2 1\n",
"14 1\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n6 7\n8 6\n13 6\n9 6\n",
"10 980000000\n5 4\n7 1\n3 2\n10 6\n2 8\n6 4\n7 9\n1 8\n3 10\n",
"4 1\n2 3\n4 2\n1 2\n",
"2 1\n1 2\n",
"8 1\n8 2\n2 5\n5 1\n7 2\n2 4\n3 5\n5 6\n",
"16 2\n1 12\n2 12\n3 12\n4 13\n5 13\n6 13\n7 14\n8 14\n9 15\n10 15\n11 15\n12 16\n13 16\n14 16\n15 16\n",
"13 1000000000\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n",
"7 1\n1 2\n1 3\n1 4\n5 1\n1 6\n1 7\n",
"21 2\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n9 11\n9 12\n10 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n12 20\n12 21\n",
"18 2\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n1 7\n8 6\n13 6\n9 6\n13 15\n15 16\n15 17\n15 18\n",
"18 2\n1 4\n2 4\n3 4\n4 13\n10 6\n11 5\n12 5\n14 5\n5 13\n6 7\n8 6\n13 6\n9 6\n13 15\n15 16\n15 17\n15 18\n",
"8 2\n8 2\n4 5\n5 1\n7 2\n2 4\n3 5\n5 6\n",
"5 1\n4 1\n3 2\n5 1\n1 2\n",
"16 3\n1 12\n2 12\n3 12\n4 13\n5 13\n6 13\n7 14\n8 14\n9 15\n10 15\n11 15\n12 16\n13 16\n14 16\n15 16\n",
"21 2\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n14 11\n9 12\n10 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n12 20\n12 21\n",
"13 2\n1 2\n2 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n",
"33 2\n3 13\n17 3\n2 6\n5 33\n4 18\n1 2\n31 5\n4 19\n3 16\n1 3\n9 2\n10 3\n5 1\n5 28\n21 4\n7 2\n1 4\n5 24\n30 5\n14 3\n3 11\n27 5\n8 2\n22 4\n12 3\n20 4\n26 5\n4 23\n32 1\n25 5\n15 3\n29 5\n",
"8 2\n8 2\n2 5\n3 1\n7 2\n2 4\n3 5\n5 6\n",
"1 1\n4 1\n3 1\n5 1\n1 2\n",
"1 2\n",
"2 2\n2 1\n",
"10 980000000\n5 4\n7 1\n3 2\n10 6\n3 8\n6 4\n7 9\n1 8\n3 10\n",
"4 1\n2 3\n4 1\n1 2\n",
"13 1000000000\n1 2\n1 3\n1 4\n1 5\n2 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n",
"33 2\n4 13\n17 3\n2 6\n5 33\n4 18\n1 2\n31 5\n4 19\n3 16\n1 3\n9 2\n10 3\n5 1\n5 28\n21 4\n7 2\n1 4\n5 24\n30 5\n14 3\n3 11\n27 5\n8 2\n22 4\n12 3\n20 4\n26 5\n4 23\n32 1\n25 5\n15 3\n29 5\n",
"14 3\n1 4\n2 4\n3 4\n4 13\n10 5\n11 5\n12 5\n14 5\n5 13\n6 7\n8 4\n13 6\n9 6\n",
"22 2\n1 4\n2 4\n3 4\n5 8\n6 8\n7 8\n9 12\n10 12\n11 12\n13 16\n14 16\n15 16\n17 20\n18 20\n19 20\n4 21\n8 21\n12 1\n4 22\n16 22\n20 22\n",
"8 1\n8 2\n2 5\n5 1\n7 2\n2 4\n3 4\n5 6\n",
"10 980000000\n5 4\n7 1\n3 2\n10 6\n2 8\n1 4\n7 9\n1 8\n3 10\n",
"4 1\n1 3\n4 2\n1 2\n",
"8 1\n8 2\n2 5\n6 1\n7 2\n2 4\n3 5\n5 6\n",
"21 2\n3 1\n4 1\n5 2\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n9 11\n9 12\n10 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n12 20\n12 21\n",
"21 2\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n20 11\n9 12\n10 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n12 20\n12 21\n",
"1 1\n4 1\n3 1\n6 1\n1 2\n",
"10 1323614652\n5 4\n7 1\n3 2\n10 6\n3 8\n6 4\n7 9\n1 8\n3 10\n",
"33 2\n4 13\n17 3\n2 6\n5 33\n4 18\n1 2\n31 5\n4 19\n3 16\n1 3\n9 2\n10 3\n5 1\n5 28\n21 4\n7 2\n1 4\n5 24\n30 5\n14 3\n3 11\n27 5\n8 2\n22 4\n12 3\n20 4\n26 5\n4 23\n32 1\n25 5\n15 6\n29 5\n",
"22 2\n1 4\n2 4\n3 4\n5 8\n6 8\n7 8\n9 14\n10 12\n11 12\n13 16\n14 16\n15 16\n17 20\n18 20\n19 20\n4 21\n8 21\n12 1\n4 22\n16 22\n20 22\n",
"8 1\n8 2\n2 5\n5 1\n7 1\n2 4\n3 4\n5 6\n",
"21 2\n3 1\n4 1\n5 2\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n9 11\n9 12\n10 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n4 20\n12 21\n",
"21 2\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n20 11\n9 12\n10 13\n10 14\n10 15\n5 16\n11 17\n11 18\n12 19\n12 20\n12 21\n",
"1 1\n4 1\n3 1\n6 1\n0 2\n",
"8 1\n8 2\n2 5\n5 1\n7 1\n1 4\n3 4\n5 6\n",
"21 2\n3 1\n4 1\n5 2\n6 2\n7 2\n8 2\n1 2\n9 1\n9 10\n9 11\n9 12\n3 13\n10 14\n10 15\n11 16\n11 17\n11 18\n12 19\n4 20\n12 21\n",
"1 1\n4 1\n3 1\n6 1\n-1 2\n",
"8 1\n8 2\n2 5\n5 1\n7 1\n1 4\n3 8\n5 6\n",
"1 1\n4 1\n3 1\n0 1\n-1 2\n",
"8 1\n8 2\n2 5\n5 1\n7 1\n1 4\n3 6\n5 6\n",
"1 1\n4 1\n3 2\n0 1\n-1 2\n",
"1 2\n4 1\n3 2\n0 1\n-1 2\n",
"1 2\n4 1\n3 2\n0 1\n-1 0\n",
"1 1\n4 1\n3 2\n0 1\n-1 0\n",
"22 2\n1 4\n2 4\n3 4\n5 8\n6 8\n7 8\n9 12\n10 12\n11 12\n13 16\n14 16\n15 13\n17 20\n18 20\n19 20\n4 21\n8 21\n12 21\n4 22\n16 22\n20 22\n",
"16 2\n1 12\n2 12\n3 12\n4 13\n5 13\n6 13\n7 16\n8 13\n9 15\n10 15\n11 15\n12 14\n13 14\n16 14\n15 14\n",
"1 1\n1 2\n",
"8 1\n8 2\n2 5\n5 1\n7 2\n2 4\n3 5\n4 6\n"
],
"output": [
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Someone give a strange birthday present to Ivan. It is hedgehog — connected undirected graph in which one vertex has degree at least 3 (we will call it center) and all other vertices has degree 1. Ivan thought that hedgehog is too boring and decided to make himself k-multihedgehog.
Let us define k-multihedgehog as follows:
* 1-multihedgehog is hedgehog: it has one vertex of degree at least 3 and some vertices of degree 1.
* For all k ≥ 2, k-multihedgehog is (k-1)-multihedgehog in which the following changes has been made for each vertex v with degree 1: let u be its only neighbor; remove vertex v, create a new hedgehog with center at vertex w and connect vertices u and w with an edge. New hedgehogs can differ from each other and the initial gift.
Thereby k-multihedgehog is a tree. Ivan made k-multihedgehog but he is not sure that he did not make any mistakes. That is why he asked you to check if his tree is indeed k-multihedgehog.
Input
First line of input contains 2 integers n, k (1 ≤ n ≤ 10^{5}, 1 ≤ k ≤ 10^{9}) — number of vertices and hedgehog parameter.
Next n-1 lines contains two integers u v (1 ≤ u, v ≤ n; u ≠ v) — indices of vertices connected by edge.
It is guaranteed that given graph is a tree.
Output
Print "Yes" (without quotes), if given graph is k-multihedgehog, and "No" (without quotes) otherwise.
Examples
Input
14 2
1 4
2 4
3 4
4 13
10 5
11 5
12 5
14 5
5 13
6 7
8 6
13 6
9 6
Output
Yes
Input
3 1
1 3
2 3
Output
No
Note
2-multihedgehog from the first example looks like this:
<image>
Its center is vertex 13. Hedgehogs created on last step are: [4 (center), 1, 2, 3], [6 (center), 7, 8, 9], [5 (center), 10, 11, 12, 13].
Tree from second example is not a hedgehog because degree of center should be at least 3.
### Input:
3 1
1 3
2 3
### Output:
No
### Input:
14 2
1 4
2 4
3 4
4 13
10 5
11 5
12 5
14 5
5 13
6 7
8 6
13 6
9 6
### Output:
Yes
### Code:
from sys import stdin
from collections import deque
n, k = map(int, stdin.readline().split())
graph = [[] for _ in range(n)]
leaf = -1
for _ in range(n-1):
a,b = map(int,stdin.readline().split())
graph[a - 1].append(b - 1)
graph[b - 1].append(a - 1)
def bfs(G, s):
# la cola comienza con el vertice desde el cual hacemos bfs
Q = deque()
Q.append(s)
# al inicio todas las distancias comienzan en infinito, por las
# restricciones del problema ningun camino va a ser de ese tamanno
infinite = 10 ** 6
d = [infinite]*n
parent = [-1]*n
valid = True
# la distancia del vertice raiz es 0
d[s] = 0
while Q:
# visitamos u
u = Q.popleft()
not_visited_count = 0
# visitamos cada adyacente de u
for v in G[u]:
# si no lo hemos visitado, le ponemos distancia y
# lo agregamos a la cola para visitar sus adyacentes
if d[v] == infinite:
d[v] = d[u] + 1
parent[v] = u
Q.append(v)
not_visited_count += 1
if not_visited_count < 3 and d[u] != k:
valid = False
# retornamos el array d, que es el de las distancias del
# nodo s al resto de los nodos del grafo
return d, parent, valid
leaf = -1
for i,v in enumerate(graph):
if len(v) == 1:
leaf = i
break
d, parent, _ = bfs(graph,leaf)
center = -1
farthest_leaf = -1
path = 2*k
for i,level in enumerate(d):
if level == path:
farthest_leaf = i
break
if len(graph[farthest_leaf]) != 1 or farthest_leaf == -1:
print("NO")
exit()
for _ in range(k):
center = parent[farthest_leaf]
farthest_leaf = center
_, _, valid = bfs(graph,center)
if valid:
print("YES")
else:
print("NO")
|
1089_L. Lazyland_28532
|
The kingdom of Lazyland is the home to n idlers. These idlers are incredibly lazy and create many problems to their ruler, the mighty King of Lazyland.
Today k important jobs for the kingdom (k ≤ n) should be performed. Every job should be done by one person and every person can do at most one job. The King allowed every idler to choose one job they wanted to do and the i-th idler has chosen the job a_i.
Unfortunately, some jobs may not be chosen by anyone, so the King has to persuade some idlers to choose another job. The King knows that it takes b_i minutes to persuade the i-th idler. He asked his minister of labour to calculate the minimum total time he needs to spend persuading the idlers to get all the jobs done. Can you help him?
Input
The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 10^5) — the number of idlers and the number of jobs.
The second line of the input contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ k) — the jobs chosen by each idler.
The third line of the input contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 10^9) — the time the King needs to spend to persuade the i-th idler.
Output
The only line of the output should contain one number — the minimum total time the King needs to spend persuading the idlers to get all the jobs done.
Examples
Input
8 7
1 1 3 1 5 3 7 1
5 7 4 8 1 3 5 2
Output
10
Input
3 3
3 1 2
5 3 4
Output
0
Note
In the first example the optimal plan is to persuade idlers 1, 6, and 8 to do jobs 2, 4, and 6.
In the second example each job was chosen by some idler, so there is no need to persuade anyone.
|
n,k = map(int,input().split())
s = list(map(int,input().split()))
p = list(map(int,input().split()))
r = {}
r2 = []
for i in range(n):
if s[i] in r:
if r[s[i]]>p[i]:
r2.append(p[i])
else:
r2.append(r[s[i]])
r[s[i]] = p[i]
else:
r[s[i]] = p[i]
r1 = k-len(r)
#print(r,r2)
print(sum(sorted(r2)[:r1]))
|
{
"input": [
"3 3\n3 1 2\n5 3 4\n",
"8 7\n1 1 3 1 5 3 7 1\n5 7 4 8 1 3 5 2\n",
"2 2\n1 1\n1117 13\n",
"2 1\n1 1\n7 13\n",
"13 11\n6 1 9 9 10 7 3 11 1 4 11 4 11\n48 19 90 85 6 46 38 99 41 67 79 1 27\n",
"1 1\n1\n1000000000\n",
"13 3\n3 1 3 1 1 1 3 3 1 3 3 3 3\n38 75 29 50 99 5 44 33 45 71 3 57 57\n",
"14 6\n2 3 6 6 6 2 5 3 5 5 5 6 5 5\n56 41 19 81 19 32 99 37 97 20 90 44 19 79\n",
"10 10\n6 6 2 5 1 1 5 5 6 6\n48 40 40 98 40 97 90 91 41 36\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6\n47 4 41 56 75 16 29 45 100 76 53 48 79 30 56 84 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 42 47 55\n",
"15 15\n12 1 9 10 9 10 2 5 10 12 2 10 2 1 8\n47 20 16 2 55 93 53 11 24 74 31 17 32 95 91\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 45 45 34 51 58 89 73 28 4 85 54 18 56 97 24\n",
"12 9\n6 8 2 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 12 80 77 94 31\n",
"19 2\n1 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 25 14 51 10 53 35 28 51 60 73 31 22 66\n",
"2 2\n2 2\n7 13\n",
"2 1\n1 1\n6 13\n",
"13 11\n6 1 9 9 10 7 3 11 1 4 11 4 11\n48 19 90 85 2 46 38 99 41 67 79 1 27\n",
"13 3\n3 1 3 1 1 1 3 3 1 3 3 3 3\n38 75 29 50 99 5 44 33 77 71 3 57 57\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 84 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 72 47 55\n",
"15 15\n12 1 9 10 9 10 2 5 10 12 2 10 2 1 8\n47 20 16 2 55 93 53 11 24 74 31 11 32 95 91\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 45 45 34 51 58 89 73 28 4 85 54 18 56 97 44\n",
"12 9\n6 8 2 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 22 80 77 94 31\n",
"2 2\n2 2\n7 12\n",
"8 7\n1 1 3 1 5 3 7 1\n5 7 4 8 1 1 5 2\n",
"13 11\n6 1 9 9 10 7 3 8 1 4 11 4 11\n48 19 90 85 2 46 38 99 41 67 79 1 27\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 84 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 72 12 55\n",
"15 15\n12 1 9 10 9 10 2 5 10 12 2 10 2 1 8\n47 20 16 2 55 93 53 11 24 74 31 6 32 95 91\n",
"12 9\n6 8 3 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 22 80 77 94 31\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 7 4\n16 45 45 34 51 58 89 73 28 4 85 87 18 20 97 44\n",
"12 9\n6 8 3 6 8 2 6 6 9 5 1 1\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 87 135 60 86\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 7 4 4 7 4\n16 45 45 34 51 58 89 73 28 4 85 87 18 20 97 44\n",
"18 12\n6 6 6 6 6 6 6 6 6 12 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 87 135 60 86\n",
"18 12\n6 6 6 6 6 6 6 6 6 12 1 3 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 87 135 60 86\n",
"16 16\n8 7 9 6 9 16 11 13 13 5 8 7 4 4 7 4\n21 45 45 34 51 58 89 73 28 4 85 87 18 20 97 44\n",
"12 9\n6 1 3 6 6 2 6 6 9 5 2 1\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"16 16\n8 7 9 6 9 16 11 13 13 5 8 7 4 5 7 4\n21 45 45 34 51 58 89 73 28 4 85 87 18 20 155 44\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 6 6 6 6\n47 4 41 56 75 24 29 6 100 112 53 48 79 30 87 135 60 87\n",
"16 16\n8 7 9 6 9 16 11 13 13 5 8 7 4 5 6 4\n21 45 45 34 51 58 89 73 28 4 85 87 18 20 155 44\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 6 6 6 6\n47 4 41 56 75 24 29 10 100 112 53 48 79 30 87 135 60 87\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 24 29 10 100 112 53 48 79 30 87 135 60 87\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 24 29 10 100 112 53 48 79 30 87 135 10 87\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 1 29 10 100 112 53 48 79 30 87 135 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 53 48 79 30 87 135 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 53 48 79 30 87 12 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 53 3 79 30 87 12 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 2 6 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 53 3 79 30 87 12 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 2 9 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 53 3 79 30 87 12 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 2 9 6 10 6 6 6\n47 4 41 26 75 0 29 10 100 112 72 3 79 30 87 12 10 87\n",
"14 6\n2 3 6 6 6 2 5 3 5 5 5 6 5 5\n56 41 19 81 19 32 99 37 97 20 142 44 19 79\n",
"10 10\n6 6 2 5 1 1 5 5 6 6\n76 40 40 98 40 97 90 91 41 36\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 7 6 6 6 6 6 6 6\n47 4 41 56 75 16 29 45 100 76 53 48 79 30 56 84 60 86\n",
"12 9\n7 8 2 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 12 80 77 94 31\n",
"8 7\n1 1 3 1 5 3 7 1\n5 14 4 8 1 3 5 2\n",
"13 11\n6 1 9 9 10 7 3 11 1 4 11 2 11\n48 19 90 85 2 46 38 99 41 67 79 1 27\n",
"13 5\n3 1 3 1 1 1 3 3 1 3 3 3 3\n38 75 29 50 99 5 44 33 77 71 3 57 57\n",
"18 12\n6 6 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 84 60 86\n",
"12 9\n6 8 2 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 21 59 22 80 77 94 31\n",
"18 12\n6 6 6 6 6 6 6 5 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 135 60 86\n",
"19 2\n1 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 25 14 51 10 53 35 28 51 60 73 51 22 66\n",
"3 3\n3 1 2\n5 3 6\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 45 45 34 51 58 89 73 28 4 85 54 18 20 97 44\n",
"19 2\n1 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 25 14 51 10 53 35 28 51 60 73 51 22 66\n",
"2 2\n1 2\n7 12\n",
"8 7\n1 1 3 1 5 3 7 1\n5 12 4 8 1 1 5 2\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 135 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 85 12 55\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 45 45 34 51 58 89 73 28 4 85 87 18 20 97 44\n",
"12 9\n6 8 3 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 56 135 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 85 2 55\n",
"12 9\n6 1 3 6 8 2 6 6 9 5 1 1\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"16 16\n8 7 9 6 9 16 11 13 13 5 8 7 4 4 7 4\n16 45 45 34 51 58 89 73 28 4 85 87 18 20 97 44\n",
"12 9\n6 1 3 6 6 2 6 6 9 5 1 1\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 87 135 60 86\n",
"16 16\n8 7 9 6 9 16 11 13 13 5 8 7 4 4 7 4\n21 45 45 34 51 58 89 73 28 4 85 87 18 20 155 44\n",
"18 12\n6 3 6 6 6 6 6 6 6 12 1 3 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 87 135 60 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 3 6 6 10 6 6 6\n47 4 41 56 75 1 29 10 100 112 53 48 79 30 87 135 10 87\n",
"18 12\n6 3 1 6 6 6 6 6 6 12 1 2 9 6 10 6 6 6\n47 4 41 56 75 0 29 10 100 112 72 3 79 30 87 12 10 87\n",
"13 3\n3 1 3 1 1 1 3 3 1 3 3 3 3\n38 75 29 50 99 5 44 33 45 71 3 24 57\n",
"19 2\n1 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 36 14 51 10 53 35 28 51 60 73 31 22 66\n",
"2 1\n1 1\n6 11\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 45 45 34 51 58 89 73 28 4 85 54 18 56 112 44\n",
"19 2\n1 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 25 14 51 10 53 26 28 51 60 73 51 22 66\n",
"2 2\n2 1\n7 12\n",
"3 3\n3 2 2\n5 3 6\n",
"8 7\n1 1 3 1 5 3 7 1\n5 7 4 8 1 1 5 1\n",
"13 11\n6 1 9 9 10 7 3 8 1 4 11 4 11\n48 19 90 85 2 46 38 99 41 65 79 1 27\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 76 53 48 79 30 56 149 60 86\n",
"18 12\n2 9 6 7 12 8 1 2 2 2 1 1 7 11 9 7 8 11\n43 40 3 7 5 55 95 1 19 61 41 15 24 10 52 72 12 55\n",
"16 16\n8 7 9 6 9 16 11 13 13 15 8 5 4 4 9 4\n16 1 45 34 51 58 89 73 28 4 85 54 18 20 97 44\n",
"12 9\n6 8 3 6 8 2 6 6 6 5 1 1\n59 27 78 92 31 26 59 22 90 77 94 31\n",
"19 2\n1 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 1 2 2\n92 91 86 3 32 40 25 9 51 10 53 35 28 51 60 73 51 22 66\n",
"8 7\n1 1 4 1 5 3 7 1\n5 12 4 8 1 1 5 2\n",
"12 9\n6 8 3 6 8 2 6 6 6 5 1 2\n59 27 78 92 31 26 59 22 65 77 94 31\n",
"18 12\n6 6 6 6 6 6 6 6 6 6 1 1 6 6 6 6 6 6\n47 4 41 56 75 24 29 45 100 112 53 48 79 30 56 135 60 86\n",
"18 12\n2 9 6 7 12 8 1 1 2 2 1 1 7 11 9 7 8 11\n43 40 2 7 5 55 95 1 19 61 41 15 24 10 52 85 2 55\n",
"12 9\n6 8 3 6 8 2 6 6 9 5 1 1\n59 27 78 92 31 31 59 22 65 77 94 31\n"
],
"output": [
"0",
"10",
"13",
"0",
"47",
"0",
"3",
"38",
"338",
"425",
"33",
"189",
"182",
"96",
"0",
"7",
"0\n",
"47\n",
"3\n",
"433\n",
"33\n",
"183\n",
"202\n",
"106\n",
"7\n",
"8\n",
"20\n",
"380\n",
"30\n",
"178\n",
"80\n",
"172\n",
"49\n",
"384\n",
"259\n",
"324\n",
"276\n",
"264\n",
"75\n",
"248\n",
"237\n",
"195\n",
"241\n",
"185\n",
"148\n",
"125\n",
"124\n",
"95\n",
"94\n",
"91\n",
"61\n",
"58\n",
"38\n",
"338\n",
"372\n",
"65\n",
"10\n",
"46\n",
"37\n",
"409\n",
"101\n",
"335\n",
"0\n",
"0\n",
"178\n",
"0\n",
"0\n",
"8\n",
"380\n",
"30\n",
"178\n",
"80\n",
"380\n",
"20\n",
"49\n",
"259\n",
"80\n",
"276\n",
"264\n",
"276\n",
"125\n",
"61\n",
"3\n",
"0\n",
"0\n",
"202\n",
"0\n",
"0\n",
"3\n",
"7\n",
"20\n",
"380\n",
"30\n",
"178\n",
"80\n",
"0\n",
"7\n",
"75\n",
"380\n",
"20\n",
"49\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The kingdom of Lazyland is the home to n idlers. These idlers are incredibly lazy and create many problems to their ruler, the mighty King of Lazyland.
Today k important jobs for the kingdom (k ≤ n) should be performed. Every job should be done by one person and every person can do at most one job. The King allowed every idler to choose one job they wanted to do and the i-th idler has chosen the job a_i.
Unfortunately, some jobs may not be chosen by anyone, so the King has to persuade some idlers to choose another job. The King knows that it takes b_i minutes to persuade the i-th idler. He asked his minister of labour to calculate the minimum total time he needs to spend persuading the idlers to get all the jobs done. Can you help him?
Input
The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 10^5) — the number of idlers and the number of jobs.
The second line of the input contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ k) — the jobs chosen by each idler.
The third line of the input contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 10^9) — the time the King needs to spend to persuade the i-th idler.
Output
The only line of the output should contain one number — the minimum total time the King needs to spend persuading the idlers to get all the jobs done.
Examples
Input
8 7
1 1 3 1 5 3 7 1
5 7 4 8 1 3 5 2
Output
10
Input
3 3
3 1 2
5 3 4
Output
0
Note
In the first example the optimal plan is to persuade idlers 1, 6, and 8 to do jobs 2, 4, and 6.
In the second example each job was chosen by some idler, so there is no need to persuade anyone.
### Input:
3 3
3 1 2
5 3 4
### Output:
0
### Input:
8 7
1 1 3 1 5 3 7 1
5 7 4 8 1 3 5 2
### Output:
10
### Code:
n,k = map(int,input().split())
s = list(map(int,input().split()))
p = list(map(int,input().split()))
r = {}
r2 = []
for i in range(n):
if s[i] in r:
if r[s[i]]>p[i]:
r2.append(p[i])
else:
r2.append(r[s[i]])
r[s[i]] = p[i]
else:
r[s[i]] = p[i]
r1 = k-len(r)
#print(r,r2)
print(sum(sorted(r2)[:r1]))
|
1108_E2. Array and Segments (Hard version)_28536
|
The only difference between easy and hard versions is a number of elements in the array.
You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.
You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.
You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].
You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.
Note that you can choose the empty set.
If there are multiple answers, you can print any.
If you are Python programmer, consider using PyPy instead of Python when you submit your code.
Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.
The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.
The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.
Output
In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.
In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.
In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.
If there are multiple answers, you can print any.
Examples
Input
5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3
Output
6
2
4 1
Input
5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5
Output
7
2
3 2
Input
1 0
1000000
Output
0
0
Note
In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.
In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.
In the third example you cannot do anything so the answer is 0.
|
def main():
n, m = map(int, input().split())
aa = list(map(int, input().split()))
res = max(aa) - min(aa)
ll, rr = [n + 1], [n + 1]
segments = res_segments = [False] * (m + 1)
bounds = {0, n, n + 1}
for _ in range(m):
l, r = map(int, input().split())
l -= 1
ll.append(l)
rr.append(r)
bounds.add(l)
bounds.add(r)
xlat = sorted(bounds)
mi, ma = [], []
for l, r in zip(xlat, xlat[1:-1]):
t = aa[l:r]
mi.append(min(t))
ma.append(max(t))
bounds = {x: i for i, x in enumerate(xlat)}
for xx in (ll, rr):
for i, x in enumerate(xx):
xx[i] = bounds[x]
il, ir = (sorted(range(m + 1), key=xx.__getitem__, reverse=True) for xx in (ll, rr))
for i in range(len(xlat) - 1):
while True:
k = il[-1]
lo = ll[k]
if lo > i:
break
segments[k] = True
for j in range(lo, rr[k]):
mi[j] -= 1
ma[j] -= 1
del il[-1]
x = max(ma) - min(mi)
if res < x:
res = x
res_segments = segments[:]
while True:
k = ir[-1]
hi = rr[k]
if hi > i:
break
segments[k] = False
for j in range(ll[k], hi):
mi[j] += 1
ma[j] += 1
del ir[-1]
print(res)
segments = [i for i, f in enumerate(res_segments) if f]
print(len(segments))
print(*segments)
if __name__ == '__main__':
main()
|
{
"input": [
"5 4\n2 -2 3 1 4\n3 5\n3 4\n2 4\n2 5\n",
"1 0\n1000000\n",
"5 4\n2 -2 3 1 2\n1 3\n4 5\n2 5\n1 3\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n4 5\n2 5\n3 3\n1 1\n5 5\n3 4\n2 4\n5 5\n",
"2 5\n-1 -7\n1 2\n2 2\n2 2\n2 2\n1 1\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n5 5\n",
"50 2\n5 -5 8 5 6 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 9 -7 -5 2 -9 -1 -1 8 -6 -5 10 -5 -2 10 5 0 10 -9 -9 3 -2\n2 21\n28 38\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"2 50\n-8 -6\n2 2\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n1 1\n2 2\n2 2\n2 2\n1 1\n1 2\n2 2\n1 1\n2 2\n1 1\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n1 1\n1 2\n1 1\n2 2\n2 2\n2 2\n1 2\n2 2\n2 2\n2 2\n1 1\n1 1\n1 2\n2 2\n1 2\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n4 5\n2 5\n3 3\n1 1\n5 5\n3 4\n2 4\n5 5\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n5 5\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n4 5\n2 5\n3 3\n1 1\n5 5\n3 4\n2 4\n5 5\n",
"1 1\n-10\n1 1\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n5 5\n",
"1 5\n9\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"50 1\n-8 8 -6 -4 -1 8 6 7 -7 3 -2 -3 6 10 2 8 -2 -4 2 9 0 7 0 9 5 6 -2 -1 -7 -9 -6 1 9 -1 -6 -5 -4 2 -2 4 8 7 -9 7 6 3 -8 -3 4 0\n27 41\n",
"50 2\n5 -5 8 5 6 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 9 -7 -5 2 -9 -1 -1 8 -6 -5 10 -5 -2 10 5 0 10 -9 -9 3 -2\n2 21\n28 38\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n5 5\n",
"100 1\n-3 4 8 -1 0 7 9 8 10 3 8 7 -8 -7 -9 -7 -8 5 7 5 -10 -5 9 -2 3 5 -10 -10 -2 7 10 9 8 8 2 3 -1 -8 -6 2 -5 4 6 -1 -5 7 10 -2 -3 2 -5 1 2 8 -7 -3 6 -6 -2 -3 -4 -1 -8 4 -10 6 -4 8 4 -9 -2 7 -4 -6 7 -1 1 -7 -4 2 -4 6 -6 -8 -9 -8 -1 -10 -1 -4 -4 -5 -9 -1 7 2 -7 -7 -2 -1\n83 92\n",
"5 1\n8 -5 -4 4 -8\n1 3\n",
"1 50\n5\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"2 50\n-8 -6\n2 2\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n1 1\n2 2\n2 2\n2 2\n1 1\n1 2\n2 2\n1 1\n2 2\n1 1\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n1 1\n1 2\n1 1\n2 2\n2 2\n2 2\n1 2\n2 2\n2 2\n2 2\n1 1\n1 1\n1 2\n2 2\n1 2\n",
"2 0\n9 0\n",
"5 4\n2 -2 3 1 2\n1 3\n4 5\n2 5\n1 3\n",
"2 50\n-8 -6\n2 2\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n1 1\n2 2\n2 2\n2 2\n1 1\n1 2\n2 2\n1 1\n2 2\n1 1\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n1 1\n1 2\n1 1\n2 2\n2 2\n2 2\n1 2\n2 2\n2 2\n2 2\n1 1\n1 1\n1 2\n2 2\n1 2\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"2 5\n-1 -7\n1 2\n2 2\n2 2\n2 2\n1 1\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"100 0\n6 0 3 6 1 -7 9 -2 -8 -4 -6 -2 7 -3 0 4 -8 10 -2 5 -2 3 9 -7 -2 0 -4 -7 3 7 7 -2 -5 2 9 7 -9 1 2 -8 9 0 8 2 -4 3 -10 0 3 8 3 -6 -8 2 0 10 0 -3 1 2 7 -6 -9 -4 7 7 -2 -4 2 -4 -4 -6 2 0 10 -6 -1 -6 -10 -2 3 8 -10 -10 10 0 1 8 -8 5 9 -6 -2 0 5 -6 -6 6 -10 -6\n",
"69 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 3\n",
"1 2\n-7\n1 1\n1 1\n",
"1 0\n-1\n",
"1 5\n9\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"2 50\n-8 -6\n2 2\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n2 2\n1 1\n1 1\n1 1\n2 2\n2 2\n1 1\n2 2\n2 2\n2 2\n1 1\n1 2\n2 2\n1 1\n2 2\n1 1\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n1 1\n1 2\n1 1\n2 2\n2 2\n2 2\n1 2\n2 2\n2 2\n2 2\n1 1\n1 1\n1 2\n2 2\n1 2\n",
"50 0\n-7 8 -10 -6 10 -2 -2 -4 0 0 1 9 -8 -7 -6 3 2 -3 10 -5 -9 7 -4 -9 1 -3 3 -3 -1 7 -4 3 -8 6 -3 -9 9 -10 -6 -10 5 3 -3 -3 3 -5 -3 -9 -7 2\n",
"2 2\n-4 7\n2 2\n2 2\n",
"1 50\n5\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"100 2\n-7 3 0 -4 -10 1 -4 -2 3 7 2 -1 2 -3 -1 -6 -5 4 -2 2 -10 7 -8 -1 -5 10 2 9 9 3 8 -1 5 -3 -10 7 -10 5 -9 -9 -1 -5 1 -3 10 5 5 -8 -8 4 -5 0 -5 10 -9 1 0 8 -4 0 6 0 -10 8 7 -8 8 7 6 3 -9 -10 1 -5 9 -4 -4 0 -10 -8 -6 -4 3 -3 1 0 0 5 5 4 -8 1 5 2 1 1 10 -3 -7 0\n69 88\n96 96\n",
"1 100\n-4\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"5 4\n2 -2 3 1 4\n3 5\n3 4\n2 4\n2 5\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n4 5\n2 5\n3 3\n1 1\n5 5\n3 4\n2 4\n5 5\n",
"5 2\n-1 -5 0 5 -1\n3 4\n2 5\n",
"1 1\n-10\n1 1\n",
"1 100\n-4\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"1 2\n-7\n1 1\n1 1\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"100 2\n-7 3 0 -4 -10 1 -4 -2 3 7 2 -1 2 -3 -1 -6 -5 4 -2 2 -10 7 -8 -1 -5 10 2 9 9 3 8 -1 5 -3 -10 7 -10 5 -9 -9 -1 -5 1 -3 10 5 5 -8 -8 4 -5 0 -5 10 -9 1 0 8 -4 0 6 0 -10 8 7 -8 8 7 6 3 -9 -10 1 -5 9 -4 -4 0 -10 -8 -6 -4 3 -3 1 0 0 5 5 4 -8 1 5 2 1 1 10 -3 -7 0\n69 88\n96 96\n",
"5 0\n0 -8 -5 -6 10\n",
"2 1\n5 8\n1 1\n",
"1 0\n-1\n",
"2 5\n-1 -7\n1 2\n2 2\n2 2\n2 2\n1 1\n",
"2 5\n-1 -7\n1 2\n2 2\n2 1\n2 2\n1 1\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 12 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -6 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"5 5\n2 6 -2 1 -6\n3 3\n4 5\n4 4\n2 3\n5 5\n",
"50 2\n5 -5 8 5 0 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 9 -7 -5 2 -9 -1 -1 8 -6 -5 10 -5 -2 10 5 0 10 -9 -9 3 -2\n2 21\n28 38\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n4 5\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n4 5\n2 5\n3 3\n1 2\n5 5\n3 4\n2 4\n5 5\n",
"1 1\n-8\n1 1\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 0 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"50 1\n-5 8 -6 -4 -1 8 6 7 -7 3 -2 -3 6 10 2 8 -2 -4 2 9 0 7 0 9 5 6 -2 -1 -7 -9 -6 1 9 -1 -6 -5 -4 2 -2 4 8 7 -9 7 6 3 -8 -3 4 0\n27 41\n",
"5 0\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 3\n5 5\n",
"100 1\n-3 4 8 0 0 7 9 8 10 3 8 7 -8 -7 -9 -7 -8 5 7 5 -10 -5 9 -2 3 5 -10 -10 -2 7 10 9 8 8 2 3 -1 -8 -6 2 -5 4 6 -1 -5 7 10 -2 -3 2 -5 1 2 8 -7 -3 6 -6 -2 -3 -4 -1 -8 4 -10 6 -4 8 4 -9 -2 7 -4 -6 7 -1 1 -7 -4 2 -4 6 -6 -8 -9 -8 -1 -10 -1 -4 -4 -5 -9 -1 7 2 -7 -7 -2 -1\n83 92\n",
"5 1\n8 -5 -4 1 -8\n1 3\n",
"5 4\n1 -2 3 1 2\n1 3\n4 5\n2 5\n1 3\n",
"2 5\n-1 -7\n1 2\n2 2\n2 2\n2 2\n1 2\n",
"100 0\n6 0 3 6 1 -7 9 -2 -8 -4 -6 -2 7 -3 0 4 -8 10 -2 5 -2 3 9 -7 -2 0 -4 -7 3 7 7 -2 -5 2 9 7 -9 1 2 -8 9 0 8 2 -4 3 -10 0 3 8 3 -8 -8 2 0 10 0 -3 1 2 7 -6 -9 -4 7 7 -2 -4 2 -4 -4 -6 2 0 10 -6 -1 -6 -10 -2 3 8 -10 -10 10 0 1 8 -8 5 9 -6 -2 0 5 -6 -6 6 -10 -6\n",
"69 1\n1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 3\n",
"2 2\n-4 7\n2 2\n1 2\n",
"100 2\n-7 3 0 -4 -10 1 -4 -2 3 7 2 -1 2 -3 -1 -6 -5 4 -2 2 -10 7 -8 -1 -5 10 2 9 9 3 8 -1 5 -3 -10 7 -10 5 -9 -9 -1 -5 1 -3 10 5 5 -8 -8 4 -5 0 -5 10 -9 1 0 8 -4 0 6 0 -10 8 7 -8 15 7 6 3 -9 -10 1 -5 9 -4 -4 0 -10 -8 -6 -4 3 -3 1 0 0 5 5 4 -8 1 5 2 1 1 10 -3 -7 0\n69 88\n96 96\n",
"5 4\n2 -1 3 1 4\n3 5\n3 4\n2 4\n2 5\n",
"2 0\n5 8\n1 1\n",
"5 4\n2 -2 3 2 4\n3 5\n3 4\n2 4\n2 5\n",
"5 4\n2 -2 3 1 2\n1 2\n4 5\n2 5\n1 3\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n20 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n44 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"5 4\n1 0 3 1 2\n1 3\n4 5\n2 5\n1 3\n",
"100 0\n6 0 3 6 1 -7 9 -2 -8 -4 -6 -2 7 -3 0 4 -8 10 -2 5 -2 3 9 -13 -2 0 -4 -7 3 7 7 -2 -5 2 9 7 -9 1 2 -8 9 0 8 2 -4 3 -10 0 3 8 3 -8 -8 2 0 10 0 -3 1 2 7 -6 -9 -4 7 7 -2 -4 2 -4 -4 -6 2 0 10 -6 -1 -6 -10 -2 3 8 -10 -10 10 0 1 8 -8 5 9 -6 -2 0 5 -6 -6 6 -10 -6\n",
"50 0\n-7 8 -10 -6 10 -2 -2 -4 0 0 1 9 -8 -11 -6 3 2 -3 10 -5 -9 7 -4 -9 1 -6 3 -3 -1 7 -4 3 -8 6 -3 -9 9 -10 -6 -10 5 3 -3 -3 3 -5 -3 -9 -7 2\n",
"5 4\n2 -1 3 1 0\n3 5\n3 4\n2 4\n2 5\n",
"2 0\n4 8\n1 1\n",
"5 4\n2 -2 3 2 0\n3 5\n3 4\n2 4\n2 5\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 36\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -2 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"5 5\n2 6 -2 1 -6\n3 5\n4 4\n4 4\n2 3\n5 5\n",
"50 2\n5 -5 8 5 6 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 9 -7 -5 2 -9 -1 -1 8 -6 -5 10 -5 -2 10 5 0 10 -9 -9 4 -2\n2 21\n28 38\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 7 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 20\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n20 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 0 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -7 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"50 5\n0 2 1 1 -2 7 -3 3 4 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"1 0\n0\n",
"50 0\n-7 8 -10 -6 10 -2 -2 -4 0 0 1 9 -8 -7 -6 3 2 -3 10 -5 -9 7 -4 -9 1 -6 3 -3 -1 7 -4 3 -8 6 -3 -9 9 -10 -6 -10 5 3 -3 -3 3 -5 -3 -9 -7 2\n",
"5 50\n-5 4 -4 -1 5\n4 5\n4 5\n1 1\n1 5\n1 1\n1 1\n3 5\n4 5\n5 5\n1 1\n3 3\n1 4\n1 3\n4 5\n4 5\n5 5\n1 3\n2 3\n3 4\n5 5\n1 2\n4 4\n2 2\n1 3\n5 5\n2 5\n2 2\n3 3\n1 1\n4 4\n2 3\n3 4\n5 5\n5 5\n5 5\n4 4\n5 5\n1 4\n3 3\n3 3\n4 4\n1 1\n2 5\n2 5\n3 3\n1 1\n5 5\n3 4\n2 4\n5 5\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -7 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"100 2\n-7 3 0 -4 -10 1 -4 -2 3 7 2 -1 2 -3 -1 -6 -5 4 -2 2 -10 7 -8 -1 -5 10 2 9 9 3 8 -1 5 0 -10 7 -10 5 -9 -9 -1 -5 1 -3 10 5 5 -8 -8 4 -5 0 -5 10 -9 1 0 8 -4 0 6 0 -10 8 7 -8 8 7 6 3 -9 -10 1 -5 9 -4 -4 0 -10 -8 -6 -4 3 -3 1 0 0 5 5 4 -8 1 5 2 1 1 10 -3 -7 0\n69 88\n96 96\n",
"2 5\n-1 -7\n1 2\n2 2\n2 1\n1 2\n1 1\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 12 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 12\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n13 24\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -6 -1 -4 -3 -4 -4 -6 6 -9 5 0 -7 -8 3 8 -4 1 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"5 5\n2 6 -2 0 -6\n3 3\n4 5\n4 4\n2 3\n5 5\n",
"50 2\n5 -5 8 5 0 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 9 -7 -5 2 -9 -1 -1 8 -6 -5 9 -5 -2 10 5 0 10 -9 -9 3 -2\n2 21\n28 38\n",
"5 5\n2 6 -2 1 -6\n3 5\n5 5\n4 4\n2 3\n4 5\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 8 -9 -9 -2 -8 6 -2 7 0 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"5 5\n0 6 -2 1 -6\n3 5\n4 4\n4 4\n2 3\n5 5\n",
"50 1\n-5 8 -6 -4 -1 8 6 7 -7 3 -2 -3 6 10 2 8 -2 -4 2 9 0 7 0 9 5 6 -2 -1 -7 -9 -6 1 9 -1 -6 -3 -4 2 -2 4 8 7 -9 7 6 3 -8 -3 4 0\n27 41\n",
"50 2\n5 -5 8 5 6 6 10 -4 8 -10 9 -10 -5 -7 -7 -3 5 -9 7 9 0 -2 8 10 1 -9 -7 -4 8 5 -7 -5 2 -9 -1 -1 8 -6 -5 10 -5 -2 10 5 0 10 -9 -9 4 -2\n2 21\n28 38\n",
"5 0\n2 6 -2 1 -6\n3 5\n4 5\n4 4\n2 5\n5 5\n",
"100 1\n-3 4 8 0 0 7 9 8 10 3 8 7 -8 -7 -9 -7 -8 5 7 5 -10 -5 9 -2 3 5 -10 -10 -2 7 10 9 8 8 2 3 -1 -8 -6 2 -5 4 6 -1 -5 7 10 -2 -3 2 -5 1 2 8 -7 -3 6 -6 -2 -3 -4 -1 -8 4 -10 6 -4 8 4 -9 -2 7 -4 -6 7 -1 1 -7 -4 2 -4 6 -6 -8 -9 -8 -1 -10 -1 -4 -4 -5 -9 -1 7 2 -7 -7 -3 -1\n83 92\n",
"5 1\n8 -5 -4 1 -12\n1 3\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 0 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 0 9 6 5 5 -10 7 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -8 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"50 5\n0 2 1 1 -2 7 -3 3 8 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -7 -6 6 -9 5 0 -9 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"50 5\n0 2 1 1 -2 7 -3 3 4 -1 6 8 -8 -3 0 1 6 1 -5 -1 -4 -3 -4 -4 0 6 -9 5 0 -7 -8 3 8 -4 3 6 -10 -3 6 1 4 1 2 -7 5 -5 5 -2 4 -5\n30 34\n8 25\n48 50\n19 48\n48 49\n",
"69 1\n1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 3\n",
"2 2\n-4 8\n2 2\n1 2\n",
"100 5\n-4 10 -7 9 7 2 8 0 4 -4 -5 1 -5 1 6 6 0 -3 8 -4 -10 10 9 6 9 9 0 1 9 5 7 7 7 5 -10 -7 -7 0 6 -9 -9 -2 -8 6 -2 7 -2 -10 -3 -3 -9 2 -9 -1 8 -9 -3 3 -9 -8 3 -9 -4 0 0 1 -8 -5 8 -4 -5 -4 6 8 3 9 6 5 5 -10 2 -1 0 3 6 6 10 -8 -9 2 3 -8 -3 -1 5 7 3 1 -7 -6\n27 59\n64 94\n79 87\n9 57\n37 91\n",
"100 2\n-7 3 0 -4 -10 1 -4 -2 3 7 2 -1 2 -3 -1 -6 -5 4 -2 2 -10 7 -8 -1 -5 10 2 9 9 3 8 -1 5 0 -10 7 -10 5 -9 -9 -1 -5 1 -3 10 5 5 -8 -8 4 -5 0 -7 10 -9 1 0 8 -4 0 6 0 -10 8 7 -8 8 7 6 3 -9 -10 1 -5 9 -4 -4 0 -10 -8 -6 -4 3 -3 1 0 0 5 5 4 -8 1 5 2 1 1 10 -3 -7 0\n69 88\n96 96\n",
"5 4\n0 -2 3 1 2\n1 2\n4 5\n2 5\n1 3\n",
"50 50\n1 -9 8 -9 5 -4 -4 3 -2 -1 3 -8 -6 -6 2 -5 -1 -2 -5 10 2 0 10 10 5 -3 12 -1 -9 9 -10 4 7 0 -6 0 -1 4 8 0 -3 -8 10 10 6 6 -3 -5 -3 -8\n28 41\n28 49\n49 49\n6 38\n22 30\n50 50\n41 45\n30 32\n17 44\n24 25\n27 39\n17 39\n50 50\n10 14\n11 12\n18 28\n11 12\n36 42\n45 49\n29 36\n32 44\n19 41\n6 36\n39 40\n32 44\n41 47\n6 47\n44 48\n31 48\n45 48\n43 48\n1 14\n46 50\n50 50\n38 40\n18 29\n19 29\n20 50\n3 21\n47 50\n6 24\n38 49\n14 48\n28 39\n36 50\n10 32\n5 12\n14 18\n13 23\n19 24\n"
],
"output": [
"7\n2\n3 4 ",
"0\n0\n",
"6\n2\n1 4 ",
"25\n20\n4 7 11 12 13 17 18 19 24 26 28 31 32 38 39 40 44 45 48 49 ",
"9\n4\n1 2 3 4 ",
"34\n17\n1 2 4 5 9 11 12 20 22 23 27 36 37 38 43 44 46 ",
"19\n1\n4 ",
"15\n3\n1 2 5 ",
"21\n1\n1 ",
"34\n17\n1 2 4 5 9 11 12 20 22 23 27 36 37 38 43 44 46 ",
"23\n25\n1 2 5 7 8 12 13 14 18 19 21 22 23 26 28 30 33 35 39 40 41 43 44 45 49 ",
"34\n17\n1 2 4 5 9 11 12 20 22 23 27 36 37 38 43 44 46 ",
"25\n20\n4 7 11 12 13 17 18 19 24 26 28 31 32 38 39 40 44 45 48 49 ",
"15\n3\n1 2 5 ",
"23\n3\n1 4 5 ",
"25\n20\n4 7 11 12 13 17 18 19 24 26 28 31 32 38 39 40 44 45 48 49 ",
"0\n0\n",
"19\n1\n4 ",
"23\n3\n1 4 5 ",
"15\n3\n1 2 5 ",
"0\n0\n",
"20\n1\n1 ",
"21\n1\n1 ",
"34\n17\n1 2 4 5 9 11 12 20 22 23 27 36 37 38 43 44 46 ",
"15\n3\n1 2 5 ",
"21\n1\n1 ",
"16\n0\n",
"0\n0\n",
"23\n25\n1 2 5 7 8 12 13 14 18 19 21 22 23 26 28 30 33 35 39 40 41 43 44 45 49 ",
"9\n0\n",
"6\n2\n1 4 ",
"23\n25\n1 2 5 7 8 12 13 14 18 19 21 22 23 26 28 30 33 35 39 40 41 43 44 45 49 ",
"23\n3\n1 4 5 ",
"19\n1\n4 ",
"9\n4\n1 2 3 4 ",
"19\n1\n4 ",
"20\n0\n",
"1\n1\n1 ",
"0\n0\n",
"0\n0\n",
"0\n0\n",
"23\n25\n1 2 5 7 8 12 13 14 18 19 21 22 23 26 28 30 33 35 39 40 41 43 44 45 49 ",
"20\n0\n",
"11\n0\n",
"0\n0\n",
"21\n1\n1 ",
"0\n0\n",
"7\n2\n3 4 ",
"25\n20\n4 7 11 12 13 17 18 19 24 26 28 31 32 38 39 40 44 45 48 49 ",
"10\n0\n",
"0\n0\n",
"0\n0\n",
"0\n0\n",
"23\n3\n1 4 5 ",
"21\n1\n1 ",
"18\n0\n",
"4\n1\n1 ",
"0\n0\n",
"9\n4\n1 2 3 4 ",
"8\n3\n2 3 4 \n",
"34\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n",
"19\n4\n1 3 4 5 \n",
"14\n4\n1 2 3 5 \n",
"21\n2\n1 2 \n",
"15\n4\n1 2 3 5 \n",
"25\n30\n3 5 6 10 11 12 13 17 18 19 21 22 23 24 27 28 29 30 31 32 36 38 39 40 41 42 45 46 48 49 \n",
"0\n0\n\n",
"23\n5\n1 2 3 4 5 \n",
"20\n1\n1 \n",
"12\n0\n\n",
"21\n1\n1 \n",
"16\n0\n\n",
"6\n2\n1 4 \n",
"9\n3\n2 3 4 \n",
"20\n0\n\n",
"1\n0\n\n",
"11\n0\n\n",
"26\n2\n1 2 \n",
"6\n2\n2 3 \n",
"3\n0\n\n",
"7\n2\n2 3 \n",
"6\n2\n1 2 \n",
"33\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n",
"4\n2\n1 4 \n",
"23\n0\n\n",
"21\n0\n\n",
"5\n4\n1 2 3 4 \n",
"4\n0\n\n",
"6\n4\n1 2 3 4 \n",
"34\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n",
"19\n4\n1 3 4 5 \n",
"14\n4\n1 2 3 5 \n",
"21\n2\n1 2 \n",
"34\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n",
"23\n5\n1 2 3 4 5 \n",
"19\n4\n1 3 4 5 \n",
"19\n4\n1 3 4 5 \n",
"0\n0\n\n",
"20\n0\n\n",
"25\n30\n3 5 6 10 11 12 13 17 18 19 21 22 23 24 27 28 29 30 31 32 36 38 39 40 41 42 45 46 48 49 \n",
"23\n5\n1 2 3 4 5 \n",
"21\n2\n1 2 \n",
"7\n2\n2 3 \n",
"34\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n",
"19\n4\n1 3 4 5 \n",
"14\n4\n1 2 3 5 \n",
"21\n2\n1 2 \n",
"15\n4\n1 2 3 5 \n",
"23\n5\n1 2 3 4 5 \n",
"14\n4\n1 2 3 5 \n",
"20\n1\n1 \n",
"21\n2\n1 2 \n",
"12\n0\n\n",
"21\n1\n1 \n",
"20\n0\n\n",
"23\n5\n1 2 3 4 5 \n",
"19\n4\n1 3 4 5 \n",
"19\n4\n1 3 4 5 \n",
"1\n0\n\n",
"12\n0\n\n",
"23\n5\n1 2 3 4 5 \n",
"21\n2\n1 2 \n",
"6\n2\n1 2 \n",
"34\n48\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The only difference between easy and hard versions is a number of elements in the array.
You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.
You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.
You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].
You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.
Note that you can choose the empty set.
If there are multiple answers, you can print any.
If you are Python programmer, consider using PyPy instead of Python when you submit your code.
Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.
The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.
The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.
Output
In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.
In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.
In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.
If there are multiple answers, you can print any.
Examples
Input
5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3
Output
6
2
4 1
Input
5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5
Output
7
2
3 2
Input
1 0
1000000
Output
0
0
Note
In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.
In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.
In the third example you cannot do anything so the answer is 0.
### Input:
5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5
### Output:
7
2
3 4
### Input:
1 0
1000000
### Output:
0
0
### Code:
def main():
n, m = map(int, input().split())
aa = list(map(int, input().split()))
res = max(aa) - min(aa)
ll, rr = [n + 1], [n + 1]
segments = res_segments = [False] * (m + 1)
bounds = {0, n, n + 1}
for _ in range(m):
l, r = map(int, input().split())
l -= 1
ll.append(l)
rr.append(r)
bounds.add(l)
bounds.add(r)
xlat = sorted(bounds)
mi, ma = [], []
for l, r in zip(xlat, xlat[1:-1]):
t = aa[l:r]
mi.append(min(t))
ma.append(max(t))
bounds = {x: i for i, x in enumerate(xlat)}
for xx in (ll, rr):
for i, x in enumerate(xx):
xx[i] = bounds[x]
il, ir = (sorted(range(m + 1), key=xx.__getitem__, reverse=True) for xx in (ll, rr))
for i in range(len(xlat) - 1):
while True:
k = il[-1]
lo = ll[k]
if lo > i:
break
segments[k] = True
for j in range(lo, rr[k]):
mi[j] -= 1
ma[j] -= 1
del il[-1]
x = max(ma) - min(mi)
if res < x:
res = x
res_segments = segments[:]
while True:
k = ir[-1]
hi = rr[k]
if hi > i:
break
segments[k] = False
for j in range(ll[k], hi):
mi[j] += 1
ma[j] += 1
del ir[-1]
print(res)
segments = [i for i, f in enumerate(res_segments) if f]
print(len(segments))
print(*segments)
if __name__ == '__main__':
main()
|
1138_B. Circus_28540
|
Polycarp is a head of a circus troupe. There are n — an even number — artists in the troupe. It is known whether the i-th artist can perform as a clown (if yes, then c_i = 1, otherwise c_i = 0), and whether they can perform as an acrobat (if yes, then a_i = 1, otherwise a_i = 0).
Split the artists into two performances in such a way that:
* each artist plays in exactly one performance,
* the number of artists in the two performances is equal (i.e. equal to n/2),
* the number of artists that can perform as clowns in the first performance is the same as the number of artists that can perform as acrobats in the second performance.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 000, n is even) — the number of artists in the troupe.
The second line contains n digits c_1 c_2 … c_n, the i-th of which is equal to 1 if the i-th artist can perform as a clown, and 0 otherwise.
The third line contains n digits a_1 a_2 … a_n, the i-th of which is equal to 1, if the i-th artist can perform as an acrobat, and 0 otherwise.
Output
Print n/2 distinct integers — the indices of the artists that should play in the first performance.
If there are multiple answers, print any.
If there is no solution, print a single integer -1.
Examples
Input
4
0011
0101
Output
1 4
Input
6
000000
111111
Output
-1
Input
4
0011
1100
Output
4 3
Input
8
00100101
01111100
Output
1 2 3 6
Note
In the first example, one of the possible divisions into two performances is as follows: in the first performance artists 1 and 4 should take part. Then the number of artists in the first performance who can perform as clowns is equal to 1. And the number of artists in the second performance who can perform as acrobats is 1 as well.
In the second example, the division is not possible.
In the third example, one of the possible divisions is as follows: in the first performance artists 3 and 4 should take part. Then in the first performance there are 2 artists who can perform as clowns. And the number of artists in the second performance who can perform as acrobats is 2 as well.
|
import sys
import random
N = int(input())
C = list(map(int, input()))
A = list(map(int, input()))
# N = random.randint(20, 40) * 2
# C = [random.randint(0, 1) for i in range(N)]
# A = [random.randint(0, 1) for i in range(N)]
def build_solution(i, j, x, y):
I = (0, 0)
J = (0, 1)
X = (1, 0)
Y = (1, 1)
ans = []
for q in range(N):
p = (C[q], A[q])
if i and p == I:
i -= 1
ans.append(q+1)
elif j and p == J:
j -= 1
ans.append(q+1)
elif x and p == X:
x -= 1
ans.append(q+1)
elif y and p == Y:
y -= 1
ans.append(q+1)
return map(str, ans)
a = b = c = d = 0
for i in range(N):
if C[i] == 0:
if A[i] == 0:
a += 1
else:
b += 1
else:
if A[i] == 0:
c += 1
else:
d += 1
# print(C)
# print(A)
# print(a, b, c, d, "N/2=", N//2)
for i in range(0, a+1):
y = - N//2 + i + b + d
if y < 0:
continue
min_j = max(0, N//2 - i - c - y)
max_j = min(b + 1, N //2 + 1)
# print(i, y, '[', min_j, max_j, ']')
for j in range(min_j, max_j):
x = N//2 - i - j - y
if x < 0:
break
# print("Check ", i, j, 'x, y:', x, y)
if not ((0 <= x <= c) and (0 <= y <= d)):
continue
# print('SOL', i, j, x, y)
sol = build_solution(i, j, x, y)
print(' '.join(sol))
exit(0)
print(-1)
# 1) loop over N
# 2) pick best actor on every iteration
# 3) try to minimize diff between teams
# if len(first) == len(second) and first.score == second.score:
# print(' '.join(map(lambda x: str(x+1), first)))
# else:
# print(-1)
# a, b, c, d = 13 5 2 1, N = 20
# i, j, x, y, SUM = 10
# i = 0
# j = 0
|
{
"input": [
"4\n0011\n1100\n",
"4\n0011\n0101\n",
"8\n00100101\n01111100\n",
"6\n000000\n111111\n",
"10\n0011101001\n1000101110\n",
"4\n0011\n1100\n",
"6\n111100\n111000\n",
"8\n11111111\n11110000\n",
"2\n10\n10\n",
"8\n11100000\n00101111\n",
"2\n10\n01\n",
"8\n01111111\n10000111\n",
"10\n1111000011\n1111111100\n",
"2\n01\n11\n",
"10\n0011101001\n1010101110\n",
"4\n0001\n1100\n",
"6\n111110\n111000\n",
"8\n11111111\n11110010\n",
"8\n11100000\n00111111\n",
"8\n11111111\n10000111\n",
"10\n1011000011\n1111111100\n",
"4\n0011\n1101\n",
"8\n00100101\n01111110\n",
"10\n0011101001\n1010111110\n",
"6\n111110\n111010\n",
"8\n11011111\n11110010\n",
"8\n11101000\n00111111\n",
"8\n11011111\n10000111\n",
"4\n0011\n1001\n",
"10\n0011101001\n1010111111\n",
"8\n11011101\n11110010\n",
"8\n11101000\n00101111\n",
"8\n10011111\n10000111\n",
"4\n0011\n1010\n",
"10\n0011101001\n1010101111\n",
"8\n11011101\n11111010\n",
"8\n11001000\n00101111\n",
"8\n00011111\n10000111\n",
"4\n0011\n1110\n",
"6\n100101\n111110\n",
"10\n0011101001\n1010101011\n",
"6\n110110\n011000\n",
"10\n1001001010\n1111111100\n",
"8\n00010111\n11111110\n",
"6\n110101\n111110\n",
"10\n0011101001\n1010101010\n",
"8\n11010101\n11011010\n",
"8\n00010111\n00000111\n",
"10\n1001011010\n1111111100\n",
"6\n110101\n011110\n",
"8\n11010101\n11011011\n",
"8\n00010111\n00100111\n",
"10\n1001011010\n1111011100\n",
"6\n110101\n001110\n",
"4\n0011\n1000\n",
"6\n000100\n111111\n",
"4\n0001\n1101\n",
"10\n1011000010\n1111111100\n",
"4\n0010\n1101\n",
"8\n00100111\n01111110\n",
"6\n000101\n111111\n",
"4\n0001\n1111\n",
"6\n111110\n011010\n",
"10\n1011000010\n1111111101\n",
"4\n0001\n0101\n",
"8\n00110111\n01111110\n",
"6\n000101\n111110\n",
"4\n0000\n1111\n",
"6\n111110\n011000\n",
"10\n1011001010\n1111111100\n",
"4\n0001\n1110\n",
"8\n00010111\n01111110\n",
"4\n0000\n1110\n",
"8\n11011101\n11011010\n",
"8\n11001000\n00001111\n",
"8\n00010111\n10000111\n",
"4\n0011\n0110\n",
"4\n1001\n1110\n",
"4\n0100\n1110\n",
"6\n111110\n001000\n",
"8\n11001000\n00001110\n",
"4\n0010\n0110\n",
"4\n1000\n1110\n",
"8\n00010111\n11110110\n",
"10\n0011101101\n1010101010\n",
"4\n1100\n1110\n",
"6\n011110\n001000\n",
"8\n11001000\n00101110\n",
"4\n0011\n0100\n",
"4\n1000\n1010\n",
"8\n00010101\n11110110\n",
"10\n0011101101\n1010101110\n",
"4\n1101\n1110\n",
"6\n011110\n001100\n",
"8\n11010101\n01011011\n"
],
"output": [
"1 2 ",
"1 4 ",
"2 3 4 5\n",
"-1",
"1 2 5 8 9\n",
"1 2 ",
"1 4 5 ",
"5 6 7 8 ",
"-1",
"3 5 6 7\n",
"2 ",
"2 3 4 5 ",
"1 2 3 5 6\n",
"2 ",
"1 2 3 5 8 ",
"1 2 ",
"1 4 6 ",
"1 5 6 8 ",
"-1\n",
"2 3 4 5 ",
"1 2 3 4 5 ",
"1 4 ",
"2 3 4 6 ",
"1 3 5 6 8 ",
"1 2 6 ",
"1 3 5 6 ",
"3 4 5 6 ",
"1 2 3 4 ",
"2 4 ",
"1 3 5 6 7 ",
"1 3 5 7 ",
"3 6 7 8 ",
"1 2 3 6 ",
"2 3 ",
"1 3 5 8 9 ",
"1 2 3 7 ",
"3 5 6 7 ",
"2 3 6 7 ",
"1 3 ",
"1 2 4 ",
"1 2 3 5 9 ",
"1 3 6 ",
"1 2 3 4 7 ",
"1 4 6 7 ",
"1 2 3 ",
"1 2 3 5 6 ",
"1 2 3 5 ",
"1 2 4 6 ",
"1 2 3 4 6 ",
"2 3 5 ",
"1 2 5 7 ",
"1 2 6 7 ",
"1 2 3 4 8 ",
"1 3 5 ",
"1 2 ",
"-1\n",
"1 4 ",
"1 2 3 4 5 ",
"-1\n",
"2 3 4 6 ",
"-1\n",
"-1\n",
"1 2 6 ",
"-1\n",
"1 4 ",
"2 3 4 5 ",
"-1\n",
"-1\n",
"1 4 6 ",
"1 2 3 4 5 ",
"-1\n",
"2 3 4 6 ",
"-1\n",
"1 2 3 7 ",
"3 5 6 7 ",
"2 3 6 7 ",
"1 3 ",
"1 2 ",
"1 2 ",
"-1\n",
"3 4 5 6 ",
"1 3 ",
"1 2 ",
"1 2 4 6 ",
"1 2 3 5 6 ",
"1 3 ",
"1 2 6 ",
"3 4 5 6 ",
"1 2 ",
"1 2 ",
"1 2 4 6 ",
"1 2 3 5 9 ",
"1 3 ",
"1 3 6 ",
"2 3 4 5 "
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Polycarp is a head of a circus troupe. There are n — an even number — artists in the troupe. It is known whether the i-th artist can perform as a clown (if yes, then c_i = 1, otherwise c_i = 0), and whether they can perform as an acrobat (if yes, then a_i = 1, otherwise a_i = 0).
Split the artists into two performances in such a way that:
* each artist plays in exactly one performance,
* the number of artists in the two performances is equal (i.e. equal to n/2),
* the number of artists that can perform as clowns in the first performance is the same as the number of artists that can perform as acrobats in the second performance.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 000, n is even) — the number of artists in the troupe.
The second line contains n digits c_1 c_2 … c_n, the i-th of which is equal to 1 if the i-th artist can perform as a clown, and 0 otherwise.
The third line contains n digits a_1 a_2 … a_n, the i-th of which is equal to 1, if the i-th artist can perform as an acrobat, and 0 otherwise.
Output
Print n/2 distinct integers — the indices of the artists that should play in the first performance.
If there are multiple answers, print any.
If there is no solution, print a single integer -1.
Examples
Input
4
0011
0101
Output
1 4
Input
6
000000
111111
Output
-1
Input
4
0011
1100
Output
4 3
Input
8
00100101
01111100
Output
1 2 3 6
Note
In the first example, one of the possible divisions into two performances is as follows: in the first performance artists 1 and 4 should take part. Then the number of artists in the first performance who can perform as clowns is equal to 1. And the number of artists in the second performance who can perform as acrobats is 1 as well.
In the second example, the division is not possible.
In the third example, one of the possible divisions is as follows: in the first performance artists 3 and 4 should take part. Then in the first performance there are 2 artists who can perform as clowns. And the number of artists in the second performance who can perform as acrobats is 2 as well.
### Input:
4
0011
1100
### Output:
1 2
### Input:
4
0011
0101
### Output:
1 4
### Code:
import sys
import random
N = int(input())
C = list(map(int, input()))
A = list(map(int, input()))
# N = random.randint(20, 40) * 2
# C = [random.randint(0, 1) for i in range(N)]
# A = [random.randint(0, 1) for i in range(N)]
def build_solution(i, j, x, y):
I = (0, 0)
J = (0, 1)
X = (1, 0)
Y = (1, 1)
ans = []
for q in range(N):
p = (C[q], A[q])
if i and p == I:
i -= 1
ans.append(q+1)
elif j and p == J:
j -= 1
ans.append(q+1)
elif x and p == X:
x -= 1
ans.append(q+1)
elif y and p == Y:
y -= 1
ans.append(q+1)
return map(str, ans)
a = b = c = d = 0
for i in range(N):
if C[i] == 0:
if A[i] == 0:
a += 1
else:
b += 1
else:
if A[i] == 0:
c += 1
else:
d += 1
# print(C)
# print(A)
# print(a, b, c, d, "N/2=", N//2)
for i in range(0, a+1):
y = - N//2 + i + b + d
if y < 0:
continue
min_j = max(0, N//2 - i - c - y)
max_j = min(b + 1, N //2 + 1)
# print(i, y, '[', min_j, max_j, ']')
for j in range(min_j, max_j):
x = N//2 - i - j - y
if x < 0:
break
# print("Check ", i, j, 'x, y:', x, y)
if not ((0 <= x <= c) and (0 <= y <= d)):
continue
# print('SOL', i, j, x, y)
sol = build_solution(i, j, x, y)
print(' '.join(sol))
exit(0)
print(-1)
# 1) loop over N
# 2) pick best actor on every iteration
# 3) try to minimize diff between teams
# if len(first) == len(second) and first.score == second.score:
# print(' '.join(map(lambda x: str(x+1), first)))
# else:
# print(-1)
# a, b, c, d = 13 5 2 1, N = 20
# i, j, x, y, SUM = 10
# i = 0
# j = 0
|
1156_D. 0-1-Tree_28544
|
You are given a tree (an undirected connected acyclic graph) consisting of n vertices and n - 1 edges. A number is written on each edge, each number is either 0 (let's call such edges 0-edges) or 1 (those are 1-edges).
Let's call an ordered pair of vertices (x, y) (x ≠ y) valid if, while traversing the simple path from x to y, we never go through a 0-edge after going through a 1-edge. Your task is to calculate the number of valid pairs in the tree.
Input
The first line contains one integer n (2 ≤ n ≤ 200000) — the number of vertices in the tree.
Then n - 1 lines follow, each denoting an edge of the tree. Each edge is represented by three integers x_i, y_i and c_i (1 ≤ x_i, y_i ≤ n, 0 ≤ c_i ≤ 1, x_i ≠ y_i) — the vertices connected by this edge and the number written on it, respectively.
It is guaranteed that the given edges form a tree.
Output
Print one integer — the number of valid pairs of vertices.
Example
Input
7
2 1 1
3 2 0
4 2 1
5 2 0
6 7 1
7 2 1
Output
34
Note
The picture corresponding to the first example:
<image>
|
import sys
input = sys.stdin.readline
class UnionFind:
def __init__(self, n):
self.parent = [-1] * n
self.cnt = n
def root(self, x):
if self.parent[x] < 0:
return x
else:
self.parent[x] = self.root(self.parent[x])
return self.parent[x]
def merge(self, x, y):
x = self.root(x)
y = self.root(y)
if x == y:
return
if self.parent[x] > self.parent[y]:
x, y = y, x
self.parent[x] += self.parent[y]
self.parent[y] = x
self.cnt -= 1
def is_same(self, x, y):
return self.root(x) == self.root(y)
def get_size(self, x):
return -self.parent[self.root(x)]
def get_cnt(self):
return self.cnt
n = int(input())
info = [list(map(int, input().split())) for i in range(n - 1)]
uf0 = UnionFind(n)
uf1 = UnionFind(n)
tree0 = [[] for i in range(n)]
tree1 = [[] for i in range(n)]
for i in range(n - 1):
a, b, cost = info[i]
a -= 1
b -= 1
if cost == 0:
tree0[a].append(b)
tree0[b].append(a)
uf0.merge(a, b)
else:
tree1[a].append(b)
tree1[b].append(a)
uf1.merge(a, b)
ans0 = [0] * n
ans1 = [0] * n
for i in range(n):
ans0[i] = uf0.get_size(i) - 1
ans1[i] = uf1.get_size(i) - 1
ans = 0
for i in range(n):
ans += ans0[i]
ans += ans1[i]
ans += ans0[i] * ans1[i]
print(ans)
|
{
"input": [
"7\n2 1 1\n3 2 0\n4 2 1\n5 2 0\n6 7 1\n7 2 1\n",
"2\n1 2 1\n",
"2\n1 2 0\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 2 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n3 1 1\n3 2 0\n4 2 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 2 0\n6 5 0\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 1 1\n4 1 1\n5 2 1\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 3 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 1 0\n4 1 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 0\n3 6 1\n4 1 0\n5 2 0\n6 7 0\n7 1 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 1 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 1 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 1 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 1 1\n4 1 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 0\n5 1 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 1 1\n4 1 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n4 1 1\n3 2 0\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n4 1 1\n3 2 1\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 3 1\n5 2 1\n6 7 0\n7 2 0\n",
"7\n4 1 1\n3 2 1\n4 2 1\n5 4 0\n6 7 1\n7 4 1\n",
"7\n4 1 1\n3 2 1\n4 2 1\n5 7 0\n6 7 1\n7 4 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 4 0\n6 7 1\n7 4 1\n",
"7\n2 1 1\n3 1 0\n4 2 1\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 1 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 3 0\n6 5 0\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 1 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 7 0\n7 3 1\n",
"7\n2 1 1\n3 1 1\n4 2 1\n5 2 1\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 2 1\n5 4 0\n6 7 1\n7 1 1\n",
"7\n2 1 1\n3 1 0\n4 2 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 7 0\n7 3 0\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 4 0\n6 7 1\n7 1 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 7 0\n7 1 0\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 7 0\n7 1 1\n",
"7\n2 1 0\n3 4 1\n4 1 0\n5 2 0\n6 7 0\n7 1 1\n",
"7\n2 1 0\n3 6 1\n4 1 0\n5 1 0\n6 7 0\n7 1 1\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 0\n6 4 0\n7 2 1\n",
"7\n4 1 1\n3 4 0\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n4 1 1\n3 4 1\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 1\n4 3 1\n5 2 1\n6 7 0\n7 2 0\n",
"7\n6 1 1\n3 2 1\n4 2 1\n5 4 0\n6 7 1\n7 4 1\n",
"7\n2 1 1\n3 1 0\n4 2 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n3 1 1\n3 2 1\n4 1 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 0\n3 4 1\n4 1 0\n5 2 0\n6 7 0\n7 3 1\n",
"7\n2 1 1\n3 1 1\n4 2 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 1 0\n4 2 0\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 3 0\n6 7 0\n7 3 0\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 1 0\n6 7 1\n7 1 1\n",
"7\n2 1 0\n3 2 1\n4 2 0\n5 2 0\n6 7 0\n7 1 0\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 0\n6 4 0\n7 3 1\n",
"7\n2 1 1\n3 4 0\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 1 0\n4 2 1\n5 2 1\n6 7 0\n6 2 1\n",
"7\n2 1 1\n3 1 1\n4 2 1\n5 2 1\n6 7 0\n7 3 1\n",
"7\n2 1 1\n3 2 1\n4 2 1\n5 3 0\n6 7 1\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n3 1 1\n3 2 1\n4 2 1\n5 2 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 3 1\n5 2 0\n6 5 0\n7 2 1\n",
"7\n2 1 1\n3 1 1\n4 1 1\n5 2 1\n6 7 0\n7 2 0\n",
"7\n2 1 0\n3 2 0\n4 1 0\n5 2 0\n6 7 0\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 0\n6 7 0\n7 1 1\n",
"7\n2 1 1\n3 1 1\n4 1 1\n5 1 1\n6 7 1\n7 2 1\n",
"7\n3 1 1\n3 2 1\n4 2 1\n5 4 0\n6 7 1\n7 2 1\n",
"7\n2 1 1\n3 2 0\n4 3 1\n5 3 1\n6 7 0\n7 2 0\n",
"7\n4 1 1\n3 2 1\n4 2 1\n5 4 1\n6 7 1\n7 4 1\n",
"7\n2 1 1\n3 4 0\n4 2 1\n5 4 0\n6 7 1\n7 4 1\n",
"7\n2 1 1\n3 2 0\n4 1 1\n5 2 1\n6 7 0\n7 2 1\n",
"7\n2 1 0\n3 2 1\n4 1 0\n5 2 0\n6 1 0\n7 1 0\n"
],
"output": [
"34\n",
"2\n",
"2\n",
"32\n",
"37\n",
"29\n",
"28\n",
"33\n",
"34\n",
"24\n",
"42\n",
"25\n",
"27\n",
"23\n",
"32\n",
"37\n",
"32\n",
"32\n",
"29\n",
"37\n",
"28\n",
"32\n",
"29\n",
"32\n",
"37\n",
"29\n",
"37\n",
"37\n",
"32\n",
"27\n",
"37\n",
"33\n",
"37\n",
"28\n",
"42\n",
"32\n",
"32\n",
"25\n",
"32\n",
"37\n",
"25\n",
"25\n",
"23\n",
"29\n",
"34\n",
"37\n",
"34\n",
"37\n",
"32\n",
"37\n",
"28\n",
"37\n",
"29\n",
"25\n",
"32\n",
"37\n",
"24\n",
"34\n",
"32\n",
"37\n",
"37\n",
"28\n",
"37\n",
"29\n",
"34\n",
"29\n",
"29\n",
"42\n",
"37\n",
"29\n",
"42\n",
"34\n",
"32\n",
"37\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a tree (an undirected connected acyclic graph) consisting of n vertices and n - 1 edges. A number is written on each edge, each number is either 0 (let's call such edges 0-edges) or 1 (those are 1-edges).
Let's call an ordered pair of vertices (x, y) (x ≠ y) valid if, while traversing the simple path from x to y, we never go through a 0-edge after going through a 1-edge. Your task is to calculate the number of valid pairs in the tree.
Input
The first line contains one integer n (2 ≤ n ≤ 200000) — the number of vertices in the tree.
Then n - 1 lines follow, each denoting an edge of the tree. Each edge is represented by three integers x_i, y_i and c_i (1 ≤ x_i, y_i ≤ n, 0 ≤ c_i ≤ 1, x_i ≠ y_i) — the vertices connected by this edge and the number written on it, respectively.
It is guaranteed that the given edges form a tree.
Output
Print one integer — the number of valid pairs of vertices.
Example
Input
7
2 1 1
3 2 0
4 2 1
5 2 0
6 7 1
7 2 1
Output
34
Note
The picture corresponding to the first example:
<image>
### Input:
7
2 1 1
3 2 0
4 2 1
5 2 0
6 7 1
7 2 1
### Output:
34
### Input:
2
1 2 1
### Output:
2
### Code:
import sys
input = sys.stdin.readline
class UnionFind:
def __init__(self, n):
self.parent = [-1] * n
self.cnt = n
def root(self, x):
if self.parent[x] < 0:
return x
else:
self.parent[x] = self.root(self.parent[x])
return self.parent[x]
def merge(self, x, y):
x = self.root(x)
y = self.root(y)
if x == y:
return
if self.parent[x] > self.parent[y]:
x, y = y, x
self.parent[x] += self.parent[y]
self.parent[y] = x
self.cnt -= 1
def is_same(self, x, y):
return self.root(x) == self.root(y)
def get_size(self, x):
return -self.parent[self.root(x)]
def get_cnt(self):
return self.cnt
n = int(input())
info = [list(map(int, input().split())) for i in range(n - 1)]
uf0 = UnionFind(n)
uf1 = UnionFind(n)
tree0 = [[] for i in range(n)]
tree1 = [[] for i in range(n)]
for i in range(n - 1):
a, b, cost = info[i]
a -= 1
b -= 1
if cost == 0:
tree0[a].append(b)
tree0[b].append(a)
uf0.merge(a, b)
else:
tree1[a].append(b)
tree1[b].append(a)
uf1.merge(a, b)
ans0 = [0] * n
ans1 = [0] * n
for i in range(n):
ans0[i] = uf0.get_size(i) - 1
ans1[i] = uf1.get_size(i) - 1
ans = 0
for i in range(n):
ans += ans0[i]
ans += ans1[i]
ans += ans0[i] * ans1[i]
print(ans)
|
1196_F. K-th Path_28551
|
You are given a connected undirected weighted graph consisting of n vertices and m edges.
You need to print the k-th smallest shortest path in this graph (paths from the vertex to itself are not counted, paths from i to j and from j to i are counted as one).
More formally, if d is the matrix of shortest paths, where d_{i, j} is the length of the shortest path between vertices i and j (1 ≤ i < j ≤ n), then you need to print the k-th element in the sorted array consisting of all d_{i, j}, where 1 ≤ i < j ≤ n.
Input
The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ min\Big((n(n-1))/(2), 2 ⋅ 10^5\Big), 1 ≤ k ≤ min\Big((n(n-1))/(2), 400\Big) — the number of vertices in the graph, the number of edges in the graph and the value of k, correspondingly.
Then m lines follow, each containing three integers x, y and w (1 ≤ x, y ≤ n, 1 ≤ w ≤ 10^9, x ≠ y) denoting an edge between vertices x and y of weight w.
It is guaranteed that the given graph is connected (there is a path between any pair of vertices), there are no self-loops (edges connecting the vertex with itself) and multiple edges (for each pair of vertices x and y, there is at most one edge between this pair of vertices in the graph).
Output
Print one integer — the length of the k-th smallest shortest path in the given graph (paths from the vertex to itself are not counted, paths from i to j and from j to i are counted as one).
Examples
Input
6 10 5
2 5 1
5 3 9
6 2 2
1 3 1
5 1 8
6 5 10
1 6 5
6 4 6
3 6 2
3 4 5
Output
3
Input
7 15 18
2 6 3
5 7 4
6 5 4
3 6 9
6 7 7
1 6 4
7 1 6
7 2 1
4 3 2
3 2 8
5 3 6
2 5 5
3 7 9
4 1 8
2 1 1
Output
9
|
import sys
input = sys.stdin.readline
N, M, K = map(int, input().split())
X = []
for _ in range(M):
x, y, w = map(int, input().split())
X.append([min(x,y), max(x,y), w])
X = (sorted(X, key = lambda x: x[2])+[[0, 0, 10**20] for _ in range(K)])[:K]
D = {}
for x, y, w in X:
if x: D[x*10**6+y] = w
flg = 1
while flg:
flg = 0
for i in range(len(X)):
x1, y1, w1 = X[i]
for j in range(i+1, len(X)):
x2, y2, w2 = X[j]
if x1==x2: a, b = min(y1,y2), max(y1,y2)
elif y1==y2: a, b = min(x1,x2), max(x1,x2)
elif x1==y2: a, b = x2, y1
elif x2==y1: a, b = x1, y2
else: a, b = 0, 0
if a:
if (a*10**6+b in D and w1+w2 < D[a*10**6+b]) or (a*10**6+b not in D and w1+w2 < X[-1][2]):
if a*10**6+b in D:
for k in range(len(X)):
if X[k][0] == a and X[k][1] == b:
X[k][2] = w1+w2
else:
x, y, w = X.pop()
if x: D.pop(x*10**6+y)
X.append([a,b,w1+w2])
D[a*10**6+b] = w1+w2
X = sorted(X, key = lambda x: x[2])
flg = 1
break
if flg:
break
print(X[-1][2])
|
{
"input": [
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 5\n3 7 9\n4 1 8\n2 1 1\n",
"6 10 5\n2 5 1\n5 3 9\n6 2 2\n1 3 1\n5 1 8\n6 5 10\n1 6 5\n6 4 6\n3 6 2\n3 4 5\n",
"2 1 1\n1 2 123456789\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1000000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n27 28 1000000000\n",
"8 7 19\n1 2 1000000000\n2 3 999999999\n3 4 999999998\n4 5 999999997\n5 6 999999996\n6 7 999999995\n7 8 999999994\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n27 28 1000000000\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 5\n3 7 9\n4 1 12\n2 1 1\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n20 28 1000000000\n",
"8 7 19\n1 2 1000000000\n2 3 999999999\n3 4 999999998\n4 5 999999997\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000100000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n27 28 1000000000\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n1 3 2\n3 2 8\n5 3 6\n2 5 5\n3 7 9\n4 1 15\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 2\n5 3 6\n2 5 5\n3 7 9\n4 1 8\n2 1 1\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1010000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n20 28 1000000000\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 4 999999998\n4 5 999999997\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 4 999999998\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 5 1713603821\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 8\n3 7 9\n4 1 8\n2 1 1\n",
"8 7 19\n1 4 1000000000\n2 3 999999999\n3 4 999999998\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"8 7 19\n1 4 1000000000\n2 3 999999999\n3 4 999999998\n4 5 84933160\n5 7 999999996\n6 7 999999995\n7 8 215677923\n",
"8 7 19\n1 4 1000000001\n2 3 999999999\n3 4 999999998\n4 5 84933160\n5 7 999999996\n6 7 999999995\n7 8 215677923\n",
"8 7 19\n1 2 1000000001\n2 3 999999999\n3 4 999999998\n4 5 84933160\n5 7 999999996\n6 7 999999995\n7 8 215677923\n",
"8 7 19\n1 2 1000000001\n2 3 999999999\n3 4 999999998\n4 5 114797370\n5 7 999999996\n6 7 999999995\n7 8 215677923\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n3 27 1000000000\n20 28 1000000000\n",
"8 7 16\n1 2 1000000000\n2 3 999999999\n3 4 999999998\n4 5 999999997\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1010000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000000000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1010000000\n20 28 1000000000\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 6 999999998\n4 5 999999997\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n2 5 1713603821\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 5\n3 7 9\n4 1 12\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 5\n3 7 9\n4 1 15\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 1 8\n5 3 6\n2 5 5\n3 7 9\n4 1 12\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 1 8\n5 3 6\n2 5 5\n3 7 9\n4 1 20\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 4\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 1 8\n5 3 6\n2 5 5\n3 7 9\n4 1 20\n2 1 1\n",
"7 15 18\n2 6 6\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 1 8\n5 3 6\n2 5 5\n3 7 9\n4 1 20\n2 1 1\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 5 999999998\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 999999994\n",
"28 27 378\n1 2 1000000000\n2 3 1000000000\n3 4 1000000000\n4 5 1000000000\n5 6 1000000000\n6 7 1000000000\n7 8 1000000000\n8 9 1000000000\n9 10 1000000000\n10 11 1000000000\n11 12 1000000000\n12 13 1000000000\n13 14 1010000000\n14 15 1000000000\n15 16 1000000000\n16 17 1000000000\n17 18 1000000000\n18 19 1000000000\n19 20 1000000000\n20 21 1000100000\n21 22 1000000000\n22 23 1000000000\n23 24 1000000000\n24 25 1000000000\n25 26 1000000000\n26 27 1000000000\n27 28 1000000000\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 4\n1 6 4\n7 1 3\n7 2 1\n4 3 2\n3 1 8\n5 3 6\n2 5 5\n3 7 9\n4 1 20\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 3\n3 2 2\n5 3 6\n2 5 5\n3 7 9\n4 1 8\n2 1 1\n",
"8 7 19\n1 3 1000000000\n2 3 999999999\n3 5 999999998\n4 5 154063658\n5 7 999999996\n6 7 545546123\n7 8 999999994\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 8\n1 6 4\n7 1 6\n7 2 1\n4 3 3\n3 2 2\n5 3 6\n2 5 5\n3 7 9\n4 1 8\n2 1 1\n",
"8 7 19\n1 4 1000000000\n2 3 999999999\n3 4 999999998\n4 5 154063658\n5 7 999999996\n6 7 999999995\n7 8 215677923\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 2 8\n5 3 6\n2 5 1\n3 7 9\n4 1 12\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 18\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 2\n3 1 2\n5 3 6\n2 5 5\n3 7 9\n4 1 12\n2 1 1\n",
"7 15 18\n2 6 3\n5 7 4\n6 5 4\n3 6 9\n6 7 7\n1 6 4\n7 1 6\n7 2 1\n4 3 3\n3 2 2\n5 3 6\n2 5 5\n3 7 9\n6 1 8\n2 1 1\n"
],
"output": [
"9\n",
"3\n",
"123456789\n",
"27000000000\n",
"3999999982\n",
"27010000000\n",
"10\n",
"26010000000\n",
"2999999997\n",
"27010100000\n",
"17\n",
"6\n",
"26020000000\n",
"2999999994\n",
"2154063655\n",
"2867667478\n",
"9\n",
"2154063654\n",
"2084933156\n",
"2084933157\n",
"2300611077\n",
"2330475287\n",
"25010000000\n",
"2999999988\n",
"26030000000\n",
"2999999989\n",
"3713603811\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"2154063655\n",
"27010100000\n",
"10\n",
"6\n",
"2154063655\n",
"6\n",
"2154063654\n",
"9\n",
"6\n",
"6\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a connected undirected weighted graph consisting of n vertices and m edges.
You need to print the k-th smallest shortest path in this graph (paths from the vertex to itself are not counted, paths from i to j and from j to i are counted as one).
More formally, if d is the matrix of shortest paths, where d_{i, j} is the length of the shortest path between vertices i and j (1 ≤ i < j ≤ n), then you need to print the k-th element in the sorted array consisting of all d_{i, j}, where 1 ≤ i < j ≤ n.
Input
The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ min\Big((n(n-1))/(2), 2 ⋅ 10^5\Big), 1 ≤ k ≤ min\Big((n(n-1))/(2), 400\Big) — the number of vertices in the graph, the number of edges in the graph and the value of k, correspondingly.
Then m lines follow, each containing three integers x, y and w (1 ≤ x, y ≤ n, 1 ≤ w ≤ 10^9, x ≠ y) denoting an edge between vertices x and y of weight w.
It is guaranteed that the given graph is connected (there is a path between any pair of vertices), there are no self-loops (edges connecting the vertex with itself) and multiple edges (for each pair of vertices x and y, there is at most one edge between this pair of vertices in the graph).
Output
Print one integer — the length of the k-th smallest shortest path in the given graph (paths from the vertex to itself are not counted, paths from i to j and from j to i are counted as one).
Examples
Input
6 10 5
2 5 1
5 3 9
6 2 2
1 3 1
5 1 8
6 5 10
1 6 5
6 4 6
3 6 2
3 4 5
Output
3
Input
7 15 18
2 6 3
5 7 4
6 5 4
3 6 9
6 7 7
1 6 4
7 1 6
7 2 1
4 3 2
3 2 8
5 3 6
2 5 5
3 7 9
4 1 8
2 1 1
Output
9
### Input:
7 15 18
2 6 3
5 7 4
6 5 4
3 6 9
6 7 7
1 6 4
7 1 6
7 2 1
4 3 2
3 2 8
5 3 6
2 5 5
3 7 9
4 1 8
2 1 1
### Output:
9
### Input:
6 10 5
2 5 1
5 3 9
6 2 2
1 3 1
5 1 8
6 5 10
1 6 5
6 4 6
3 6 2
3 4 5
### Output:
3
### Code:
import sys
input = sys.stdin.readline
N, M, K = map(int, input().split())
X = []
for _ in range(M):
x, y, w = map(int, input().split())
X.append([min(x,y), max(x,y), w])
X = (sorted(X, key = lambda x: x[2])+[[0, 0, 10**20] for _ in range(K)])[:K]
D = {}
for x, y, w in X:
if x: D[x*10**6+y] = w
flg = 1
while flg:
flg = 0
for i in range(len(X)):
x1, y1, w1 = X[i]
for j in range(i+1, len(X)):
x2, y2, w2 = X[j]
if x1==x2: a, b = min(y1,y2), max(y1,y2)
elif y1==y2: a, b = min(x1,x2), max(x1,x2)
elif x1==y2: a, b = x2, y1
elif x2==y1: a, b = x1, y2
else: a, b = 0, 0
if a:
if (a*10**6+b in D and w1+w2 < D[a*10**6+b]) or (a*10**6+b not in D and w1+w2 < X[-1][2]):
if a*10**6+b in D:
for k in range(len(X)):
if X[k][0] == a and X[k][1] == b:
X[k][2] = w1+w2
else:
x, y, w = X.pop()
if x: D.pop(x*10**6+y)
X.append([a,b,w1+w2])
D[a*10**6+b] = w1+w2
X = sorted(X, key = lambda x: x[2])
flg = 1
break
if flg:
break
print(X[-1][2])
|
1214_A. Optimal Currency Exchange_28555
|
Andrew was very excited to participate in Olympiad of Metropolises. Days flew by quickly, and Andrew is already at the airport, ready to go home. He has n rubles left, and would like to exchange them to euro and dollar bills. Andrew can mix dollar bills and euro bills in whatever way he wants. The price of one dollar is d rubles, and one euro costs e rubles.
Recall that there exist the following dollar bills: 1, 2, 5, 10, 20, 50, 100, and the following euro bills — 5, 10, 20, 50, 100, 200 (note that, in this problem we do not consider the 500 euro bill, it is hard to find such bills in the currency exchange points). Andrew can buy any combination of bills, and his goal is to minimize the total number of rubles he will have after the exchange.
Help him — write a program that given integers n, e and d, finds the minimum number of rubles Andrew can get after buying dollar and euro bills.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 10^8) — the initial sum in rubles Andrew has.
The second line of the input contains one integer d (30 ≤ d ≤ 100) — the price of one dollar in rubles.
The third line of the input contains integer e (30 ≤ e ≤ 100) — the price of one euro in rubles.
Output
Output one integer — the minimum number of rubles Andrew can have after buying dollar and euro bills optimally.
Examples
Input
100
60
70
Output
40
Input
410
55
70
Output
5
Input
600
60
70
Output
0
Note
In the first example, we can buy just 1 dollar because there is no 1 euro bill.
In the second example, optimal exchange is to buy 5 euro and 1 dollar.
In the third example, optimal exchange is to buy 10 dollars in one bill.
|
n=int(input())
d=int(input())
e=int(input())
arr=100
a,b=min(d,5*e),max(d,5*e)
for i in range(0,n//b+1):
arr=min(arr,(n-i*b)%a)
print(arr)
|
{
"input": [
"410\n55\n70\n",
"600\n60\n70\n",
"100\n60\n70\n",
"8642\n70\n90\n",
"999\n66\n74\n",
"1000\n60\n80\n",
"90852542\n95\n34\n",
"100000000\n31\n33\n",
"99999998\n60\n75\n",
"99\n100\n100\n",
"10000\n68\n78\n",
"11750\n49\n50\n",
"13795\n97\n31\n",
"150\n100\n30\n",
"16091\n51\n96\n",
"50\n60\n70\n",
"1\n30\n30\n",
"90\n80\n89\n",
"130\n100\n30\n",
"100005\n60\n70\n",
"169\n59\n37\n",
"100000\n35\n35\n",
"100000000\n98\n99\n",
"99999999\n90\n100\n",
"1750\n45\n50\n",
"150\n31\n30\n",
"59\n87\n30\n",
"99750\n50\n51\n",
"898\n99\n30\n",
"9876543\n66\n88\n",
"99999\n70\n75\n",
"1000\n63\n70\n",
"54321\n63\n70\n",
"311\n31\n30\n",
"511\n100\n31\n",
"39610651\n75\n98\n",
"12149750\n45\n50\n",
"420\n65\n70\n",
"99998\n68\n78\n",
"30\n31\n30\n",
"100000000\n30\n30\n",
"99\n97\n33\n",
"495\n30\n31\n",
"420\n70\n65\n",
"99999989\n31\n30\n",
"400\n30\n100\n",
"23456789\n66\n100\n",
"8642\n26\n90\n",
"999\n82\n74\n",
"1000\n60\n138\n",
"90852542\n95\n64\n",
"99\n100\n101\n",
"50\n60\n128\n",
"1\n29\n30\n",
"90\n145\n89\n",
"130\n110\n30\n",
"169\n59\n34\n",
"99999999\n36\n100\n",
"150\n31\n27\n",
"59\n85\n30\n",
"9876543\n66\n44\n",
"30\n36\n30\n",
"495\n60\n31\n",
"600\n77\n70\n",
"100\n109\n70\n",
"1750\n51\n30\n",
"1000\n126\n139\n",
"311\n13\n26\n",
"99\n18\n33\n",
"600\n16\n70\n",
"999\n10\n111\n",
"100000000\n58\n33\n",
"99999998\n79\n75\n",
"10000\n135\n78\n",
"11750\n49\n1\n",
"13795\n70\n31\n",
"16091\n51\n89\n",
"100005\n113\n70\n",
"100000\n35\n3\n",
"100000000\n98\n85\n",
"1750\n51\n50\n",
"99750\n50\n97\n",
"898\n99\n10\n",
"1000\n126\n70\n",
"54321\n63\n115\n",
"311\n31\n26\n",
"39610651\n75\n16\n",
"12149750\n53\n50\n",
"420\n65\n41\n",
"99998\n68\n110\n",
"100000000\n60\n30\n",
"99\n12\n33\n",
"420\n70\n119\n",
"99999989\n31\n49\n",
"400\n30\n101\n",
"410\n24\n70\n",
"8642\n11\n90\n",
"999\n82\n111\n",
"1000\n77\n138\n",
"100000000\n58\n18\n",
"99999998\n79\n136\n",
"99\n101\n101\n",
"10000\n135\n20\n",
"11750\n78\n1\n",
"13795\n70\n49\n",
"16091\n51\n45\n",
"50\n50\n128\n",
"1\n29\n33\n",
"90\n145\n137\n",
"130\n010\n30\n",
"100005\n145\n70\n",
"169\n59\n40\n",
"100000\n35\n1\n",
"150\n42\n27\n",
"99750\n50\n8\n",
"898\n99\n1\n",
"9876543\n25\n44\n",
"54321\n6\n115\n",
"39610651\n75\n22\n",
"12149750\n53\n53\n",
"420\n65\n3\n",
"99998\n68\n010\n",
"30\n51\n30\n",
"495\n60\n53\n",
"420\n70\n214\n",
"99999989\n31\n97\n",
"400\n30\n111\n",
"410\n24\n127\n",
"100\n158\n70\n",
"8642\n11\n150\n",
"1000\n77\n184\n",
"99\n110\n101\n",
"10000\n135\n18\n",
"11750\n78\n2\n",
"13795\n29\n49\n",
"16091\n33\n45\n",
"50\n50\n124\n",
"1\n29\n25\n",
"90\n145\n42\n",
"130\n010\n13\n",
"100005\n145\n72\n",
"169\n59\n42\n",
"100000\n35\n2\n"
],
"output": [
"5\n",
"0\n",
"40\n",
"2\n",
"9\n",
"0\n",
"2\n",
"0\n",
"8\n",
"99\n",
"2\n",
"0\n",
"0\n",
"0\n",
"2\n",
"50\n",
"1\n",
"10\n",
"30\n",
"5\n",
"51\n",
"5\n",
"0\n",
"9\n",
"0\n",
"0\n",
"59\n",
"0\n",
"1\n",
"17\n",
"4\n",
"20\n",
"1\n",
"1\n",
"1\n",
"1\n",
"0\n",
"5\n",
"0\n",
"30\n",
"10\n",
"2\n",
"0\n",
"0\n",
"0\n",
"10\n",
"1\n",
"0\n",
"13\n",
"10\n",
"2\n",
"99\n",
"50\n",
"1\n",
"90\n",
"20\n",
"51\n",
"3\n",
"15\n",
"59\n",
"17\n",
"30\n",
"5\n",
"19\n",
"100\n",
"16\n",
"53\n",
"12\n",
"9\n",
"8\n",
"4\n",
"0\n",
"0\n",
"10\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"20\n",
"0\n",
"1\n",
"1\n",
"0\n",
"10\n",
"0\n",
"10\n",
"3\n",
"0\n",
"0\n",
"10\n",
"2\n",
"0\n",
"15\n",
"2\n",
"0\n",
"0\n",
"99\n",
"0\n",
"0\n",
"5\n",
"2\n",
"0\n",
"1\n",
"90\n",
"0\n",
"0\n",
"51\n",
"0\n",
"15\n",
"0\n",
"0\n",
"3\n",
"0\n",
"1\n",
"30\n",
"0\n",
"0\n",
"30\n",
"15\n",
"0\n",
"0\n",
"10\n",
"2\n",
"100\n",
"0\n",
"3\n",
"99\n",
"10\n",
"0\n",
"0\n",
"2\n",
"0\n",
"1\n",
"90\n",
"0\n",
"0\n",
"51\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Andrew was very excited to participate in Olympiad of Metropolises. Days flew by quickly, and Andrew is already at the airport, ready to go home. He has n rubles left, and would like to exchange them to euro and dollar bills. Andrew can mix dollar bills and euro bills in whatever way he wants. The price of one dollar is d rubles, and one euro costs e rubles.
Recall that there exist the following dollar bills: 1, 2, 5, 10, 20, 50, 100, and the following euro bills — 5, 10, 20, 50, 100, 200 (note that, in this problem we do not consider the 500 euro bill, it is hard to find such bills in the currency exchange points). Andrew can buy any combination of bills, and his goal is to minimize the total number of rubles he will have after the exchange.
Help him — write a program that given integers n, e and d, finds the minimum number of rubles Andrew can get after buying dollar and euro bills.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 10^8) — the initial sum in rubles Andrew has.
The second line of the input contains one integer d (30 ≤ d ≤ 100) — the price of one dollar in rubles.
The third line of the input contains integer e (30 ≤ e ≤ 100) — the price of one euro in rubles.
Output
Output one integer — the minimum number of rubles Andrew can have after buying dollar and euro bills optimally.
Examples
Input
100
60
70
Output
40
Input
410
55
70
Output
5
Input
600
60
70
Output
0
Note
In the first example, we can buy just 1 dollar because there is no 1 euro bill.
In the second example, optimal exchange is to buy 5 euro and 1 dollar.
In the third example, optimal exchange is to buy 10 dollars in one bill.
### Input:
410
55
70
### Output:
5
### Input:
600
60
70
### Output:
0
### Code:
n=int(input())
d=int(input())
e=int(input())
arr=100
a,b=min(d,5*e),max(d,5*e)
for i in range(0,n//b+1):
arr=min(arr,(n-i*b)%a)
print(arr)
|
1237_C2. Balanced Removals (Harder)_28559
|
This is a harder version of the problem. In this version, n ≤ 50 000.
There are n distinct points in three-dimensional space numbered from 1 to n. The i-th point has coordinates (x_i, y_i, z_i). The number of points n is even.
You'd like to remove all n points using a sequence of n/2 snaps. In one snap, you can remove any two points a and b that have not been removed yet and form a perfectly balanced pair. A pair of points a and b is perfectly balanced if no other point c (that has not been removed yet) lies within the axis-aligned minimum bounding box of points a and b.
Formally, point c lies within the axis-aligned minimum bounding box of points a and b if and only if min(x_a, x_b) ≤ x_c ≤ max(x_a, x_b), min(y_a, y_b) ≤ y_c ≤ max(y_a, y_b), and min(z_a, z_b) ≤ z_c ≤ max(z_a, z_b). Note that the bounding box might be degenerate.
Find a way to remove all points in n/2 snaps.
Input
The first line contains a single integer n (2 ≤ n ≤ 50 000; n is even), denoting the number of points.
Each of the next n lines contains three integers x_i, y_i, z_i (-10^8 ≤ x_i, y_i, z_i ≤ 10^8), denoting the coordinates of the i-th point.
No two points coincide.
Output
Output n/2 pairs of integers a_i, b_i (1 ≤ a_i, b_i ≤ n), denoting the indices of points removed on snap i. Every integer between 1 and n, inclusive, must appear in your output exactly once.
We can show that it is always possible to remove all points. If there are many solutions, output any of them.
Examples
Input
6
3 1 0
0 3 0
2 2 0
1 0 0
1 3 0
0 1 0
Output
3 6
5 1
2 4
Input
8
0 1 1
1 0 1
1 1 0
1 1 1
2 2 2
3 2 2
2 3 2
2 2 3
Output
4 5
1 6
2 7
3 8
Note
In the first example, here is what points and their corresponding bounding boxes look like (drawn in two dimensions for simplicity, as all points lie on z = 0 plane). Note that order of removing matters: for example, points 5 and 1 don't form a perfectly balanced pair initially, but they do after point 3 is removed.
<image>
|
def solve_z(points):
cur = None
d = {}
for p in points:
if p[0] not in d:
d[p[0]] = []
d[p[0]].append(p)
for k in d:
d[k] = sorted(d[k], key = lambda x: x[1])
for k in sorted(d.keys()):
n = len(d[k])
for i in range(0, n, 2):
if i + 1 == n:
if cur is None:
cur = str(d[k][i][3])
else:
print(cur+ ' ' +str(d[k][i][3]))
cur = None
else:
p1, p2 = d[k][i][3], d[k][i+1][3]
print(str(p1) + ' ' + str(p2))
return cur
n = int(input())
P = [list(map(int, input().split())) + [i+1] for i in range(n)]
d_z = {}
for p in P:
if p[2] not in d_z:
d_z[p[2]] = []
d_z[p[2]].append(p)
cur = None
for k in sorted(d_z.keys()):
next_ = solve_z(d_z[k])
if next_ is not None:
if cur is None:
cur = next_
else:
print(cur+' '+next_)
cur = None
#6
#3 1 0
#0 3 0
#2 2 0
#1 0 0
#1 3 0
#0 1 0
|
{
"input": [
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 0\n0 1 0\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 2 3\n",
"4\n-42939263 80157803 90523514\n-42939263 94977529 90523514\n-42939263 94977529 -3280468\n-42939263 80157803 -3280468\n",
"2\n34319950 -11299623 -19866275\n34319950 -11299623 98728529\n",
"2\n100000000 -100000000 -100000000\n-100000000 -100000000 -100000000\n",
"2\n-100000000 -100000000 -100000000\n-100000000 -100000000 100000000\n",
"4\n-53055455 42895224 28613596\n-53061404 42895224 39577025\n-53061404 42895224 28613596\n-53055455 42895224 39577025\n",
"2\n-100000000 100000000 -100000000\n-100000000 -100000000 -100000000\n",
"2\n-100000000 -100000000 -100000000\n100000000 -100000000 -100000000\n",
"2\n35627406 -93449884 80249079\n52771770 -93449884 80249079\n",
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 0\n0 1 0\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 2 3\n",
"2\n-32839949 -68986721 41592956\n-32839949 -31435211 41592956\n",
"8\n-100000000 -100000000 -100000000\n100000000 100000000 100000000\n-100000000 100000000 100000000\n-100000000 -100000000 100000000\n100000000 100000000 -100000000\n100000000 -100000000 -100000000\n-100000000 100000000 -100000000\n100000000 -100000000 100000000\n",
"2\n62887961 73879338 -68804433\n62887961 63665147 -68804433\n",
"4\n32117556 7831842 -38931866\n32117556 -42244261 -38931866\n-24487444 -42244261 -38931866\n-24487444 7831842 -38931866\n",
"4\n-42939263 80157803 90523514\n-42939263 94977529 64247458\n-42939263 94977529 -3280468\n-42939263 80157803 -3280468\n",
"2\n34319950 -11299623 -19866275\n34319950 -222228 98728529\n",
"2\n100000000 -100000000 -100000000\n-100000000 -100000000 -171045861\n",
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 0\n0 2 0\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 4 3\n",
"8\n-100000000 -100000000 -100000000\n100000000 100001000 100000000\n-100000000 100000000 100000000\n-100000000 -100000000 100000000\n100000000 100000000 -100000000\n100000000 -100000000 -100000000\n-100000000 100000000 -100000000\n100000000 -100000000 100000000\n",
"4\n32117556 4239882 -38931866\n32117556 -42244261 -38931866\n-24487444 -42244261 -38931866\n-24487444 7831842 -38931866\n",
"8\n0 1 2\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 2 3\n",
"4\n-42939263 101881696 90523514\n-42939263 94977529 64247458\n-42939263 94977529 -3280468\n-42939263 80157803 -3280468\n",
"6\n0 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 0\n0 2 0\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n3 3 2\n2 4 3\n",
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 -1\n1 1 0\n",
"6\n0 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 0\n1 2 0\n",
"4\n-42939263 101881696 90523514\n-42939263 94977529 64247458\n-42939263 94977529 -460572\n-8336053 80157803 -3280468\n",
"6\n0 1 0\n0 3 0\n0 2 0\n1 0 0\n1 3 0\n1 2 0\n",
"4\n32117556 4239882 -38931866\n32117556 -42244261 -46020877\n-24487444 -42244261 -38931866\n-5751467 7831842 -45745935\n",
"6\n0 1 0\n0 3 0\n0 4 0\n1 0 0\n1 3 0\n1 2 0\n",
"2\n-100000000 -100000000 -100000000\n-100000000 -66583883 100000000\n",
"2\n-100000000 100000000 -100000000\n-100000000 -100000000 -164816150\n",
"2\n-65652541 -100000000 -100000000\n100000000 -100000000 -100000000\n",
"2\n15781034 -93449884 80249079\n52771770 -93449884 80249079\n",
"2\n-32839949 -68986721 68917885\n-32839949 -31435211 41592956\n",
"2\n62887961 73879338 -68804433\n26919603 63665147 -68804433\n",
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 -1\n0 1 0\n",
"2\n34319950 -11299623 -19866275\n34319950 -222228 134477576\n",
"2\n100000010 -100000000 -100000000\n-100000000 -100000000 -171045861\n",
"2\n-165691664 -100000000 -100000000\n-100000000 -66583883 100000000\n",
"2\n-100000000 100000010 -100000000\n-100000000 -100000000 -164816150\n",
"2\n-65652541 -100000000 -100000000\n100000000 -100000000 -42390165\n",
"2\n15781034 -93449884 20051959\n52771770 -93449884 80249079\n",
"2\n-32839949 -68986721 68917885\n-25790425 -31435211 41592956\n",
"2\n62887961 131512713 -68804433\n26919603 63665147 -68804433\n",
"4\n32117556 4239882 -38931866\n32117556 -42244261 -46020877\n-24487444 -42244261 -38931866\n-24487444 7831842 -38931866\n",
"8\n0 1 2\n1 0 0\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 2 3\n",
"4\n-42939263 101881696 90523514\n-42939263 94977529 64247458\n-42939263 94977529 -460572\n-42939263 80157803 -3280468\n",
"2\n34319950 -11299623 -19866275\n9150889 -222228 134477576\n",
"2\n100000010 -100000000 -100000000\n-100000000 -100000000 -158924809\n",
"2\n-165691664 -100000000 -100000000\n-100000000 -66583883 000000000\n",
"2\n-100000000 100000010 -100000000\n-100000000 -100000000 -137953987\n",
"2\n-65652541 -68402136 -100000000\n100000000 -100000000 -42390165\n",
"2\n15781034 -76909018 20051959\n52771770 -93449884 80249079\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n3 3 2\n2 4 4\n",
"2\n-32839949 -68986721 67205973\n-25790425 -31435211 41592956\n",
"2\n62887961 131512713 -68804433\n26919603 65468611 -68804433\n",
"4\n32117556 4239882 -38931866\n32117556 -42244261 -46020877\n-24487444 -42244261 -38931866\n-24487444 7831842 -45745935\n",
"6\n3 1 0\n0 3 0\n2 2 0\n1 0 0\n1 3 -2\n1 1 0\n",
"8\n-1 1 2\n1 0 0\n1 1 0\n1 1 1\n2 2 2\n3 2 2\n2 3 2\n2 2 3\n",
"2\n34319950 -11299623 -19866275\n9150889 -115081 134477576\n",
"2\n100000010 -100000000 -100000000\n-100000000 -100000000 -221918514\n",
"2\n-165691664 -3693680 -100000000\n-100000000 -66583883 000000000\n",
"2\n-100000000 100000010 -100000000\n-100000000 -100000000 -72974119\n",
"2\n-65652541 -68402136 -100000000\n100100000 -100000000 -42390165\n",
"2\n15781034 -76909018 20051959\n3025109 -93449884 80249079\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n5 2 2\n3 3 2\n2 4 4\n",
"2\n-32839949 -68986721 75726443\n-25790425 -31435211 41592956\n",
"2\n62887961 131512713 -4892751\n26919603 65468611 -68804433\n",
"8\n-1 1 2\n1 0 0\n1 1 0\n1 1 1\n2 2 2\n5 2 2\n2 3 2\n2 2 3\n",
"4\n-42939263 101881696 90523514\n-42939263 94977529 44705189\n-42939263 94977529 -460572\n-8336053 80157803 -3280468\n",
"2\n34319950 -11299623 -19866275\n9150889 -115081 14346061\n",
"2\n100000010 -100000000 -100000000\n-100000000 -100000000 -133957340\n",
"2\n-165691664 -3693680 -199581656\n-100000000 -66583883 000000000\n",
"2\n-124067869 100000010 -100000000\n-100000000 -100000000 -72974119\n",
"2\n-65652541 -68402136 -100000000\n100100000 -100000000 -12856070\n",
"2\n15781034 -109253818 20051959\n3025109 -93449884 80249079\n",
"8\n0 1 1\n1 0 1\n1 1 0\n1 1 1\n2 2 2\n8 2 2\n3 3 2\n2 4 4\n",
"2\n-32839949 -68986721 75726443\n-25790425 -8936179 41592956\n",
"2\n62887961 131512713 -4892751\n26919603 87621048 -68804433\n",
"4\n32117556 7140523 -38931866\n32117556 -42244261 -46020877\n-24487444 -42244261 -38931866\n-5751467 7831842 -45745935\n",
"4\n-42939263 101881696 120845255\n-42939263 94977529 44705189\n-42939263 94977529 -460572\n-8336053 80157803 -3280468\n",
"2\n34319950 -11299623 -19866275\n9150889 -115081 18689305\n",
"2\n100000010 -100000000 -100000000\n-5253442 -100000000 -133957340\n",
"2\n-165691664 -3693680 -199581656\n-100000000 -66583883 001000000\n",
"2\n-124067869 100000010 -100000000\n-100000000 -100000000 -143988809\n",
"2\n-65652541 -38723319 -100000000\n100100000 -100000000 -12856070\n",
"2\n15781034 -109253818 20051959\n3025109 -136507604 80249079\n",
"6\n0 1 0\n0 5 0\n0 4 0\n1 0 0\n1 3 0\n1 2 0\n"
],
"output": [
"6 2\n4 5\n3 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"4 1\n3 2\n",
"1 2\n",
"2 1\n",
"1 2\n",
"3 2\n1 4\n",
"2 1\n",
"1 2\n",
"1 2\n",
"6 2\n4 5\n3 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"1 2\n",
"1 4\n7 3\n6 8\n5 2\n",
"2 1\n",
"3 4\n2 1\n",
"4 1\n3 2\n",
"1 2\n",
"2 1\n",
"6 2\n4 5\n3 1\n",
"3 4\n5 7\n1 2\n8 6\n",
"1 4\n7 3\n6 8\n5 2\n",
"3 4\n2 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"3 2\n4 1\n",
"1 6\n4 5\n2 3\n",
"3 4\n5 8\n6 7\n1 2\n",
"4 6\n2 5\n3 1\n",
"1 2\n4 6\n5 3\n",
"3 2\n1 4\n",
"1 3\n4 6\n2 5\n",
"2 1\n3 4\n",
"1 2\n4 6\n3 5\n",
"1 2\n",
"2 1\n",
"1 2\n",
"1 2\n",
"1 2\n",
"2 1\n",
"6 2\n4 5\n3 1\n",
"1 2\n",
"2 1\n",
"1 2\n",
"2 1\n",
"1 2\n",
"1 2\n",
"1 2\n",
"2 1\n",
"3 4\n2 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"3 2\n4 1\n",
"2 1\n",
"2 1\n",
"1 2\n",
"2 1\n",
"1 2\n",
"1 2\n",
"3 4\n5 8\n6 7\n1 2\n",
"1 2\n",
"2 1\n",
"3 4\n2 1\n",
"4 6\n2 5\n3 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"2 1\n",
"2 1\n",
"1 2\n",
"2 1\n",
"1 2\n",
"2 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"1 2\n",
"2 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"3 2\n1 4\n",
"2 1\n",
"2 1\n",
"1 2\n",
"1 2\n",
"1 2\n",
"2 1\n",
"3 4\n5 8\n1 2\n7 6\n",
"1 2\n",
"2 1\n",
"2 1\n3 4\n",
"3 2\n1 4\n",
"2 1\n",
"2 1\n",
"1 2\n",
"1 2\n",
"1 2\n",
"2 1\n",
"1 3\n4 6\n2 5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This is a harder version of the problem. In this version, n ≤ 50 000.
There are n distinct points in three-dimensional space numbered from 1 to n. The i-th point has coordinates (x_i, y_i, z_i). The number of points n is even.
You'd like to remove all n points using a sequence of n/2 snaps. In one snap, you can remove any two points a and b that have not been removed yet and form a perfectly balanced pair. A pair of points a and b is perfectly balanced if no other point c (that has not been removed yet) lies within the axis-aligned minimum bounding box of points a and b.
Formally, point c lies within the axis-aligned minimum bounding box of points a and b if and only if min(x_a, x_b) ≤ x_c ≤ max(x_a, x_b), min(y_a, y_b) ≤ y_c ≤ max(y_a, y_b), and min(z_a, z_b) ≤ z_c ≤ max(z_a, z_b). Note that the bounding box might be degenerate.
Find a way to remove all points in n/2 snaps.
Input
The first line contains a single integer n (2 ≤ n ≤ 50 000; n is even), denoting the number of points.
Each of the next n lines contains three integers x_i, y_i, z_i (-10^8 ≤ x_i, y_i, z_i ≤ 10^8), denoting the coordinates of the i-th point.
No two points coincide.
Output
Output n/2 pairs of integers a_i, b_i (1 ≤ a_i, b_i ≤ n), denoting the indices of points removed on snap i. Every integer between 1 and n, inclusive, must appear in your output exactly once.
We can show that it is always possible to remove all points. If there are many solutions, output any of them.
Examples
Input
6
3 1 0
0 3 0
2 2 0
1 0 0
1 3 0
0 1 0
Output
3 6
5 1
2 4
Input
8
0 1 1
1 0 1
1 1 0
1 1 1
2 2 2
3 2 2
2 3 2
2 2 3
Output
4 5
1 6
2 7
3 8
Note
In the first example, here is what points and their corresponding bounding boxes look like (drawn in two dimensions for simplicity, as all points lie on z = 0 plane). Note that order of removing matters: for example, points 5 and 1 don't form a perfectly balanced pair initially, but they do after point 3 is removed.
<image>
### Input:
6
3 1 0
0 3 0
2 2 0
1 0 0
1 3 0
0 1 0
### Output:
6 2
4 5
3 1
### Input:
8
0 1 1
1 0 1
1 1 0
1 1 1
2 2 2
3 2 2
2 3 2
2 2 3
### Output:
3 4
5 8
1 2
7 6
### Code:
def solve_z(points):
cur = None
d = {}
for p in points:
if p[0] not in d:
d[p[0]] = []
d[p[0]].append(p)
for k in d:
d[k] = sorted(d[k], key = lambda x: x[1])
for k in sorted(d.keys()):
n = len(d[k])
for i in range(0, n, 2):
if i + 1 == n:
if cur is None:
cur = str(d[k][i][3])
else:
print(cur+ ' ' +str(d[k][i][3]))
cur = None
else:
p1, p2 = d[k][i][3], d[k][i+1][3]
print(str(p1) + ' ' + str(p2))
return cur
n = int(input())
P = [list(map(int, input().split())) + [i+1] for i in range(n)]
d_z = {}
for p in P:
if p[2] not in d_z:
d_z[p[2]] = []
d_z[p[2]].append(p)
cur = None
for k in sorted(d_z.keys()):
next_ = solve_z(d_z[k])
if next_ is not None:
if cur is None:
cur = next_
else:
print(cur+' '+next_)
cur = None
#6
#3 1 0
#0 3 0
#2 2 0
#1 0 0
#1 3 0
#0 1 0
|
1255_C. League of Leesins_28563
|
Bob is an avid fan of the video game "League of Leesins", and today he celebrates as the League of Leesins World Championship comes to an end!
The tournament consisted of n (n ≥ 5) teams around the world. Before the tournament starts, Bob has made a prediction of the rankings of each team, from 1-st to n-th. After the final, he compared the prediction with the actual result and found out that the i-th team according to his prediction ended up at the p_i-th position (1 ≤ p_i ≤ n, all p_i are unique). In other words, p is a permutation of 1, 2, ..., n.
As Bob's favorite League player is the famous "3ga", he decided to write down every 3 consecutive elements of the permutation p. Formally, Bob created an array q of n-2 triples, where q_i = (p_i, p_{i+1}, p_{i+2}) for each 1 ≤ i ≤ n-2. Bob was very proud of his array, so he showed it to his friend Alice.
After learning of Bob's array, Alice declared that she could retrieve the permutation p even if Bob rearranges the elements of q and the elements within each triple. Of course, Bob did not believe in such magic, so he did just the same as above to see Alice's respond.
For example, if n = 5 and p = [1, 4, 2, 3, 5], then the original array q will be [(1, 4, 2), (4, 2, 3), (2, 3, 5)]. Bob can then rearrange the numbers within each triple and the positions of the triples to get [(4, 3, 2), (2, 3, 5), (4, 1, 2)]. Note that [(1, 4, 2), (4, 2, 2), (3, 3, 5)] is not a valid rearrangement of q, as Bob is not allowed to swap numbers belong to different triples.
As Alice's friend, you know for sure that Alice was just trying to show off, so you decided to save her some face by giving her any permutation p that is consistent with the array q she was given.
Input
The first line contains a single integer n (5 ≤ n ≤ 10^5) — the size of permutation p.
The i-th of the next n-2 lines contains 3 integers q_{i, 1}, q_{i, 2}, q_{i, 3} (1 ≤ q_{i, j} ≤ n) — the elements of the i-th triple of the rearranged (shuffled) array q_i, in random order. Remember, that the numbers within each triple can be rearranged and also the positions of the triples can be rearranged.
It is guaranteed that there is at least one permutation p that is consistent with the input.
Output
Print n distinct integers p_1, p_2, …, p_n (1 ≤ p_i ≤ n) such that p is consistent with array q.
If there are multiple answers, print any.
Example
Input
5
4 3 2
2 3 5
4 1 2
Output
1 4 2 3 5
|
def zip_sorted(a,b):
# sorted by a
a,b = zip(*sorted(zip(a,b)))
# sorted by b
sorted(zip(a, b), key=lambda x: x[1])
return a,b
def return_nxt(i,a,b):
visited.add(i)
c = (set(mem2[i])-set([a,b])).pop()
final.append(c)
if len(final)==n:
return -1,b,c
new_idx = ((set(mem1[b])-visited)&(set(mem1[c])-visited)).pop()
return new_idx,b,c
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
S = lambda : list(map(str,input().split()))
from collections import defaultdict
mem1 = defaultdict(list)
mem2 = defaultdict(list)
n,=I()
for t1 in range(n-2):
a,b,c=I()
mem2[t1] = [a,b,c]
mem1[a].append(t1)
mem1[b].append(t1)
mem1[c].append(t1)
start1 = -1
start2 = -1
start_idx = -1
for i in mem1:
if len(mem1[i])==1:
start1 = i
idx = mem1[i][0]
start_idx = mem1[i][0]
for j in range(len(mem2[idx])):
val = mem2[idx][j]
if len(mem1[val])==2:
start2 = val
break
break
final = [start1,start2]
visited = set()
for i in range(n-2):
start_idx,start1,start2 = return_nxt(start_idx,start1,start2)
print(*final)
|
{
"input": [
"5\n4 3 2\n2 3 5\n4 1 2\n",
"5\n4 5 3\n2 5 1\n1 3 5\n",
"9\n7 5 3\n8 9 4\n8 1 7\n8 9 1\n1 5 7\n2 3 5\n6 3 2\n",
"5\n2 3 4\n2 4 1\n5 3 2\n",
"8\n3 7 6\n6 2 3\n2 6 8\n2 4 8\n4 1 8\n1 5 4\n",
"6\n1 6 5\n4 5 1\n2 4 1\n4 2 3\n",
"9\n1 8 9\n9 6 4\n2 1 3\n1 2 8\n3 5 2\n6 7 4\n8 9 4\n",
"7\n7 6 5\n7 2 1\n6 7 1\n1 2 3\n5 4 6\n",
"5\n1 2 3\n2 3 4\n3 4 5\n",
"7\n2 5 3\n5 2 4\n1 7 4\n1 6 7\n4 7 5\n",
"8\n8 3 1\n3 4 6\n8 5 1\n7 4 6\n8 6 3\n7 4 2\n",
"5\n2 3 1\n5 1 3\n5 3 4\n",
"8\n2 5 4\n3 5 2\n3 1 5\n1 8 3\n6 7 8\n8 7 1\n",
"6\n4 2 3\n6 5 1\n5 1 4\n4 1 3\n",
"5\n5 4 3\n4 3 2\n3 2 1\n",
"7\n1 4 7\n2 1 7\n4 7 5\n5 4 3\n2 6 1\n",
"5\n5 2 3\n4 5 3\n1 5 4\n",
"6\n4 1 5\n1 6 3\n1 6 4\n3 2 6\n",
"6\n4 3 5\n3 4 6\n4 6 2\n2 6 1\n",
"8\n3 7 5\n2 1 6\n3 7 6\n8 2 1\n6 3 1\n4 2 8\n",
"9\n6 9 8\n2 3 4\n2 3 1\n5 6 8\n4 6 5\n7 8 9\n3 5 4\n",
"6\n4 2 3\n6 5 1\n5 1 3\n4 1 3\n",
"5\n2 5 1\n5 1 3\n5 3 4\n",
"7\n7 6 5\n7 3 1\n6 7 1\n1 2 3\n5 4 6\n",
"5\n4 3 2\n4 3 5\n4 1 2\n",
"5\n4 5 2\n2 3 5\n4 1 2\n",
"5\n5 4 2\n4 3 2\n3 2 1\n",
"5\n1 2 3\n1 3 4\n3 4 5\n",
"6\n4 1 5\n1 6 2\n1 6 4\n3 2 6\n",
"5\n2 5 1\n5 2 3\n5 3 4\n",
"5\n5 1 2\n4 3 2\n3 2 1\n",
"6\n4 1 5\n1 6 2\n1 2 4\n3 2 6\n",
"9\n7 5 2\n8 9 4\n8 1 7\n8 9 1\n1 5 7\n2 3 5\n6 3 2\n",
"7\n1 5 7\n2 1 7\n4 7 5\n5 4 3\n2 6 1\n",
"5\n1 3 2\n2 3 5\n4 1 2\n",
"9\n1 8 9\n9 6 4\n2 1 3\n1 2 8\n3 5 2\n6 7 4\n8 9 6\n",
"6\n1 6 5\n4 5 1\n3 4 1\n4 2 3\n",
"6\n4 2 3\n6 3 1\n5 2 4\n4 1 3\n",
"5\n1 2 3\n1 3 5\n3 4 5\n",
"5\n2 3 4\n2 4 1\n5 1 2\n",
"5\n2 5 1\n5 2 3\n2 3 4\n",
"5\n1 3 2\n2 3 5\n4 1 3\n",
"6\n4 2 3\n6 5 2\n5 2 3\n4 1 3\n",
"5\n5 2 3\n4 2 5\n1 5 4\n",
"5\n5 4 2\n5 3 2\n3 2 1\n",
"5\n5 4 2\n4 3 2\n3 4 1\n",
"5\n4 3 2\n2 3 5\n4 1 3\n",
"5\n1 3 2\n2 4 5\n4 1 2\n",
"5\n1 3 2\n1 3 5\n4 1 2\n",
"5\n4 5 2\n2 5 1\n1 3 5\n",
"5\n5 4 3\n5 3 2\n3 2 1\n",
"5\n1 2 4\n1 3 4\n3 4 5\n",
"5\n1 3 4\n2 4 5\n4 1 2\n",
"5\n3 4 2\n5 3 2\n4 2 1\n",
"5\n4 3 2\n1 3 5\n4 1 3\n",
"5\n1 3 2\n2 1 5\n4 2 5\n",
"7\n2 5 3\n5 3 4\n1 7 4\n1 6 7\n4 7 5\n",
"6\n4 1 5\n1 5 2\n1 2 3\n3 2 6\n",
"5\n1 2 5\n1 4 5\n3 4 5\n",
"5\n1 2 5\n1 4 5\n3 2 5\n",
"5\n2 3 4\n2 4 1\n5 3 4\n",
"5\n2 5 4\n2 4 1\n5 3 2\n",
"5\n1 2 4\n2 3 4\n3 4 5\n",
"5\n1 2 5\n1 3 5\n3 4 5\n",
"5\n1 3 2\n2 1 5\n4 2 3\n",
"5\n5 4 2\n5 3 2\n4 2 1\n",
"5\n5 4 3\n4 3 2\n4 2 1\n",
"5\n2 5 1\n5 1 3\n5 2 4\n",
"5\n5 4 2\n1 3 2\n4 2 1\n"
],
"output": [
"1 4 2 3 5\n",
"2 1 5 3 4\n",
"4 9 8 1 7 5 3 2 6\n",
"1 4 2 3 5\n",
"5 1 4 8 2 6 3 7\n",
"3 2 4 1 5 6\n",
"5 3 2 1 8 9 4 6 7\n",
"3 2 1 7 6 5 4\n",
"1 2 3 4 5\n",
"3 2 5 4 7 1 6\n",
"2 7 4 6 3 8 1 5\n",
"2 1 3 5 4\n",
"4 2 5 3 1 8 7 6\n",
"2 3 4 1 5 6\n",
"1 2 3 4 5\n",
"3 5 4 7 1 2 6\n",
"1 4 5 3 2\n",
"2 3 6 1 4 5\n",
"1 2 6 4 3 5\n",
"4 8 2 1 6 3 7 5\n",
"1 2 3 4 5 6 8 9 7\n",
"2 4 3 1 5 6\n",
"2 1 5 3 4\n",
"2 3 1 7 6 5 4\n",
"1 2 4 3 5\n",
"1 4 2 5 3\n",
"1 3 2 4 5\n",
"2 1 3 4 5\n",
"3 2 6 1 4 5\n",
"1 2 5 3 4\n",
"4 3 2 1 5\n",
"3 6 2 1 4 5\n",
"4 9 8 1 7 5 2 3 6\n",
"3 4 5 7 1 2 6\n",
"4 1 2 3 5\n",
"5 3 2 1 8 9 6 4 7\n",
"2 3 4 1 5 6\n",
"5 2 4 3 1 6\n",
"2 1 3 5 4\n",
"3 4 2 1 5\n",
"1 5 2 3 4\n",
"4 1 3 2 5\n",
"1 4 3 2 5 6\n",
"1 4 5 2 3\n",
"1 3 2 5 4\n",
"1 3 4 2 5\n",
"1 4 3 2 5\n",
"3 1 2 4 5\n",
"4 2 1 3 5\n",
"3 1 5 2 4\n",
"1 2 3 5 4\n",
"2 1 4 3 5\n",
"3 1 4 2 5\n",
"1 4 2 3 5\n",
"2 4 3 1 5\n",
"3 1 2 5 4\n",
"2 3 5 4 7 1 6\n",
"4 5 1 2 3 6\n",
"2 1 5 4 3\n",
"3 2 5 1 4\n",
"1 2 4 3 5\n",
"1 4 2 5 3\n",
"1 2 4 3 5\n",
"2 1 5 3 4\n",
"4 3 2 1 5\n",
"1 4 2 5 3\n",
"1 2 4 3 5\n",
"3 1 5 2 4\n",
"3 1 2 4 5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bob is an avid fan of the video game "League of Leesins", and today he celebrates as the League of Leesins World Championship comes to an end!
The tournament consisted of n (n ≥ 5) teams around the world. Before the tournament starts, Bob has made a prediction of the rankings of each team, from 1-st to n-th. After the final, he compared the prediction with the actual result and found out that the i-th team according to his prediction ended up at the p_i-th position (1 ≤ p_i ≤ n, all p_i are unique). In other words, p is a permutation of 1, 2, ..., n.
As Bob's favorite League player is the famous "3ga", he decided to write down every 3 consecutive elements of the permutation p. Formally, Bob created an array q of n-2 triples, where q_i = (p_i, p_{i+1}, p_{i+2}) for each 1 ≤ i ≤ n-2. Bob was very proud of his array, so he showed it to his friend Alice.
After learning of Bob's array, Alice declared that she could retrieve the permutation p even if Bob rearranges the elements of q and the elements within each triple. Of course, Bob did not believe in such magic, so he did just the same as above to see Alice's respond.
For example, if n = 5 and p = [1, 4, 2, 3, 5], then the original array q will be [(1, 4, 2), (4, 2, 3), (2, 3, 5)]. Bob can then rearrange the numbers within each triple and the positions of the triples to get [(4, 3, 2), (2, 3, 5), (4, 1, 2)]. Note that [(1, 4, 2), (4, 2, 2), (3, 3, 5)] is not a valid rearrangement of q, as Bob is not allowed to swap numbers belong to different triples.
As Alice's friend, you know for sure that Alice was just trying to show off, so you decided to save her some face by giving her any permutation p that is consistent with the array q she was given.
Input
The first line contains a single integer n (5 ≤ n ≤ 10^5) — the size of permutation p.
The i-th of the next n-2 lines contains 3 integers q_{i, 1}, q_{i, 2}, q_{i, 3} (1 ≤ q_{i, j} ≤ n) — the elements of the i-th triple of the rearranged (shuffled) array q_i, in random order. Remember, that the numbers within each triple can be rearranged and also the positions of the triples can be rearranged.
It is guaranteed that there is at least one permutation p that is consistent with the input.
Output
Print n distinct integers p_1, p_2, …, p_n (1 ≤ p_i ≤ n) such that p is consistent with array q.
If there are multiple answers, print any.
Example
Input
5
4 3 2
2 3 5
4 1 2
Output
1 4 2 3 5
### Input:
5
4 3 2
2 3 5
4 1 2
### Output:
1 4 2 3 5
### Input:
5
4 5 3
2 5 1
1 3 5
### Output:
2 1 5 3 4
### Code:
def zip_sorted(a,b):
# sorted by a
a,b = zip(*sorted(zip(a,b)))
# sorted by b
sorted(zip(a, b), key=lambda x: x[1])
return a,b
def return_nxt(i,a,b):
visited.add(i)
c = (set(mem2[i])-set([a,b])).pop()
final.append(c)
if len(final)==n:
return -1,b,c
new_idx = ((set(mem1[b])-visited)&(set(mem1[c])-visited)).pop()
return new_idx,b,c
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
S = lambda : list(map(str,input().split()))
from collections import defaultdict
mem1 = defaultdict(list)
mem2 = defaultdict(list)
n,=I()
for t1 in range(n-2):
a,b,c=I()
mem2[t1] = [a,b,c]
mem1[a].append(t1)
mem1[b].append(t1)
mem1[c].append(t1)
start1 = -1
start2 = -1
start_idx = -1
for i in mem1:
if len(mem1[i])==1:
start1 = i
idx = mem1[i][0]
start_idx = mem1[i][0]
for j in range(len(mem2[idx])):
val = mem2[idx][j]
if len(mem1[val])==2:
start2 = val
break
break
final = [start1,start2]
visited = set()
for i in range(n-2):
start_idx,start1,start2 = return_nxt(start_idx,start1,start2)
print(*final)
|
1279_B. Verse For Santa_28567
|
New Year is coming! Vasya has prepared a New Year's verse and wants to recite it in front of Santa Claus.
Vasya's verse contains n parts. It takes a_i seconds to recite the i-th part. Vasya can't change the order of parts in the verse: firstly he recites the part which takes a_1 seconds, secondly — the part which takes a_2 seconds, and so on. After reciting the verse, Vasya will get the number of presents equal to the number of parts he fully recited.
Vasya can skip at most one part of the verse while reciting it (if he skips more than one part, then Santa will definitely notice it).
Santa will listen to Vasya's verse for no more than s seconds. For example, if s = 10, a = [100, 9, 1, 1], and Vasya skips the first part of verse, then he gets two presents.
Note that it is possible to recite the whole verse (if there is enough time).
Determine which part Vasya needs to skip to obtain the maximum possible number of gifts. If Vasya shouldn't skip anything, print 0. If there are multiple answers, print any of them.
You have to process t test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The first line of each test case contains two integers n and s (1 ≤ n ≤ 10^5, 1 ≤ s ≤ 10^9) — the number of parts in the verse and the maximum number of seconds Santa will listen to Vasya, respectively.
The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the time it takes to recite each part of the verse.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
Output
For each test case print one integer — the number of the part that Vasya needs to skip to obtain the maximum number of gifts. If Vasya shouldn't skip any parts, print 0.
Example
Input
3
7 11
2 9 1 3 18 1 4
4 35
11 9 10 7
1 8
5
Output
2
1
0
Note
In the first test case if Vasya skips the second part then he gets three gifts.
In the second test case no matter what part of the verse Vasya skips.
In the third test case Vasya can recite the whole verse.
|
import sys
input = sys.stdin.readline
t = int(input())
while t > 0:
n, s = map(int, input().split())
a = list(map(int, input().split()))
ans = 0
for i in range(n):
if a[ans] < a[i]:
ans = i
s -= a[i]
if (s < 0): break
if s >= 0:
ans = -1
print(ans + 1)
t -= 1
|
{
"input": [
"3\n7 11\n2 9 1 3 18 1 4\n4 35\n11 9 10 7\n1 8\n5\n",
"7\n10 11\n2 2 2 6 5 3 4 4 4 100000000\n4 102\n98 1 3 99\n4 103\n5 98 1 97\n11 1000000000\n100000000 100000002 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 99999999\n8 90\n20 8 20 20 20 20 1 1\n3 1000000000\n1000000000 1000000000 1000000000\n11 1000000000\n1 3 5 1000000000 1 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"4\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 999999999 1000000000 1000000000 1000000000\n5 1000000000\n1 999999999 999999998 1 1000000000\n",
"1\n6 1000000000\n1 999999999 999999998 1 999999999 1\n",
"1\n6 1000000000\n999999999 999999999 999999999 1 1 1\n",
"1\n5 999999999\n1000000000 999999999 1000000000 1000000000 1000000000\n",
"1\n9 1000000000\n999999999 9 999999990 999999999 999999999 999999999 999999999 9 999999999\n",
"1\n4 1000000000\n999999998 1000000000 2 999999999\n",
"1\n24 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n7 1000000000\n500000000 999999999 500000000 1000000000 1000000000 1000000000 294967297\n",
"1\n4 1000000000\n500000000 1000000000 500000000 300000000\n",
"1\n5 10\n1 8 10 1 10\n",
"5\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 999999999 1000000000 1000000000 1000000000\n5 1000000000\n1 999999999 999999998 1 1000000000\n10 1000000000\n1 999999998 1 999999999 1 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n4 1000000000\n2 999999999 999999998 1000000000\n",
"1\n7 1000000000\n1 1 1000000000 1 1 1000000000 1000000000\n",
"1\n6 1000000000\n99 999999999 123000 900000000 900000000 12\n",
"1\n24 1000000000\n999999996 2 2 2 2 2 999999990 999999992 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1\n5 850068230\n198760381 693554507 54035836 441101531 438381286\n",
"1\n30 333807280\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 424487323 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 106976325 17650089 649905801 145670799 21998257 220175998 567636481 73795226 10024990 230718118\n",
"1\n10 1000000000\n5 6 7 4 1000000000 10 74 1000000000 1000000000 1000000000\n",
"1\n6 1000000000\n999999999 999999999 1 999999999 1 1\n",
"1\n6 999999999\n1000000000 999999999 1000000000 1000000000 1000000000 1\n",
"1\n8 999999999\n1 999899998 1 1000000000 1 1000000000 1000000000 1\n",
"1\n5 999999999\n1000000000 1 1000000000 1000000000 1000000000\n",
"1\n10 10\n1 9 2 3 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"2\n9 1000000000\n999999999 9 999999990 999999999 999999999 999999999 999999999 9 999999999\n8 1000000000\n999999999 999999990 999999999 999999999 999999999 999999999 999999999 999999999\n",
"6\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 999999999 1000000000 1000000000 1000000000\n5 1000000000\n1 999999999 999999998 1 1000000000\n10 1000000000\n1 999999999 1 999999997 1 1000000000 1000000000 1000000000 1000000000 1000000000\n4 999999999\n1000000000 1 1000000000 1000000000\n",
"1\n8 1000000000\n999999996 2 2 2 2 2 999999990 999999992\n",
"1\n4 1000000000\n1 1000000000 999999998 1000000000\n",
"1\n4 1000000000\n999999999 1000000000 1 999999999\n",
"1\n25 2\n2 1 1 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n1 10\n4\n",
"1\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n",
"1\n4 1000000000\n1 1000000000 999999999 1000000000\n",
"1\n4 2\n1000000000 1 1000000000 1000000000\n",
"1\n8 1000000000\n1 1000000000 999999999 1000000000 294967296 1000000000 1000000000 1000000000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n6 1000000000\n1 999999999 999999998 1 1012258995 1\n",
"1\n5 9\n1 8 10 1 10\n",
"5\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 184318275 1000000000 1000000000 1000000000\n5 1000000000\n1 999999999 999999998 1 1000000000\n10 1000000000\n1 999999998 1 999999999 1 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n10 1000000000\n5 0 7 4 1000000000 10 74 1000000000 1000000000 1000000000\n",
"1\n8 999999999\n1 360305987 1 1000000000 1 1000000000 1000000000 1\n",
"2\n9 1000000000\n999999999 9 999999990 999999999 999999999 999999999 999999999 9 999999999\n8 1000000000\n999999999 999999990 999999999 999999999 1587762833 999999999 999999999 999999999\n",
"6\n5 1000000000\n2 999999999 999999998 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 999999999 1000000000 1000000000 1000000000\n5 1000000000\n2 999999999 999999998 1 1000000000\n10 1000000000\n1 999999999 1 999999997 1 1000000000 1000000000 1000000000 1000000000 1000000000\n4 999999999\n1000000000 1 1000000000 1000000000\n",
"1\n1 10\n5\n",
"3\n7 11\n3 9 1 3 18 1 4\n4 35\n11 9 10 7\n1 8\n5\n",
"3\n7 11\n3 9 1 3 18 1 4\n4 35\n4 9 10 7\n1 8\n5\n",
"1\n6 1000000000\n999999999 999999999 999999999 1 1 2\n",
"1\n4 999999999\n1000000000 999999999 1000000000 1000000000 1000000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 999999999 999999999 9 999999999\n",
"1\n24 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 110000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n7 1000000000\n500000000 999999999 500000000 1000000001 1000000000 1000000000 294967297\n",
"1\n4 1000000000\n166138173 1000000000 500000000 300000000\n",
"1\n4 1000000000\n2 1054207185 999999998 1000000000\n",
"1\n6 1000000000\n99 999999999 25219 900000000 900000000 12\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1\n5 850068230\n198760381 718595817 54035836 441101531 438381286\n",
"1\n30 333807280\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 424487323 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 106976325 17650089 649905801 145670799 21998257 220175998 390589630 73795226 10024990 230718118\n",
"1\n6 1244825309\n1000000000 999999999 1000000000 1000000000 1000000000 1\n",
"1\n5 999999999\n1010000000 1 1000000000 1000000000 1000000000\n",
"1\n4 1000000000\n1 1100000000 999999998 1000000000\n",
"1\n4 1000000000\n879646039 1000000000 1 999999999\n",
"1\n25 2\n2 1 1 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1010000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n4 1000010000\n1 1000000000 999999999 1000000000\n",
"1\n8 1000000000\n1 1000000000 98690276 1000000000 294967296 1000000000 1000000000 1000000000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 100000000 100000000 100000000 100000000 000000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n6 1000000000\n1 1693700912 999999998 1 1012258995 1\n",
"1\n4 999999999\n1000000000 999999999 1000000000 1000000000 1010000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 999999999 999999999 9 335574820\n",
"1\n24 1\n2 1 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 110000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n4 1000000100\n166138173 1000000000 500000000 300000000\n",
"5\n5 1000000000\n2 999999999 242505307 1000000000 1000000000\n4 1000000000\n2 999999999 999999998 1000000000\n6 1000000000\n1 1000000000 184318275 1000000000 1000000000 1000000000\n5 1000000000\n1 999999999 999999998 1 1000000000\n10 1000000000\n1 999999998 1 999999999 1 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n6 1000000000\n91 999999999 25219 900000000 900000000 12\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1\n",
"1\n5 850068230\n198760381 718595817 66039011 441101531 438381286\n",
"1\n30 333807280\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 424487323 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 106976325 17650089 649905801 145670799 34389058 220175998 390589630 73795226 10024990 230718118\n",
"1\n5 1000000000\n5 0 7 4 1000000000 10 74 1000000000 1000000000 1000000000\n",
"1\n8 999999999\n1 655102112 1 1000000000 1 1000000000 1000000000 1\n",
"1\n5 999999999\n1010000000 0 1000000000 1000000000 1000000000\n",
"1\n4 1000000000\n1 1100000000 999999998 1000100000\n",
"1\n25 2\n2 1 1 1000010000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1010000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1\n1 10\n2\n",
"1\n4 1000110000\n1 1000000000 999999999 1000000000\n",
"1\n8 1000000000\n1 1000000000 98690276 1000000000 294967296 1000000000 1000000000 1000010000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 100000000 100000000 100000000 100000000 000000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n4 1708271163\n1000000000 999999999 1000000000 1000000000 1010000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 1476745735 999999999 9 335574820\n",
"1\n24 1\n3 1 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 110000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n4 1000000100\n166138173 1000000010 500000000 300000000\n",
"1\n6 1000000000\n91 999999999 25219 900000000 900000000 4\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0\n",
"1\n5 1531535681\n198760381 718595817 66039011 441101531 438381286\n",
"1\n30 333807280\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 281979110 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 106976325 17650089 649905801 145670799 34389058 220175998 390589630 73795226 10024990 230718118\n",
"1\n5 1000000000\n5 0 7 4 1000010000 10 74 1000000000 1000000000 1000000000\n",
"1\n8 999999999\n1 655102112 1 1000000000 1 1000000000 1000000010 1\n",
"1\n5 999999999\n1011000000 0 1000000000 1000000000 1000000000\n",
"1\n4 1000000000\n2 1100000000 999999998 1000100000\n",
"1\n25 2\n2 1 1 1000010000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1010000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000100 1000000000\n",
"1\n1 9\n2\n",
"1\n4 1000110000\n2 1000000000 999999999 1000000000\n",
"1\n8 1000000000\n1 1000000000 98690276 1000000000 294967296 1100000000 1000000000 1000010000\n",
"3\n7 11\n3 9 1 3 18 1 1\n4 35\n4 9 10 7\n1 8\n5\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000000 100000000 100000000 100100000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 100000000 100000000 100000000 100000000 000000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 1476745735 630539938 9 335574820\n",
"1\n24 1\n3 1 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n6 1000000000\n91 1495486292 25219 900000000 900000000 4\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 2 1 1 0 1 1 1 1 0\n",
"1\n30 206961452\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 281979110 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 106976325 17650089 649905801 145670799 34389058 220175998 390589630 73795226 10024990 230718118\n",
"1\n5 1000000000\n10 0 7 4 1000010000 10 74 1000000000 1000000000 1000000000\n",
"1\n8 999999999\n1 655102112 1 1000010000 1 1000000000 1000000010 1\n",
"1\n25 2\n2 1 1 1000011000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1010000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000100 1000000000\n",
"1\n1 9\n1\n",
"1\n4 1000110000\n2 1000000000 802152789 1000000000\n",
"1\n8 1000000100\n1 1000000000 98690276 1000000000 294967296 1100000000 1000000000 1000010000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000000 100000000 100000000 100100000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 000000000 100000000 100000000 100000000 000000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 1780703501 630539938 9 335574820\n",
"1\n24 1\n3 1 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n6 1000000000\n91 1495486292 25219 900000000 900000000 1\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 2 1 1 0 1 2 1 1 0\n",
"1\n30 206961452\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 281979110 580244209 553065169 569140721 84508456 315856135 145805595 650034885 140825197 17745281 106540897 28580639 111465247 207869094 17650089 649905801 145670799 34389058 220175998 390589630 73795226 10024990 230718118\n",
"1\n8 999999999\n1 655102112 1 1000010000 1 1000000100 1000000010 1\n",
"1\n25 4\n2 1 1 1000011000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1010000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000100 1000000000\n",
"1\n1 9\n0\n",
"1\n4 1000110001\n2 1000000000 802152789 1000000000\n",
"1\n8 1000000100\n1 1000000000 98690276 1000000000 294967296 1100000100 1000000000 1000010000\n",
"1\n50 1\n2 1 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000000 100001000 100000000 100100000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000001 000000000 100000000 100000000 100000000 000000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n9 1000000010\n999999999 9 999999990 999999999 999999999 1780703501 178742556 9 335574820\n",
"1\n24 1\n3 1 100000100 100000000 100000000 100100000 100000000 100000000 100000000 100000000 100000000 100000000 100000100 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\n",
"1\n6 1000000000\n151 1495486292 25219 900000000 900000000 1\n",
"1\n24 1000000000\n999999996 2 3 2 2 2 999999990 999999992 1 1 1 1 1 1 1 2 1 2 0 1 2 1 1 0\n",
"1\n30 206961452\n241052576 14440862 145724506 113325577 417499967 8081113 32419669 281979110 580244209 553065169 569140721 84508456 428877168 145805595 650034885 140825197 17745281 106540897 28580639 111465247 207869094 17650089 649905801 145670799 34389058 220175998 390589630 73795226 10024990 230718118\n"
],
"output": [
"2\n1\n0\n",
"4\n4\n2\n2\n1\n1\n4\n",
"1\n",
"2\n2\n2\n2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"3\n",
"2\n2\n2\n2\n4\n",
"2\n",
"3\n",
"2\n",
"1\n",
"2\n",
"1\n",
"5\n",
"1\n",
"1\n",
"4\n",
"1\n",
"2\n",
"1\n1\n",
"2\n2\n2\n2\n2\n1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"0\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"3\n",
"2\n2\n2\n2\n4\n",
"5\n",
"4\n",
"1\n1\n",
"2\n2\n2\n2\n2\n1\n",
"0\n",
"2\n1\n0\n",
"2\n0\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n2\n2\n2\n4\n",
"2\n",
"1\n",
"2\n",
"1\n",
"5\n",
"4\n",
"1\n",
"2\n",
"1\n",
"0\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"5\n",
"4\n",
"1\n",
"2\n",
"1\n",
"0\n",
"2\n",
"2\n",
"2\n0\n0\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"5\n",
"4\n",
"1\n",
"0\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"4\n",
"4\n",
"0\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
New Year is coming! Vasya has prepared a New Year's verse and wants to recite it in front of Santa Claus.
Vasya's verse contains n parts. It takes a_i seconds to recite the i-th part. Vasya can't change the order of parts in the verse: firstly he recites the part which takes a_1 seconds, secondly — the part which takes a_2 seconds, and so on. After reciting the verse, Vasya will get the number of presents equal to the number of parts he fully recited.
Vasya can skip at most one part of the verse while reciting it (if he skips more than one part, then Santa will definitely notice it).
Santa will listen to Vasya's verse for no more than s seconds. For example, if s = 10, a = [100, 9, 1, 1], and Vasya skips the first part of verse, then he gets two presents.
Note that it is possible to recite the whole verse (if there is enough time).
Determine which part Vasya needs to skip to obtain the maximum possible number of gifts. If Vasya shouldn't skip anything, print 0. If there are multiple answers, print any of them.
You have to process t test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The first line of each test case contains two integers n and s (1 ≤ n ≤ 10^5, 1 ≤ s ≤ 10^9) — the number of parts in the verse and the maximum number of seconds Santa will listen to Vasya, respectively.
The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the time it takes to recite each part of the verse.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
Output
For each test case print one integer — the number of the part that Vasya needs to skip to obtain the maximum number of gifts. If Vasya shouldn't skip any parts, print 0.
Example
Input
3
7 11
2 9 1 3 18 1 4
4 35
11 9 10 7
1 8
5
Output
2
1
0
Note
In the first test case if Vasya skips the second part then he gets three gifts.
In the second test case no matter what part of the verse Vasya skips.
In the third test case Vasya can recite the whole verse.
### Input:
3
7 11
2 9 1 3 18 1 4
4 35
11 9 10 7
1 8
5
### Output:
2
1
0
### Input:
7
10 11
2 2 2 6 5 3 4 4 4 100000000
4 102
98 1 3 99
4 103
5 98 1 97
11 1000000000
100000000 100000002 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 99999999
8 90
20 8 20 20 20 20 1 1
3 1000000000
1000000000 1000000000 1000000000
11 1000000000
1 3 5 1000000000 1 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
### Output:
4
4
2
2
1
1
4
### Code:
import sys
input = sys.stdin.readline
t = int(input())
while t > 0:
n, s = map(int, input().split())
a = list(map(int, input().split()))
ans = 0
for i in range(n):
if a[ans] < a[i]:
ans = i
s -= a[i]
if (s < 0): break
if s >= 0:
ans = -1
print(ans + 1)
t -= 1
|
1322_C. Instant Noodles_28573
|
Wu got hungry after an intense training session, and came to a nearby store to buy his favourite instant noodles. After Wu paid for his purchase, the cashier gave him an interesting task.
You are given a bipartite graph with positive integers in all vertices of the right half. For a subset S of vertices of the left half we define N(S) as the set of all vertices of the right half adjacent to at least one vertex in S, and f(S) as the sum of all numbers in vertices of N(S). Find the greatest common divisor of f(S) for all possible non-empty subsets S (assume that GCD of empty set is 0).
Wu is too tired after his training to solve this problem. Help him!
Input
The first line contains a single integer t (1 ≤ t ≤ 500 000) — the number of test cases in the given test set. Test case descriptions follow.
The first line of each case description contains two integers n and m (1~≤~n,~m~≤~500 000) — the number of vertices in either half of the graph, and the number of edges respectively.
The second line contains n integers c_i (1 ≤ c_i ≤ 10^{12}). The i-th number describes the integer in the vertex i of the right half of the graph.
Each of the following m lines contains a pair of integers u_i and v_i (1 ≤ u_i, v_i ≤ n), describing an edge between the vertex u_i of the left half and the vertex v_i of the right half. It is guaranteed that the graph does not contain multiple edges.
Test case descriptions are separated with empty lines. The total value of n across all test cases does not exceed 500 000, and the total value of m across all test cases does not exceed 500 000 as well.
Output
For each test case print a single integer — the required greatest common divisor.
Example
Input
3
2 4
1 1
1 1
1 2
2 1
2 2
3 4
1 1 1
1 1
1 2
2 2
2 3
4 7
36 31 96 29
1 2
1 3
1 4
2 2
2 4
3 1
4 3
Output
2
1
12
Note
The greatest common divisor of a set of integers is the largest integer g such that all elements of the set are divisible by g.
In the first sample case vertices of the left half and vertices of the right half are pairwise connected, and f(S) for any non-empty subset is 2, thus the greatest common divisor of these values if also equal to 2.
In the second sample case the subset \{1\} in the left half is connected to vertices \{1, 2\} of the right half, with the sum of numbers equal to 2, and the subset \{1, 2\} in the left half is connected to vertices \{1, 2, 3\} of the right half, with the sum of numbers equal to 3. Thus, f(\{1\}) = 2, f(\{1, 2\}) = 3, which means that the greatest common divisor of all values of f(S) is 1.
|
from sys import stdin
from math import gcd
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
T = int(input())
for _ in range(T):
n, m = map(int, input().split())
values = list(map(int, input().split()))
neigh_values = [0]*n
y_neigh = [[] for i in range(n)]
di = [[] for i in range(n)]
for i in range(m):
x, y = map(int, input().split())
neigh_values[x - 1] += values[y - 1]
di[x - 1].append(y - 1)
y_neigh[y - 1].append(x - 1)
# group indices with the same neighboring set
y_n = {}
for i in range(n):
nst = frozenset(y_neigh[i])
if nst != set():
if nst in y_n:
y_n[nst].append(i)
else:
y_n[nst] = [i]
curr = 0
for nst in y_n.values():
tosum = [values[i] for i in nst]
curr = gcd(curr, sum(tosum))
print (curr)
if _ != T - 1:
blank = input()
|
{
"input": [
"3\n2 4\n1 1\n1 1\n1 2\n2 1\n2 2\n\n3 4\n1 1 1\n1 1\n1 2\n2 2\n2 3\n\n4 7\n36 31 96 29\n1 2\n1 3\n1 4\n2 2\n2 4\n3 1\n4 3\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n14 1\n16 1\n21 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 1\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n33 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n40 1\n40 2\n",
"1\n8 12\n2 3 2 3 2 3 3 2\n1 1\n1 2\n2 3\n2 4\n3 5\n3 6\n4 7\n4 8\n5 1\n5 3\n5 6\n5 7\n",
"7\n3 3\n1 1 1\n1 1\n1 2\n1 3\n\n3 2\n1 1 1\n1 1\n1 2\n\n4 8\n1 1 1 1\n1 1\n1 2\n2 3\n2 4\n3 1\n3 2\n3 3\n3 4\n\n5 12\n1 1 1 1 1\n1 1\n1 2\n1 3\n1 4\n2 3\n2 4\n2 5\n2 1\n3 5\n3 1\n3 2\n3 3\n\n1 1\n1\n1 1\n\n5 1\n1 1 1 1 1\n1 1\n\n2 2\n1 1\n1 1\n1 2\n",
"3\n1 1\n1000000000000\n1 1\n\n5 5\n1000000000000 1000000000000 1000000000000 1000000000000 1000000000000\n2 1\n2 2\n2 3\n2 4\n2 5\n\n2 2\n2 999999999999\n1 1\n2 2\n",
"1\n13 3\n3 5 1 1 1 1 1 1 1 1 1 1 1\n2 1\n3 1\n13 2\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n21 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n8 12\n2 3 2 3 2 3 3 2\n1 1\n1 2\n2 3\n2 4\n5 5\n3 6\n4 7\n4 8\n5 1\n5 3\n5 6\n5 7\n",
"3\n1 1\n1000010000000\n1 1\n\n5 5\n1000000000000 1000000000000 1000000000000 1000000000000 1000000000000\n2 1\n2 2\n2 3\n2 4\n2 5\n\n2 2\n2 999999999999\n1 1\n2 2\n",
"3\n1 1\n1000010000000\n1 1\n\n5 5\n1000000000000 1000000000000 1000000000000 1000000000000 1000000000000\n3 1\n2 2\n2 3\n2 4\n2 5\n\n2 2\n2 999999999999\n1 1\n2 2\n",
"1\n40 18\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n33 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n40 1\n40 2\n",
"1\n13 3\n3 5 1 1 1 1 1 1 1 1 1 1 2\n2 1\n3 1\n13 2\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n21 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n33 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 13 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n40 1\n40 2\n",
"1\n8 12\n2 3 2 3 2 3 3 2\n1 1\n1 2\n2 3\n2 4\n5 5\n3 6\n4 7\n4 8\n5 1\n5 3\n4 6\n5 7\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n35 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 10 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 13 16 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n40 1\n40 2\n",
"1\n8 11\n2 3 2 3 2 3 3 2\n1 1\n1 2\n2 3\n2 4\n5 5\n3 6\n4 7\n4 8\n5 1\n5 3\n4 6\n5 7\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n35 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 10 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 13 16 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n15 1\n40 2\n",
"1\n8 11\n2 3 2 3 2 3 3 2\n1 1\n1 2\n1 3\n2 4\n5 5\n3 6\n4 7\n4 8\n5 1\n5 3\n4 6\n5 7\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 19 10 10 10 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n35 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 13 16 10 10 10 10 10 10 14 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n15 1\n40 2\n",
"1\n100 31\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 10 10 10 10 10 10 10 10 10 10 10 10 10 19 10 10 11 10 10 10 10 10\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n14 1\n16 1\n35 1\n25 1\n30 1\n31 1\n33 1\n34 1\n35 1\n37 1\n38 1\n40 1\n42 1\n43 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 10 10 10 10 10 10 10 10 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 14 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 17 10 10 15 10 10 10 10 10 10 10 10 10 10 13 16 10 10 10 10 10 10 14 10 10 10 10 10 10 10 10 10 10 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n15 1\n40 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 10 10 10 10 10 10 10 10 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n12 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 14 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 12\n10 10 10 10 17 10 10 15 10 10 10 10 10 10 10 10 10 10 13 16 10 10 10 10 10 10 14 10 10 10 10 10 10 10 10 10 20 10 10 10\n1 1\n9 1\n12 1\n15 1\n18 1\n19 1\n20 1\n24 1\n25 1\n29 1\n15 1\n40 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 15 10 10 10 10 10 10 10 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n12 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 14 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n38 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 15 10 10 10 10 10 10 10 6 10 10 10 10 10 10 10 10 10 10 10 10 10 16 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n12 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 14 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n23 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 15 10 10 10 10 10 10 10 6 10 10 10 10 1 10 10 10 10 10 10 10 10 16 10 10 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n12 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n",
"1\n100 27\n10 10 10 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 14 10 10 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17\n1 1\n2 1\n3 1\n4 1\n9 1\n13 1\n24 1\n26 1\n27 1\n30 1\n32 1\n20 1\n35 1\n23 1\n39 1\n44 1\n45 1\n46 1\n48 1\n54 1\n55 1\n56 1\n57 1\n59 1\n60 1\n100 1\n100 2\n",
"1\n40 18\n10 10 19 10 10 10 10 10 10 15 10 10 10 10 10 10 10 6 10 10 10 10 1 10 10 10 10 10 10 10 10 16 10 3 8 10 10 9 3 10\n1 1\n2 1\n4 1\n5 1\n6 1\n7 1\n12 1\n9 1\n11 1\n17 1\n18 1\n19 1\n20 1\n24 1\n26 1\n28 2\n29 1\n30 1\n"
],
"output": [
"2\n1\n12\n",
"10\n",
"10\n",
"10\n",
"10\n",
"1\n",
"3\n2\n2\n1\n1\n1\n2\n",
"1000000000000\n5000000000000\n1\n",
"1\n",
"10\n",
"1\n",
"1000010000000\n5000000000000\n1\n",
"1000010000000\n1000000000000\n1\n",
"10\n",
"10\n",
"10\n",
"1\n",
"10\n",
"10\n",
"10\n",
"10\n",
"1\n",
"10\n",
"10\n",
"10\n",
"10\n",
"1\n",
"10\n",
"10\n",
"10\n",
"10\n",
"1\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n",
"10\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Wu got hungry after an intense training session, and came to a nearby store to buy his favourite instant noodles. After Wu paid for his purchase, the cashier gave him an interesting task.
You are given a bipartite graph with positive integers in all vertices of the right half. For a subset S of vertices of the left half we define N(S) as the set of all vertices of the right half adjacent to at least one vertex in S, and f(S) as the sum of all numbers in vertices of N(S). Find the greatest common divisor of f(S) for all possible non-empty subsets S (assume that GCD of empty set is 0).
Wu is too tired after his training to solve this problem. Help him!
Input
The first line contains a single integer t (1 ≤ t ≤ 500 000) — the number of test cases in the given test set. Test case descriptions follow.
The first line of each case description contains two integers n and m (1~≤~n,~m~≤~500 000) — the number of vertices in either half of the graph, and the number of edges respectively.
The second line contains n integers c_i (1 ≤ c_i ≤ 10^{12}). The i-th number describes the integer in the vertex i of the right half of the graph.
Each of the following m lines contains a pair of integers u_i and v_i (1 ≤ u_i, v_i ≤ n), describing an edge between the vertex u_i of the left half and the vertex v_i of the right half. It is guaranteed that the graph does not contain multiple edges.
Test case descriptions are separated with empty lines. The total value of n across all test cases does not exceed 500 000, and the total value of m across all test cases does not exceed 500 000 as well.
Output
For each test case print a single integer — the required greatest common divisor.
Example
Input
3
2 4
1 1
1 1
1 2
2 1
2 2
3 4
1 1 1
1 1
1 2
2 2
2 3
4 7
36 31 96 29
1 2
1 3
1 4
2 2
2 4
3 1
4 3
Output
2
1
12
Note
The greatest common divisor of a set of integers is the largest integer g such that all elements of the set are divisible by g.
In the first sample case vertices of the left half and vertices of the right half are pairwise connected, and f(S) for any non-empty subset is 2, thus the greatest common divisor of these values if also equal to 2.
In the second sample case the subset \{1\} in the left half is connected to vertices \{1, 2\} of the right half, with the sum of numbers equal to 2, and the subset \{1, 2\} in the left half is connected to vertices \{1, 2, 3\} of the right half, with the sum of numbers equal to 3. Thus, f(\{1\}) = 2, f(\{1, 2\}) = 3, which means that the greatest common divisor of all values of f(S) is 1.
### Input:
3
2 4
1 1
1 1
1 2
2 1
2 2
3 4
1 1 1
1 1
1 2
2 2
2 3
4 7
36 31 96 29
1 2
1 3
1 4
2 2
2 4
3 1
4 3
### Output:
2
1
12
### Input:
1
100 31
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
1 1
2 1
3 1
4 1
5 1
6 1
14 1
16 1
21 1
25 1
30 1
31 1
33 1
34 1
35 1
37 1
38 1
40 1
42 1
43 1
45 1
46 1
48 1
54 1
55 1
56 1
57 1
59 1
60 1
100 1
100 2
### Output:
10
### Code:
from sys import stdin
from math import gcd
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
T = int(input())
for _ in range(T):
n, m = map(int, input().split())
values = list(map(int, input().split()))
neigh_values = [0]*n
y_neigh = [[] for i in range(n)]
di = [[] for i in range(n)]
for i in range(m):
x, y = map(int, input().split())
neigh_values[x - 1] += values[y - 1]
di[x - 1].append(y - 1)
y_neigh[y - 1].append(x - 1)
# group indices with the same neighboring set
y_n = {}
for i in range(n):
nst = frozenset(y_neigh[i])
if nst != set():
if nst in y_n:
y_n[nst].append(i)
else:
y_n[nst] = [i]
curr = 0
for nst in y_n.values():
tosum = [values[i] for i in nst]
curr = gcd(curr, sum(tosum))
print (curr)
if _ != T - 1:
blank = input()
|
1341_B. Nastya and Door_28577
|
On February 14 Denis decided to give Valentine to Nastya and did not come up with anything better than to draw a huge red heart on the door of the length k (k ≥ 3). Nastya was very confused by this present, so she decided to break the door, throwing it on the mountains.
Mountains are described by a sequence of heights a_1, a_2, ..., a_n in order from left to right (k ≤ n). It is guaranteed that neighboring heights are not equal to each other (that is, a_i ≠ a_{i+1} for all i from 1 to n-1).
Peaks of mountains on the segment [l,r] (from l to r) are called indexes i such that l < i < r, a_{i - 1} < a_i and a_i > a_{i + 1}. It is worth noting that the boundary indexes l and r for the segment are not peaks. For example, if n=8 and a=[3,1,4,1,5,9,2,6], then the segment [1,8] has only two peaks (with indexes 3 and 6), and there are no peaks on the segment [3, 6].
To break the door, Nastya throws it to a segment [l,l+k-1] of consecutive mountains of length k (1 ≤ l ≤ n-k+1). When the door touches the peaks of the mountains, it breaks into two parts, after that these parts will continue to fall in different halves and also break into pieces when touching the peaks of the mountains, and so on. Formally, the number of parts that the door will break into will be equal to p+1, where p is the number of peaks on the segment [l,l+k-1].
Nastya wants to break it into as many pieces as possible. Help her choose such a segment of mountains [l, l+k-1] that the number of peaks on it is maximum. If there are several optimal segments, Nastya wants to find one for which the value l is minimal.
Formally, you need to choose a segment of mountains [l, l+k-1] that has the maximum number of peaks. Among all such segments, you need to find the segment that has the minimum possible value l.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then the descriptions of the test cases follow.
The first line of each test case contains two integers n and k (3 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of mountains and the length of the door.
The second line of the input data set contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10 ^ 9, a_i ≠ a_{i + 1}) — the heights of mountains.
It is guaranteed that the sum of n over all the test cases will not exceed 2 ⋅ 10^5.
Output
For each test case, output two integers t and l — the maximum number of parts that the door can split into, and the left border of the segment of length k that the door should be reset to.
Example
Input
5
8 6
1 2 4 1 2 4 1 2
5 3
3 2 3 2 1
10 4
4 3 4 3 2 3 2 1 0 1
15 7
3 7 4 8 2 3 4 5 21 2 3 4 2 1 3
7 5
1 2 3 4 5 6 1
Output
3 2
2 2
2 1
3 1
2 3
Note
In the first example, you need to select a segment of mountains from 2 to 7. In this segment, the indexes 3 and 6 are peaks, so the answer is 3 (only 2 peaks, so the door will break into 3 parts). It is not difficult to notice that the mountain segments [1, 6] and [3, 8] are not suitable since they only have a 1 peak (for the first segment, the 6 index is not a peak, and for the second segment, the 3 index is not a peak).
In the second example, you need to select a segment of mountains from 2 to 4. In this segment, the index 3 is a peak, so the answer is 2 (only 1 peak, so the door will break into 2 parts).
In the third example, you need to select a segment of mountains from 1 to 4. In this segment, the index 3 is a peak, so the answer is 2 (only 1 peak, so the door will break into 2 parts). You can see that on the segments [2, 5], [4, 7] and [5, 8] the number of peaks is also 1, but these segments have a left border greater than the segment [1, 4], so they are not the correct answer.
|
from sys import stdin, stdout
def find(A,N,K):
arr=[0]*N
for i in range(1,N-1):
if A[i-1]<A[i]>A[i+1]: arr[i]=1
i,j=0,2
c=0
# print(arr)
while(j<K):
if arr[j-1]: c+=1
# print(j,c)
j+=1
m=[c,i]
# print(c,i,j)
while(j<N):
if arr[i+1]: c-=1
if arr[j-1]: c+=1
i+=1
j+=1
# print(c,i,j,arr[j-1],arr[i+1])
m=max(m, [c,i], key=lambda x: (x[0],-x[1]))
# print(c,m)
m[1]+=1
m[0]+=1
# print('-', i,j)
return ' '.join(map(str,m))
def main():
for _ in range(int(stdin.readline())):
N,K=list(map(int, stdin.readline().split()))
arr=list(map(int, stdin.readline().split()))
print(find(arr,N,K))
main()
|
{
"input": [
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 2 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 8 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 12\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 6 1\n",
"5\n8 6\n1 2 8 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 12\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 0 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 2 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 4 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 2 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 8\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 8 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 13\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 0 5 6 1\n",
"5\n8 6\n1 2 7 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 1 3 2 3 2 1 -1 1\n15 12\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 0 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 0 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 14\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n0 2 3 4 8 9 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 8 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 7 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 2 4 8 1 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 7 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 12\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 0 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 9 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 4 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 1 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 0 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 9 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 0 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n0 2 3 4 8 9 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 3 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n2 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n2 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 4 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 4 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 0 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 3 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 3 1 4 5 21 2 0 4 0 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 0 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 3 1 4 5 21 2 0 4 0 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 4 0 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 9 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 0\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n3 3 4 3 2 1 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 8 2 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n5 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 0 2\n5 3\n3 2 3 2 1\n10 4\n4 3 7 3 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 0 1\n15 7\n3 2 4 8 1 3 4 5 21 2 3 4 2 1 3\n7 5\n2 2 3 4 5 6 1\n",
"5\n8 6\n1 2 8 1 2 4 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 3 2 3 2 1 -1 2\n15 12\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 4 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 6 1\n",
"5\n8 6\n1 2 4 1 2 11 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 1 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 2 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 4 4 2 1 3\n7 5\n1 2 3 4 8 9 1\n",
"5\n8 6\n1 2 4 1 2 7 1 4\n5 3\n3 2 3 2 1\n10 4\n4 4 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 1 1 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 4 7 1 2\n5 3\n3 2 3 0 1\n10 4\n4 3 4 2 2 3 2 1 -1 1\n15 7\n3 7 4 8 2 3 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 8 16 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 3 2 3 0 1 -1 1\n15 7\n3 7 4 8 2 1 5 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 14 1 2\n5 3\n1 2 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 3 4 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 6 2 3 0 1 -1 0\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 1\n",
"5\n8 6\n1 2 4 1 2 14 1 2\n5 3\n2 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 7 2 8 2 2 4 5 21 2 3 4 2 2 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 4\n7 4 7 1 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 4 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n2 1 3 2 1\n10 4\n4 3 4 3 2 1 2 1 -1 2\n15 7\n3 4 2 8 2 2 4 5 21 2 3 4 2 4 3\n7 5\n1 2 3 4 5 6 1\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 1 1 5 21 2 3 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 7\n3 14 4 8 2 0 4 5 21 2 0 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n9 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 1 3\n7 5\n1 2 3 4 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 4 2 6 4\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 1 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 2 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 11\n3 14 4 8 3 1 4 5 21 2 0 4 2 0 3\n7 5\n1 2 3 2 2 6 2\n",
"5\n8 6\n1 2 4 1 2 7 1 2\n5 3\n3 2 3 2 1\n10 8\n7 4 7 6 2 3 0 1 -1 1\n15 10\n3 14 4 8 3 1 4 5 21 2 0 4 0 0 3\n7 5\n2 2 3 2 2 6 2\n"
],
"output": [
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 7\n2 3\n",
"3 2\n2 2\n2 1\n4 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 2\n",
"3 2\n2 2\n2 1\n4 1\n2 1\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n4 2\n3 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n2 1\n3 1\n2 1\n",
"3 2\n2 1\n2 1\n3 7\n2 3\n",
"3 1\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n5 1\n2 1\n",
"3 2\n2 2\n2 2\n4 1\n2 1\n",
"3 2\n2 2\n2 1\n5 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 7\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 2\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n4 1\n2 1\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n4 2\n3 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 2\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 7\n2 3\n",
"3 2\n2 2\n2 1\n4 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 2\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 2\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n2 1\n3 1\n3 3\n",
"3 2\n2 2\n2 1\n3 1\n2 3\n",
"3 2\n2 2\n4 2\n3 1\n3 3\n",
"3 2\n2 2\n4 2\n3 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n3 3\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n",
"3 2\n2 2\n4 2\n4 1\n2 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
On February 14 Denis decided to give Valentine to Nastya and did not come up with anything better than to draw a huge red heart on the door of the length k (k ≥ 3). Nastya was very confused by this present, so she decided to break the door, throwing it on the mountains.
Mountains are described by a sequence of heights a_1, a_2, ..., a_n in order from left to right (k ≤ n). It is guaranteed that neighboring heights are not equal to each other (that is, a_i ≠ a_{i+1} for all i from 1 to n-1).
Peaks of mountains on the segment [l,r] (from l to r) are called indexes i such that l < i < r, a_{i - 1} < a_i and a_i > a_{i + 1}. It is worth noting that the boundary indexes l and r for the segment are not peaks. For example, if n=8 and a=[3,1,4,1,5,9,2,6], then the segment [1,8] has only two peaks (with indexes 3 and 6), and there are no peaks on the segment [3, 6].
To break the door, Nastya throws it to a segment [l,l+k-1] of consecutive mountains of length k (1 ≤ l ≤ n-k+1). When the door touches the peaks of the mountains, it breaks into two parts, after that these parts will continue to fall in different halves and also break into pieces when touching the peaks of the mountains, and so on. Formally, the number of parts that the door will break into will be equal to p+1, where p is the number of peaks on the segment [l,l+k-1].
Nastya wants to break it into as many pieces as possible. Help her choose such a segment of mountains [l, l+k-1] that the number of peaks on it is maximum. If there are several optimal segments, Nastya wants to find one for which the value l is minimal.
Formally, you need to choose a segment of mountains [l, l+k-1] that has the maximum number of peaks. Among all such segments, you need to find the segment that has the minimum possible value l.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then the descriptions of the test cases follow.
The first line of each test case contains two integers n and k (3 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of mountains and the length of the door.
The second line of the input data set contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10 ^ 9, a_i ≠ a_{i + 1}) — the heights of mountains.
It is guaranteed that the sum of n over all the test cases will not exceed 2 ⋅ 10^5.
Output
For each test case, output two integers t and l — the maximum number of parts that the door can split into, and the left border of the segment of length k that the door should be reset to.
Example
Input
5
8 6
1 2 4 1 2 4 1 2
5 3
3 2 3 2 1
10 4
4 3 4 3 2 3 2 1 0 1
15 7
3 7 4 8 2 3 4 5 21 2 3 4 2 1 3
7 5
1 2 3 4 5 6 1
Output
3 2
2 2
2 1
3 1
2 3
Note
In the first example, you need to select a segment of mountains from 2 to 7. In this segment, the indexes 3 and 6 are peaks, so the answer is 3 (only 2 peaks, so the door will break into 3 parts). It is not difficult to notice that the mountain segments [1, 6] and [3, 8] are not suitable since they only have a 1 peak (for the first segment, the 6 index is not a peak, and for the second segment, the 3 index is not a peak).
In the second example, you need to select a segment of mountains from 2 to 4. In this segment, the index 3 is a peak, so the answer is 2 (only 1 peak, so the door will break into 2 parts).
In the third example, you need to select a segment of mountains from 1 to 4. In this segment, the index 3 is a peak, so the answer is 2 (only 1 peak, so the door will break into 2 parts). You can see that on the segments [2, 5], [4, 7] and [5, 8] the number of peaks is also 1, but these segments have a left border greater than the segment [1, 4], so they are not the correct answer.
### Input:
5
8 6
1 2 4 1 2 4 1 2
5 3
3 2 3 2 1
10 4
4 3 4 3 2 3 2 1 0 1
15 7
3 7 4 8 2 3 4 5 21 2 3 4 2 1 3
7 5
1 2 3 4 5 6 1
### Output:
3 2
2 2
2 1
3 1
2 3
### Input:
5
8 6
1 2 4 1 2 4 1 2
5 3
3 2 3 2 1
10 4
4 3 4 3 2 3 2 1 -1 1
15 7
3 7 4 8 2 3 4 5 21 2 3 4 2 1 3
7 5
1 2 3 4 5 6 1
### Output:
3 2
2 2
2 1
3 1
2 3
### Code:
from sys import stdin, stdout
def find(A,N,K):
arr=[0]*N
for i in range(1,N-1):
if A[i-1]<A[i]>A[i+1]: arr[i]=1
i,j=0,2
c=0
# print(arr)
while(j<K):
if arr[j-1]: c+=1
# print(j,c)
j+=1
m=[c,i]
# print(c,i,j)
while(j<N):
if arr[i+1]: c-=1
if arr[j-1]: c+=1
i+=1
j+=1
# print(c,i,j,arr[j-1],arr[i+1])
m=max(m, [c,i], key=lambda x: (x[0],-x[1]))
# print(c,m)
m[1]+=1
m[0]+=1
# print('-', i,j)
return ' '.join(map(str,m))
def main():
for _ in range(int(stdin.readline())):
N,K=list(map(int, stdin.readline().split()))
arr=list(map(int, stdin.readline().split()))
print(find(arr,N,K))
main()
|
1363_B. Subsequence Hate_28581
|
Shubham has a binary string s. A binary string is a string containing only characters "0" and "1".
He can perform the following operation on the string any amount of times:
* Select an index of the string, and flip the character at that index. This means, if the character was "0", it becomes "1", and vice versa.
A string is called good if it does not contain "010" or "101" as a subsequence — for instance, "1001" contains "101" as a subsequence, hence it is not a good string, while "1000" doesn't contain neither "010" nor "101" as subsequences, so it is a good string.
What is the minimum number of operations he will have to perform, so that the string becomes good? It can be shown that with these operations we can make any string good.
A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases.
Each of the next t lines contains a binary string s (1 ≤ |s| ≤ 1000).
Output
For every string, output the minimum number of operations required to make it good.
Example
Input
7
001
100
101
010
0
1
001100
Output
0
0
1
1
0
0
2
Note
In test cases 1, 2, 5, 6 no operations are required since they are already good strings.
For the 3rd test case: "001" can be achieved by flipping the first character — and is one of the possible ways to get a good string.
For the 4th test case: "000" can be achieved by flipping the second character — and is one of the possible ways to get a good string.
For the 7th test case: "000000" can be achieved by flipping the third and fourth characters — and is one of the possible ways to get a good string.
|
for t in range(int(input())):
s=input()
one=s.count("1")
z=s.count("0")
if one==0 or z==0:
print(0)
else:
cost=one
mi=10**9
for i in s:
if i=="0":
cost+=1
else:
cost-=1
if mi>cost:
mi=cost
cost=z
for i in s:
if i=="1":
cost+=1
else:
cost-=1
if mi>cost:
mi=cost
print(mi)
|
{
"input": [
"7\n001\n100\n101\n010\n0\n1\n001100\n",
"14\n110\n110011011110100111\n10111101000010100\n001111\n0\n00\n0111000\n1010111011110011011\n11100100011101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101110\n101100\n0001100101001100\n111110101100\n01100\n0110111100\n110101\n10000011001010010001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n0111000\n1010111011110011011\n11100100011101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101111\n101100\n0001100101001100\n111110101100\n01100\n0110111100\n110101\n10000011001010010001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n001\n100\n101\n010\n0\n0\n001100\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n0111000\n1010111011110011011\n10100100011101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101111\n101100\n0001100101001110\n111110101100\n01100\n0110111100\n110101\n10000011001010010001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n001\n100\n101\n000\n0\n0\n001100\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101111\n101100\n0001100101001110\n111010101100\n01100\n0110111100\n110101\n10000011001010010001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n0111000\n1010110011110011011\n10100100010101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101111\n101100\n0001100101001110\n111010101100\n01100\n0110111100\n110001\n10000011001010010001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n0111000\n1010110011110011011\n10000100010101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111101101111\n101100\n0001100101001110\n111010101100\n01100\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n011\n100\n101\n000\n0\n0\n011100\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111001101111\n101100\n0001100101001110\n111010101100\n01100\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n011\n100\n100\n000\n0\n0\n011100\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101101\n010110000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n000\n100100011010\n001\n010101\n101\n1100111001101111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"14\n100\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101100\n010110000111\n1111101\n000101100101111100\n01000101000\n0110\n",
"18\n000\n100100011010\n001\n010101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"18\n000\n100100011010\n001\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n101\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n111001\n10000011001010110001\n0001\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1011010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000011101000010\n1001111110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000011101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110101100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101010101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101010101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n001\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011000001101000010\n1011110110001000\n",
"18\n100\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001010101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n100\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001010101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n100\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n100\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n100\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n100\n100100011000\n101\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100100011000\n101\n110101\n100\n1100111101111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001000101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001100101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001100101100\n00100\n0110101100\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0101110101001110\n001100101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010111\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010111\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n010111\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n010111\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n011111\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n00101\n0110101110\n111111\n10000011001011110001\n0001\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n110\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n00111\n0110101110\n111111\n10000011001011110001\n0001\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n010\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n00111\n0110101110\n111111\n10000011001011110001\n0001\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n010\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n10111\n0110101110\n111111\n10000011001011110001\n0001\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n010\n010011\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n10111\n0110101110\n111111\n10000011001011110001\n0001\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"14\n110\n110011011110100111\n10111101000010100\n000111\n0\n00\n0111000\n1010111011110011011\n10100100010101101\n010100000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"7\n011\n100\n101\n000\n0\n0\n001100\n",
"7\n011\n000\n101\n000\n0\n0\n001100\n",
"18\n010\n100100011010\n001\n010101\n101\n1100111001101111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n011\n100\n100\n100\n0\n0\n011100\n",
"14\n100\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101101\n010110000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"7\n011\n100\n000\n100\n0\n0\n011100\n",
"14\n100\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101100\n010110000111\n1111101\n000101100101111100\n01001101000\n0110\n",
"18\n000\n100100011010\n001\n010101\n101\n1100011001101111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n011\n000\n000\n100\n0\n0\n011100\n",
"7\n011\n000\n000\n110\n0\n0\n011100\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101100\n010110000111\n1111101\n000101100101111100\n01000101000\n0110\n",
"18\n000\n100100011010\n001\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n110001\n10000011001010110001\n0011\n00001010110100000101\n11011101110\n011000011101000010\n1001111110001000\n",
"7\n011\n000\n000\n110\n1\n0\n011100\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n00\n1111000\n1010110011110011011\n10000100010101100\n010110000111\n1111101\n000101100101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n001\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n111001\n10000011001010110001\n0011\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"18\n000\n100100011010\n001\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n111001\n10000011001010110001\n0001\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100011001111111\n101100\n0001100101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n0\n1\n1011010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n101\n110101\n101\n1100011001111111\n101100\n0001110101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"14\n000\n110011011110100111\n10111101000010100\n000111\n1\n1\n1011010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110111100\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101010\n011000011101000010\n1001111110001000\n",
"14\n000\n110011011110100101\n10111101000010100\n000111\n1\n1\n1011010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"14\n000\n110011011110100101\n10111101000010100\n000111\n1\n1\n0011010\n1010110011110011011\n10000110010101100\n010110000111\n1111101\n000101000101111100\n01000101001\n0110\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n111010101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010110100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011010\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n101000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000101\n11011101000\n011000001101000010\n1001110110001000\n",
"18\n000\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011000001101000010\n1011110110001000\n",
"18\n000\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n101\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001000101100\n01110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n100\n110101\n101\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001010110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n1011110110001000\n",
"18\n100\n100100011000\n101\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100100011000\n101\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100100011000\n101\n110101\n100\n1100111001111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100100011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001000101100\n00110\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100100011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001000101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001100101100\n00100\n0110101100\n111101\n10000011001011110001\n0001\n00001010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n111\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001100101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0001110101001110\n001100101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0101110101001110\n001100101100\n00100\n0110101110\n111101\n10000011001011110001\n0001\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n101\n010101\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00011010010100000001\n11011101000\n011100001101000010\n0011110110001000\n",
"18\n110\n100000011000\n100\n011011\n100\n1100111101111111\n101100\n0101110101001110\n001100101101\n00100\n0110101110\n111101\n10000011001011110001\n0011\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n",
"18\n110\n100000011000\n100\n011011\n100\n1100111101111111\n001100\n0101110101001110\n001100101101\n00101\n0110101110\n111101\n10000011001011110001\n0011\n00111010010100000001\n11011101000\n011100001101000010\n0011110110001100\n"
],
"output": [
"0\n0\n1\n1\n0\n0\n2\n",
"0\n6\n4\n0\n0\n0\n1\n6\n6\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n4\n1\n6\n2\n1\n2\n2\n6\n0\n6\n2\n6\n3\n",
"0\n6\n4\n0\n0\n0\n1\n6\n6\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n4\n1\n6\n2\n1\n2\n2\n6\n0\n6\n2\n6\n3\n",
"0\n0\n1\n1\n0\n0\n2\n",
"0\n6\n4\n0\n0\n0\n1\n6\n5\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n4\n1\n5\n2\n1\n2\n2\n6\n0\n6\n2\n6\n3\n",
"0\n0\n1\n0\n0\n0\n2\n",
"1\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n2\n6\n0\n6\n2\n6\n3\n",
"0\n6\n4\n0\n0\n0\n1\n7\n6\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n6\n0\n6\n2\n6\n3\n",
"0\n6\n4\n0\n0\n0\n1\n7\n5\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n0\n1\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n2\n1\n6\n4\n1\n",
"1\n4\n0\n2\n1\n5\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n4\n1\n",
"0\n4\n0\n2\n1\n5\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n3\n1\n",
"0\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n5\n3\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n6\n3\n1\n5\n3\n1\n",
"0\n6\n4\n0\n0\n0\n1\n7\n6\n3\n1\n5\n3\n1\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n6\n4\n0\n0\n0\n2\n7\n6\n3\n1\n5\n3\n1\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n5\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n3\n1\n7\n0\n6\n2\n5\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n6\n2\n5\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n4\n0\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n1\n2\n1\n4\n1\n5\n5\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n0\n2\n1\n4\n1\n5\n5\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n0\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n0\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n0\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n3\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n5\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n5\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n6\n5\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n1\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n1\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n5\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n5\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n6\n2\n5\n5\n",
"0\n2\n0\n0\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n6\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n2\n6\n4\n1\n3\n1\n7\n0\n6\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n2\n6\n4\n1\n3\n0\n7\n0\n6\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n2\n6\n4\n0\n3\n0\n7\n0\n6\n2\n5\n5\n",
"0\n2\n1\n1\n0\n3\n2\n6\n4\n0\n3\n0\n7\n0\n6\n2\n5\n5\n",
"0\n2\n1\n1\n0\n3\n2\n6\n4\n1\n3\n0\n7\n0\n6\n2\n5\n5\n",
"0\n2\n1\n1\n0\n3\n1\n6\n4\n1\n3\n0\n7\n0\n6\n2\n5\n5\n",
"0\n6\n4\n0\n0\n0\n1\n6\n6\n2\n1\n6\n4\n1\n",
"0\n0\n1\n0\n0\n0\n2\n",
"0\n0\n1\n0\n0\n0\n2\n",
"1\n4\n0\n2\n1\n5\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n4\n1\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n4\n1\n",
"0\n4\n0\n2\n1\n5\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n3\n1\n",
"0\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n2\n6\n3\n",
"0\n0\n0\n0\n0\n0\n1\n",
"0\n6\n4\n0\n0\n0\n0\n7\n5\n3\n1\n6\n3\n1\n",
"0\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n4\n0\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n6\n4\n0\n0\n0\n2\n7\n6\n3\n1\n5\n3\n1\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n6\n4\n0\n0\n0\n2\n7\n6\n3\n1\n5\n3\n1\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n2\n1\n7\n0\n6\n3\n6\n3\n",
"0\n6\n4\n0\n0\n0\n2\n7\n6\n3\n1\n5\n3\n1\n",
"0\n6\n4\n0\n0\n0\n2\n7\n6\n3\n1\n5\n3\n1\n",
"0\n4\n1\n2\n1\n4\n1\n5\n3\n1\n3\n1\n7\n0\n6\n2\n5\n4\n",
"0\n4\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n3\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n1\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n0\n2\n1\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n3\n",
"0\n3\n1\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n4\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n3\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n3\n1\n2\n0\n3\n1\n5\n4\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n5\n1\n3\n1\n7\n0\n4\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n5\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n5\n5\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n6\n5\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n1\n2\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n5\n2\n5\n4\n",
"0\n2\n0\n1\n0\n3\n1\n6\n4\n1\n3\n1\n7\n0\n6\n2\n5\n5\n",
"0\n2\n0\n1\n0\n3\n2\n6\n4\n1\n3\n1\n7\n0\n6\n2\n5\n5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Shubham has a binary string s. A binary string is a string containing only characters "0" and "1".
He can perform the following operation on the string any amount of times:
* Select an index of the string, and flip the character at that index. This means, if the character was "0", it becomes "1", and vice versa.
A string is called good if it does not contain "010" or "101" as a subsequence — for instance, "1001" contains "101" as a subsequence, hence it is not a good string, while "1000" doesn't contain neither "010" nor "101" as subsequences, so it is a good string.
What is the minimum number of operations he will have to perform, so that the string becomes good? It can be shown that with these operations we can make any string good.
A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases.
Each of the next t lines contains a binary string s (1 ≤ |s| ≤ 1000).
Output
For every string, output the minimum number of operations required to make it good.
Example
Input
7
001
100
101
010
0
1
001100
Output
0
0
1
1
0
0
2
Note
In test cases 1, 2, 5, 6 no operations are required since they are already good strings.
For the 3rd test case: "001" can be achieved by flipping the first character — and is one of the possible ways to get a good string.
For the 4th test case: "000" can be achieved by flipping the second character — and is one of the possible ways to get a good string.
For the 7th test case: "000000" can be achieved by flipping the third and fourth characters — and is one of the possible ways to get a good string.
### Input:
7
001
100
101
010
0
1
001100
### Output:
0
0
1
1
0
0
2
### Input:
14
110
110011011110100111
10111101000010100
001111
0
00
0111000
1010111011110011011
11100100011101101
010100000111
1111101
000101100101111100
01001101000
0110
### Output:
0
6
4
0
0
0
1
6
6
2
1
6
4
1
### Code:
for t in range(int(input())):
s=input()
one=s.count("1")
z=s.count("0")
if one==0 or z==0:
print(0)
else:
cost=one
mi=10**9
for i in s:
if i=="0":
cost+=1
else:
cost-=1
if mi>cost:
mi=cost
cost=z
for i in s:
if i=="1":
cost+=1
else:
cost-=1
if mi>cost:
mi=cost
print(mi)
|
1404_D. Game of Pairs_28586
|
This is an interactive problem.
Consider a fixed positive integer n. Two players, First and Second play a game as follows:
1. First considers the 2n numbers 1, 2, ..., 2n, and partitions them as he wants into n disjoint pairs.
2. Then, Second chooses exactly one element from each of the pairs that First created (he chooses elements he wants).
To determine the winner of the game, we compute the sum of the numbers chosen by Second. If the sum of all these numbers is a multiple of 2n, then Second wins. Otherwise, First wins.
You are given the integer n. Your task is to decide which player you wish to play as and win the game.
Interaction
The interaction begins by reading the integer n (1 ≤ n ≤ 5 ⋅ 10^5).
After reading, print a single line containing either First or Second, denoting who you want to play as. The interaction then varies depending on who you chose to play as.
If you chose to play as First, print a single line containing 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair for 1≤ i ≤ 2n. Thus, 1 ≤ p_i ≤ n, and every number between 1 and n inclusive should appear exactly twice.
If you chose to play as Second, the interactor will print 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair. As a response, print n integers a_1, a_2, ..., a_n in a single line. These should contain exactly one number from each pair.
Regardless of who you chose to play as the interactor will finish by printing a single integer: 0 if your answer for the test case is correct (that is, you are playing as First and it cannot choose adequate numbers from your pairs, or you are playing as Second and your chosen numbers add up to a multiple of 2n), or -1 if it is incorrect. In particular, the interactor will not print the chosen numbers if you choose to play First and lose. In either case, your program should terminate immediately after reading this number.
If at any point you make an invalid interaction, the interactor will print -1 and finish the interaction. You will receive a Wrong Answer verdict. Make sure to terminate immediately to avoid getting other verdicts.
After printing something do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
* fflush(stdout) or cout.flush() in C++;
* System.out.flush() in Java;
* flush(output) in Pascal;
* stdout.flush() in Python;
* see documentation for other languages.
Hack Format
To hack, use the following format:
The first line contains an integer n (1 ≤ n ≤ 5 ⋅ 10^5).
The second line contains 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair if the solution being hacked chooses to play as Second. If the solution being hacked chooses to play as First, those pairs don't matter but the p_1, p_2, ..., p_{2n} must still form a valid partition of 1, 2, ..., 2n into n disjoint pairs.
Examples
Input
2
1 1 2 2
0
Output
Second
1 3
Input
2
0
Output
First
2 1 2 1
Note
In the first sample, n = 2, and you decide to play as Second. The judge chooses the pairs (1, 2) and (3, 4), and you reply with the numbers 1 and 3. This is a valid choice since it contains exactly one number from each pair, and the sum 1 + 3 = 4 is divisible by 4.
In the second sample, n = 2 again, and you play as First. You choose the pairs (2, 4) and (1, 3). The judge fails to choose a number from each pair such that their sum is divisible by 4, so the answer is correct.
Note that the sample tests are just for illustration of the interaction protocol, and don't necessarily correspond to the behavior of the real interactor.
|
import sys
n = int(input())
if n % 2:
print('Second')
sys.stdout.flush()
l = list(map(lambda x: int(x)-1,input().split()))
rev1 = [-1]*n
rev2 = [-1]*n
revs = [0]*n
for i in range(2 * n):
revs[l[i]] += i
if rev1[l[i]] == -1:
rev1[l[i]] = i
else:
rev2[l[i]] = i
out = [0] * (2 * n)
curr = 0
todo = 2*n
q = []
while todo:
while out[curr] and curr < 2*n:
curr += 1
if curr == 2*n:
break
out[curr] = 1
todo -= 1
q = [curr]
while q:
v = q.pop()
mod = v % n
other = (2 * mod + n) - v
if out[other] == 0:
out[other] = 3 - out[v]
todo -= 1
q.append(other)
other = revs[l[v]] - v
if out[other] == 0:
out[other] = 3 - out[v]
todo -= 1
q.append(other)
s1 = 0
for i in range(2 * n):
if out[i] == 1:
s1 += i + 1
if s1 % (2 * n) == 0:
want = 1
else:
want = 2
rout = []
for i in range(2 * n):
if out[i] == want:
rout.append(i + 1)
print(' '.join(map(str,rout)))
sys.stdout.flush()
else:
print('First')
sys.stdout.flush()
l = [1+(i%n) for i in range(2*n)]
print(' '.join(map(str,l)))
sys.stdout.flush()
|
{
"input": [
"2\n\n\n0",
"2\n\n1 1 2 2\n\n0\n",
"2\n1 2 1 2\n",
"4\n2 4 3 1 3 4 2 1\n",
"10\n1 10 6 4 3 5 10 9 3 8 1 2 6 4 7 5 2 9 7 8\n",
"1\n1 1\n",
"5\n2 4 2 1 5 3 3 1 5 4\n",
"10\n10 1 9 8 7 2 4 5 6 3 10 1 9 8 7 2 4 5 6 3\n",
"4\n1 4 4 2 3 1 2 3\n",
"5\n5 3 4 2 1 2 1 4 5 3\n",
"2\n1 2 1 4\n",
"4\n2 4 3 2 3 4 2 1\n",
"10\n1 10 6 4 3 5 10 9 3 8 1 2 6 4 7 5 2 1 7 8\n",
"10\n10 1 9 8 7 2 4 5 6 1 10 1 9 8 7 2 4 5 6 3\n",
"4\n0 4 4 2 3 1 2 3\n",
"2\n\n\n1",
"2\n\n1 1 3 2\n\n0\n",
"2\n2 2 1 4\n",
"4\n1 4 3 2 3 4 2 1\n",
"10\n1 10 6 4 3 5 10 9 3 8 1 2 6 4 7 5 4 1 7 8\n",
"10\n10 1 9 8 11 2 4 5 6 1 10 1 9 8 7 2 4 5 6 3\n",
"4\n0 4 4 2 4 1 2 3\n",
"2\n\n\n2",
"2\n\n0 1 3 2\n\n0\n",
"2\n2 0 1 4\n",
"4\n1 4 3 2 3 4 4 1\n",
"10\n1 10 6 4 3 5 10 9 3 8 1 2 6 0 7 5 4 1 7 8\n",
"10\n10 1 9 8 11 2 4 5 6 1 10 1 9 8 2 2 4 5 6 3\n",
"4\n0 4 4 2 4 2 2 3\n",
"2\n\n\n-1",
"2\n\n0 1 5 2\n\n0\n",
"2\n3 0 1 4\n",
"4\n1 4 3 1 3 4 4 1\n",
"10\n1 10 6 4 3 5 5 9 3 8 1 2 6 0 7 5 4 1 7 8\n",
"10\n10 1 9 8 11 2 4 5 6 1 1 1 9 8 2 2 4 5 6 3\n",
"4\n0 4 4 2 4 4 2 3\n",
"2\n\n\n4",
"2\n\n0 1 5 2\n\n-1\n",
"2\n3 0 1 5\n",
"4\n1 4 3 1 3 4 7 1\n",
"10\n1 14 6 4 3 5 5 9 3 8 1 2 6 0 7 5 4 1 7 8\n",
"10\n3 1 9 8 11 2 4 5 6 1 1 1 9 8 2 2 4 5 6 3\n",
"4\n0 3 4 2 4 2 2 3\n",
"2\n\n\n6",
"2\n\n0 0 5 2\n\n-1\n",
"2\n3 0 1 9\n",
"4\n1 4 2 1 3 4 7 1\n",
"10\n1 16 6 4 3 5 5 9 3 8 1 2 6 0 7 5 4 1 7 8\n",
"10\n3 1 9 8 17 2 4 5 6 1 1 1 9 8 2 2 4 5 6 3\n",
"4\n0 3 4 2 4 2 4 3\n",
"2\n\n\n12",
"2\n\n0 -1 5 2\n\n-1\n",
"2\n3 0 2 9\n",
"4\n1 4 2 1 3 4 4 1\n",
"10\n1 16 6 4 3 5 5 9 3 8 1 2 6 0 7 5 4 1 1 8\n",
"10\n3 1 9 14 17 2 4 5 6 1 1 1 9 8 2 2 4 5 6 3\n",
"4\n0 3 4 2 4 2 0 3\n"
],
"output": [
"First\n1 2 1 2 \n",
"First\n1 2 1 2 \n",
"First\n1 2 1 2 \n",
"First\n1 2 3 4 1 2 3 4 \n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 \n",
"Second\n2 \n",
"Second\n2 3 4 5 6 \n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 \n",
"First\n1 2 3 4 1 2 3 4 \n",
"Second\n6 7 8 9 10 \n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 1 2\n",
"First\n1 2 3 4 1 2 3 4\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"First\n1 2 3 4 1 2 3 4\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This is an interactive problem.
Consider a fixed positive integer n. Two players, First and Second play a game as follows:
1. First considers the 2n numbers 1, 2, ..., 2n, and partitions them as he wants into n disjoint pairs.
2. Then, Second chooses exactly one element from each of the pairs that First created (he chooses elements he wants).
To determine the winner of the game, we compute the sum of the numbers chosen by Second. If the sum of all these numbers is a multiple of 2n, then Second wins. Otherwise, First wins.
You are given the integer n. Your task is to decide which player you wish to play as and win the game.
Interaction
The interaction begins by reading the integer n (1 ≤ n ≤ 5 ⋅ 10^5).
After reading, print a single line containing either First or Second, denoting who you want to play as. The interaction then varies depending on who you chose to play as.
If you chose to play as First, print a single line containing 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair for 1≤ i ≤ 2n. Thus, 1 ≤ p_i ≤ n, and every number between 1 and n inclusive should appear exactly twice.
If you chose to play as Second, the interactor will print 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair. As a response, print n integers a_1, a_2, ..., a_n in a single line. These should contain exactly one number from each pair.
Regardless of who you chose to play as the interactor will finish by printing a single integer: 0 if your answer for the test case is correct (that is, you are playing as First and it cannot choose adequate numbers from your pairs, or you are playing as Second and your chosen numbers add up to a multiple of 2n), or -1 if it is incorrect. In particular, the interactor will not print the chosen numbers if you choose to play First and lose. In either case, your program should terminate immediately after reading this number.
If at any point you make an invalid interaction, the interactor will print -1 and finish the interaction. You will receive a Wrong Answer verdict. Make sure to terminate immediately to avoid getting other verdicts.
After printing something do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
* fflush(stdout) or cout.flush() in C++;
* System.out.flush() in Java;
* flush(output) in Pascal;
* stdout.flush() in Python;
* see documentation for other languages.
Hack Format
To hack, use the following format:
The first line contains an integer n (1 ≤ n ≤ 5 ⋅ 10^5).
The second line contains 2n integers p_1, p_2, ..., p_{2n}, denoting that the number i belongs to the p_i-th pair if the solution being hacked chooses to play as Second. If the solution being hacked chooses to play as First, those pairs don't matter but the p_1, p_2, ..., p_{2n} must still form a valid partition of 1, 2, ..., 2n into n disjoint pairs.
Examples
Input
2
1 1 2 2
0
Output
Second
1 3
Input
2
0
Output
First
2 1 2 1
Note
In the first sample, n = 2, and you decide to play as Second. The judge chooses the pairs (1, 2) and (3, 4), and you reply with the numbers 1 and 3. This is a valid choice since it contains exactly one number from each pair, and the sum 1 + 3 = 4 is divisible by 4.
In the second sample, n = 2 again, and you play as First. You choose the pairs (2, 4) and (1, 3). The judge fails to choose a number from each pair such that their sum is divisible by 4, so the answer is correct.
Note that the sample tests are just for illustration of the interaction protocol, and don't necessarily correspond to the behavior of the real interactor.
### Input:
2
0
### Output:
First
1 2 1 2
### Input:
2
1 1 2 2
0
### Output:
First
1 2 1 2
### Code:
import sys
n = int(input())
if n % 2:
print('Second')
sys.stdout.flush()
l = list(map(lambda x: int(x)-1,input().split()))
rev1 = [-1]*n
rev2 = [-1]*n
revs = [0]*n
for i in range(2 * n):
revs[l[i]] += i
if rev1[l[i]] == -1:
rev1[l[i]] = i
else:
rev2[l[i]] = i
out = [0] * (2 * n)
curr = 0
todo = 2*n
q = []
while todo:
while out[curr] and curr < 2*n:
curr += 1
if curr == 2*n:
break
out[curr] = 1
todo -= 1
q = [curr]
while q:
v = q.pop()
mod = v % n
other = (2 * mod + n) - v
if out[other] == 0:
out[other] = 3 - out[v]
todo -= 1
q.append(other)
other = revs[l[v]] - v
if out[other] == 0:
out[other] = 3 - out[v]
todo -= 1
q.append(other)
s1 = 0
for i in range(2 * n):
if out[i] == 1:
s1 += i + 1
if s1 % (2 * n) == 0:
want = 1
else:
want = 2
rout = []
for i in range(2 * n):
if out[i] == want:
rout.append(i + 1)
print(' '.join(map(str,rout)))
sys.stdout.flush()
else:
print('First')
sys.stdout.flush()
l = [1+(i%n) for i in range(2*n)]
print(' '.join(map(str,l)))
sys.stdout.flush()
|
1426_A. Floor Number_28590
|
Vasya goes to visit his classmate Petya. Vasya knows that Petya's apartment number is n.
There is only one entrance in Petya's house and the distribution of apartments is the following: the first floor contains 2 apartments, every other floor contains x apartments each. Apartments are numbered starting from one, from the first floor. I.e. apartments on the first floor have numbers 1 and 2, apartments on the second floor have numbers from 3 to (x + 2), apartments on the third floor have numbers from (x + 3) to (2 ⋅ x + 2), and so on.
Your task is to find the number of floor on which Petya lives. Assume that the house is always high enough to fit at least n apartments.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.
The only line of the test case contains two integers n and x (1 ≤ n, x ≤ 1000) — the number of Petya's apartment and the number of apartments on each floor of the house except the first one (there are two apartments on the first floor).
Output
For each test case, print the answer: the number of floor on which Petya lives.
Example
Input
4
7 3
1 5
22 5
987 13
Output
3
1
5
77
Note
Consider the first test case of the example: the first floor contains apartments with numbers 1 and 2, the second one contains apartments with numbers 3, 4 and 5, the third one contains apartments with numbers 6, 7 and 8. Therefore, Petya lives on the third floor.
In the second test case of the example, Petya lives in the apartment 1 which is on the first floor.
|
from functools import reduce
import os
import sys
from collections import *
#from fractions import *
from math import *
from bisect import *
from heapq import *
from io import BytesIO, IOBase
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value(): return tuple(map(int, input().split())) # multiple values
def arr(): return [int(i) for i in input().split()] # array input
def sarr(): return [int(i) for i in input()] #array from string
def starr(): return [str(x) for x in input().split()] #string array
def inn(): return int(input()) # integer input
def svalue(): return tuple(map(str, input().split())) #multiple string values
def parr(): return [(value()) for i in range(n)] # array of pairs
mo = 1000000007
inf=1e18
div=998244353
#print("Case #{}:".format(_+1),end=" ")
# ----------------------------CODE------------------------------#
for _ in range(inn()):
n,k=value()
if(n<=2):
print(1)
else:
n-=2
res=ceil(n/k)
print(res+1)
|
{
"input": [
"4\n7 3\n1 5\n22 5\n987 13\n",
"7\n7 3\n1 5\n22 5\n987 13\n7 3\n1 5\n22 5\n",
"7\n7 3\n1 5\n12 5\n987 13\n7 3\n1 5\n22 5\n",
"4\n8 3\n1 5\n22 5\n987 13\n",
"7\n7 3\n1 5\n12 5\n987 3\n7 3\n1 5\n22 5\n",
"4\n8 3\n1 5\n22 5\n987 5\n",
"7\n7 3\n1 5\n12 5\n987 3\n7 5\n1 5\n22 5\n",
"4\n8 3\n1 5\n22 5\n859 5\n",
"4\n8 3\n1 5\n29 5\n859 5\n",
"7\n7 3\n1 5\n12 6\n987 3\n7 2\n1 5\n22 5\n",
"7\n7 3\n1 5\n12 6\n987 3\n12 2\n2 5\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 3\n12 2\n2 5\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 4\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 4\n5 2\n2 10\n22 6\n",
"7\n7 3\n1 3\n29 6\n987 4\n5 2\n2 10\n22 6\n",
"7\n7 3\n1 3\n29 6\n987 4\n5 2\n2 10\n22 3\n",
"7\n7 3\n1 3\n29 6\n987 4\n5 2\n2 13\n44 3\n",
"7\n7 3\n1 4\n29 6\n987 4\n5 2\n2 13\n6 3\n",
"7\n7 3\n2 4\n29 6\n987 4\n5 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 6\n987 4\n3 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 10\n987 4\n3 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 10\n987 3\n3 2\n2 13\n5 4\n",
"7\n5 3\n2 4\n29 10\n987 3\n3 2\n2 13\n5 4\n",
"7\n5 3\n2 4\n29 10\n987 3\n1 2\n2 13\n5 4\n",
"7\n7 2\n1 5\n22 5\n987 13\n7 3\n1 5\n22 5\n",
"4\n7 3\n1 5\n22 5\n1849 13\n",
"4\n8 2\n1 5\n22 5\n987 13\n",
"4\n16 3\n1 5\n22 5\n987 5\n",
"7\n7 3\n1 5\n12 10\n987 3\n7 5\n1 5\n22 5\n",
"4\n8 3\n1 5\n11 5\n859 5\n",
"7\n7 3\n1 5\n12 6\n465 3\n7 5\n1 5\n22 5\n",
"4\n8 3\n1 5\n29 5\n859 7\n",
"4\n6 3\n1 5\n29 5\n859 6\n",
"7\n7 3\n1 5\n2 6\n987 3\n7 2\n2 5\n22 5\n",
"7\n7 3\n1 3\n12 6\n987 3\n12 2\n2 5\n22 9\n",
"7\n4 3\n1 3\n18 6\n987 3\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n1865 4\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 4\n12 2\n2 10\n22 12\n",
"7\n7 3\n1 3\n24 6\n987 4\n5 2\n2 10\n22 3\n",
"7\n7 3\n1 3\n29 6\n987 4\n5 2\n2 13\n44 1\n",
"7\n7 3\n1 4\n29 6\n987 4\n5 4\n2 13\n44 3\n",
"7\n7 3\n1 4\n29 6\n1656 4\n5 2\n2 13\n6 3\n",
"7\n7 3\n3 4\n29 6\n987 4\n5 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 6\n987 8\n3 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 10\n1422 4\n3 2\n2 13\n5 4\n",
"7\n7 2\n2 4\n29 10\n987 3\n3 2\n2 13\n5 4\n",
"7\n5 3\n2 4\n29 10\n987 3\n1 2\n4 13\n5 4\n",
"7\n7 2\n1 5\n22 5\n987 13\n7 3\n1 5\n38 5\n",
"4\n12 3\n1 5\n22 5\n1849 13\n",
"7\n7 3\n1 5\n12 9\n987 6\n7 3\n1 5\n22 5\n",
"4\n12 3\n1 5\n22 5\n987 5\n",
"4\n8 3\n1 5\n11 5\n1296 5\n",
"4\n8 3\n1 5\n37 5\n859 7\n",
"4\n2 3\n1 5\n29 5\n859 6\n",
"4\n6 3\n1 5\n32 7\n859 5\n",
"7\n7 3\n2 3\n18 6\n106 3\n12 2\n2 5\n22 5\n",
"7\n2 3\n1 3\n18 6\n987 3\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n1865 4\n12 2\n4 10\n22 5\n",
"7\n7 3\n1 4\n29 6\n5 4\n5 2\n2 10\n22 6\n",
"7\n7 3\n1 3\n24 10\n987 4\n5 2\n2 10\n22 3\n",
"7\n7 3\n2 4\n29 6\n987 8\n3 2\n2 13\n9 4\n",
"7\n3 3\n2 3\n29 10\n987 4\n3 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 10\n1005 4\n3 2\n2 13\n5 4\n",
"7\n5 3\n3 4\n29 10\n987 3\n1 2\n4 13\n5 4\n",
"7\n7 2\n1 5\n22 5\n987 13\n7 3\n1 5\n38 2\n",
"7\n7 3\n1 5\n12 9\n987 6\n7 2\n1 5\n22 5\n",
"4\n8 4\n1 5\n23 5\n987 13\n",
"4\n19 3\n1 5\n22 5\n987 5\n",
"4\n8 3\n1 5\n11 5\n160 5\n",
"4\n3 3\n1 5\n32 7\n859 5\n",
"7\n2 3\n1 3\n18 6\n1232 3\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n1865 3\n12 2\n4 10\n22 5\n",
"7\n6 1\n1 3\n18 6\n987 4\n12 2\n2 10\n22 12\n",
"7\n7 3\n1 3\n20 6\n987 4\n5 1\n2 10\n26 6\n",
"7\n7 4\n3 4\n29 6\n987 5\n5 2\n2 13\n6 4\n",
"7\n7 3\n2 4\n29 6\n987 13\n3 2\n2 13\n9 4\n",
"7\n7 3\n1 5\n12 6\n987 3\n7 5\n1 5\n22 5\n",
"4\n6 3\n1 5\n29 5\n859 5\n",
"7\n7 3\n1 5\n12 6\n987 3\n7 2\n2 5\n22 5\n",
"4\n6 3\n1 5\n29 8\n859 5\n",
"7\n7 3\n1 3\n12 6\n987 3\n12 2\n2 5\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 3\n12 2\n2 10\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 4\n12 2\n2 10\n22 6\n",
"7\n7 3\n1 3\n29 6\n987 4\n5 2\n2 13\n22 3\n",
"7\n7 3\n1 4\n29 6\n987 4\n5 2\n2 13\n44 3\n",
"7\n7 3\n2 4\n29 6\n987 4\n5 2\n2 13\n6 3\n",
"7\n7 3\n2 4\n29 10\n987 4\n3 2\n2 13\n5 4\n",
"7\n7 3\n1 5\n12 9\n987 13\n7 3\n1 5\n22 5\n",
"4\n6 3\n1 5\n29 7\n859 5\n",
"7\n7 3\n1 10\n12 6\n987 3\n12 2\n2 5\n22 5\n",
"7\n7 3\n2 3\n18 6\n987 3\n12 2\n2 5\n22 5\n",
"7\n7 3\n1 3\n18 6\n987 4\n5 2\n2 10\n26 6\n",
"7\n7 3\n1 4\n29 6\n987 4\n5 2\n2 10\n22 6\n",
"7\n7 3\n2 3\n29 10\n987 4\n3 2\n2 13\n6 4\n",
"7\n5 3\n1 4\n29 10\n987 3\n3 2\n2 13\n5 4\n",
"4\n8 4\n1 5\n22 5\n987 13\n",
"7\n7 3\n1 10\n12 10\n987 3\n7 5\n1 5\n22 5\n",
"7\n7 3\n1 10\n12 6\n987 3\n3 2\n2 5\n22 5\n",
"7\n6 3\n1 3\n18 6\n987 4\n12 2\n2 10\n22 12\n",
"7\n7 3\n1 3\n20 6\n987 4\n5 2\n2 10\n26 6\n",
"7\n8 3\n1 4\n29 6\n1656 4\n5 2\n2 13\n6 3\n",
"7\n7 4\n3 4\n29 6\n987 4\n5 2\n2 13\n6 4\n"
],
"output": [
"3\n1\n5\n77\n",
"3\n1\n5\n77\n3\n1\n5\n",
"3\n1\n3\n77\n3\n1\n5\n",
"3\n1\n5\n77\n",
"3\n1\n3\n330\n3\n1\n5\n",
"3\n1\n5\n198\n",
"3\n1\n3\n330\n2\n1\n5\n",
"3\n1\n5\n173\n",
"3\n1\n7\n173\n",
"3\n1\n3\n330\n4\n1\n5\n",
"3\n1\n3\n330\n6\n1\n5\n",
"3\n1\n4\n330\n6\n1\n5\n",
"3\n1\n4\n248\n6\n1\n5\n",
"3\n1\n4\n248\n3\n1\n5\n",
"3\n1\n6\n248\n3\n1\n5\n",
"3\n1\n6\n248\n3\n1\n8\n",
"3\n1\n6\n248\n3\n1\n15\n",
"3\n1\n6\n248\n3\n1\n3\n",
"3\n1\n6\n248\n3\n1\n2\n",
"3\n1\n6\n248\n2\n1\n2\n",
"3\n1\n4\n248\n2\n1\n2\n",
"3\n1\n4\n330\n2\n1\n2\n",
"2\n1\n4\n330\n2\n1\n2\n",
"2\n1\n4\n330\n1\n1\n2\n",
"4\n1\n5\n77\n3\n1\n5\n",
"3\n1\n5\n144\n",
"4\n1\n5\n77\n",
"6\n1\n5\n198\n",
"3\n1\n2\n330\n2\n1\n5\n",
"3\n1\n3\n173\n",
"3\n1\n3\n156\n2\n1\n5\n",
"3\n1\n7\n124\n",
"3\n1\n7\n144\n",
"3\n1\n1\n330\n4\n1\n5\n",
"3\n1\n3\n330\n6\n1\n4\n",
"2\n1\n4\n330\n6\n1\n5\n",
"3\n1\n4\n467\n6\n1\n5\n",
"3\n1\n4\n248\n6\n1\n3\n",
"3\n1\n5\n248\n3\n1\n8\n",
"3\n1\n6\n248\n3\n1\n43\n",
"3\n1\n6\n248\n2\n1\n15\n",
"3\n1\n6\n415\n3\n1\n3\n",
"3\n2\n6\n248\n3\n1\n2\n",
"3\n1\n6\n125\n2\n1\n2\n",
"3\n1\n4\n356\n2\n1\n2\n",
"4\n1\n4\n330\n2\n1\n2\n",
"2\n1\n4\n330\n1\n2\n2\n",
"4\n1\n5\n77\n3\n1\n9\n",
"5\n1\n5\n144\n",
"3\n1\n3\n166\n3\n1\n5\n",
"5\n1\n5\n198\n",
"3\n1\n3\n260\n",
"3\n1\n8\n124\n",
"1\n1\n7\n144\n",
"3\n1\n6\n173\n",
"3\n1\n4\n36\n6\n1\n5\n",
"1\n1\n4\n330\n6\n1\n5\n",
"3\n1\n4\n467\n6\n2\n5\n",
"3\n1\n6\n2\n3\n1\n5\n",
"3\n1\n4\n248\n3\n1\n8\n",
"3\n1\n6\n125\n2\n1\n3\n",
"2\n1\n4\n248\n2\n1\n2\n",
"3\n1\n4\n252\n2\n1\n2\n",
"2\n2\n4\n330\n1\n2\n2\n",
"4\n1\n5\n77\n3\n1\n19\n",
"3\n1\n3\n166\n4\n1\n5\n",
"3\n1\n6\n77\n",
"7\n1\n5\n198\n",
"3\n1\n3\n33\n",
"2\n1\n6\n173\n",
"1\n1\n4\n411\n6\n1\n5\n",
"3\n1\n4\n622\n6\n2\n5\n",
"5\n1\n4\n248\n6\n1\n3\n",
"3\n1\n4\n248\n4\n1\n5\n",
"3\n2\n6\n198\n3\n1\n2\n",
"3\n1\n6\n77\n2\n1\n3\n",
"3\n1\n3\n330\n2\n1\n5\n",
"3\n1\n7\n173\n",
"3\n1\n3\n330\n4\n1\n5\n",
"3\n1\n5\n173\n",
"3\n1\n3\n330\n6\n1\n5\n",
"3\n1\n4\n330\n6\n1\n5\n",
"3\n1\n4\n248\n6\n1\n5\n",
"3\n1\n6\n248\n3\n1\n8\n",
"3\n1\n6\n248\n3\n1\n15\n",
"3\n1\n6\n248\n3\n1\n3\n",
"3\n1\n4\n248\n2\n1\n2\n",
"3\n1\n3\n77\n3\n1\n5\n",
"3\n1\n5\n173\n",
"3\n1\n3\n330\n6\n1\n5\n",
"3\n1\n4\n330\n6\n1\n5\n",
"3\n1\n4\n248\n3\n1\n5\n",
"3\n1\n6\n248\n3\n1\n5\n",
"3\n1\n4\n248\n2\n1\n2\n",
"2\n1\n4\n330\n2\n1\n2\n",
"3\n1\n5\n77\n",
"3\n1\n2\n330\n2\n1\n5\n",
"3\n1\n3\n330\n2\n1\n5\n",
"3\n1\n4\n248\n6\n1\n3\n",
"3\n1\n4\n248\n3\n1\n5\n",
"3\n1\n6\n415\n3\n1\n3\n",
"3\n2\n6\n248\n3\n1\n2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vasya goes to visit his classmate Petya. Vasya knows that Petya's apartment number is n.
There is only one entrance in Petya's house and the distribution of apartments is the following: the first floor contains 2 apartments, every other floor contains x apartments each. Apartments are numbered starting from one, from the first floor. I.e. apartments on the first floor have numbers 1 and 2, apartments on the second floor have numbers from 3 to (x + 2), apartments on the third floor have numbers from (x + 3) to (2 ⋅ x + 2), and so on.
Your task is to find the number of floor on which Petya lives. Assume that the house is always high enough to fit at least n apartments.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.
The only line of the test case contains two integers n and x (1 ≤ n, x ≤ 1000) — the number of Petya's apartment and the number of apartments on each floor of the house except the first one (there are two apartments on the first floor).
Output
For each test case, print the answer: the number of floor on which Petya lives.
Example
Input
4
7 3
1 5
22 5
987 13
Output
3
1
5
77
Note
Consider the first test case of the example: the first floor contains apartments with numbers 1 and 2, the second one contains apartments with numbers 3, 4 and 5, the third one contains apartments with numbers 6, 7 and 8. Therefore, Petya lives on the third floor.
In the second test case of the example, Petya lives in the apartment 1 which is on the first floor.
### Input:
4
7 3
1 5
22 5
987 13
### Output:
3
1
5
77
### Input:
7
7 3
1 5
22 5
987 13
7 3
1 5
22 5
### Output:
3
1
5
77
3
1
5
### Code:
from functools import reduce
import os
import sys
from collections import *
#from fractions import *
from math import *
from bisect import *
from heapq import *
from io import BytesIO, IOBase
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value(): return tuple(map(int, input().split())) # multiple values
def arr(): return [int(i) for i in input().split()] # array input
def sarr(): return [int(i) for i in input()] #array from string
def starr(): return [str(x) for x in input().split()] #string array
def inn(): return int(input()) # integer input
def svalue(): return tuple(map(str, input().split())) #multiple string values
def parr(): return [(value()) for i in range(n)] # array of pairs
mo = 1000000007
inf=1e18
div=998244353
#print("Case #{}:".format(_+1),end=" ")
# ----------------------------CODE------------------------------#
for _ in range(inn()):
n,k=value()
if(n<=2):
print(1)
else:
n-=2
res=ceil(n/k)
print(res+1)
|
1472_G. Moving to the Capital_28594
|
There are n cities in Berland. The city numbered 1 is the capital. Some pairs of cities are connected by a one-way road of length 1.
Before the trip, Polycarp for each city found out the value of d_i — the shortest distance from the capital (the 1-st city) to the i-th city.
Polycarp begins his journey in the city with number s and, being in the i-th city, chooses one of the following actions:
1. Travel from the i-th city to the j-th city if there is a road from the i-th city to the j-th and d_i < d_j;
2. Travel from the i-th city to the j-th city if there is a road from the i-th city to the j-th and d_i ≥ d_j;
3. Stop traveling.
Since the government of Berland does not want all people to come to the capital, so Polycarp no more than once can take the second action from the list. in other words, he can perform the second action 0 or 1 time during his journey. Polycarp, on the other hand, wants to be as close to the capital as possible.
<image>
For example, if n = 6 and the cities are connected, as in the picture above, then Polycarp could have made the following travels (not all possible options):
* 2 → 5 → 1 → 2 → 5;
* 3 → 6 → 2;
* 1 → 3 → 6 → 2 → 5.
Polycarp wants for each starting city i to find out how close he can get to the capital. More formally: he wants to find the minimal value of d_j that Polycarp can get from the city i to the city j according to the rules described above.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
Each test case is preceded by an empty line.
The first line of each test case contains two integers n (2 ≤ n ≤ 2 ⋅ 10^5) and m (1 ≤ m ≤ 2 ⋅ 10^5) — number of cities and roads, respectively.
This is followed by m lines describing the roads. Each road is characterized by two integers u and v (1 ≤ u, v ≤ n, u ≠ v) — the numbers of cities connected by a one-way road.
It is guaranteed that the sums of n and m over all test cases do not exceed 2 ⋅ 10^5.
It is guaranteed that for each pair of different cities (u, v) there is at most one road from u to v (but a pair of roads from u to v and from v to u — is valid).
It is guaranteed that there is a path from the capital to all cities.
Output
For each test case, on a separate line output n numbers, the i-th of which is equal to the minimum possible distance from the capital to the city where Polycarp ended his journey.
Example
Input
3
6 7
1 2
1 3
2 5
2 4
5 1
3 6
6 2
2 2
1 2
2 1
6 8
1 2
1 5
2 6
6 1
2 3
3 4
4 2
5 4
Output
0 0 1 2 0 1
0 0
0 0 2 1 1 0
|
import sys
from sys import stdin
from collections import deque
def NC_Dij(lis,start):
ret = [float("inf")] * len(lis)
ret[start] = 0
q = deque([start])
plis = [i for i in range(len(lis))]
while len(q) > 0:
now = q.popleft()
for nex in lis[now]:
if ret[nex] > ret[now] + 1:
ret[nex] = ret[now] + 1
plis[nex] = now
q.append(nex)
return ret,plis
tt = int(stdin.readline())
for loop in range(tt):
stdin.readline()
n,m = map(int,stdin.readline().split())
lis = [ [] for i in range(n) ]
for i in range(m):
u,v = map(int,stdin.readline().split())
u -= 1
v -= 1
lis[u].append(v)
dlis,tmp = NC_Dij(lis,0)
dind = []
for i in range(n):
dind.append((dlis[i],i))
dind.sort()
dind.reverse()
ans = [None] * n
for nd,ind in dind:
now = nd
for nex in lis[ind]:
if dlis[nex] > nd:
now = min(now,ans[nex])
else:
now = min(now,dlis[nex])
ans[ind] = now
print (*ans)
|
{
"input": [
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n2 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n1 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 4\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n1 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 3\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 2\n5 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 2\n5 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 2\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n3 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 3\n2 3\n2 5\n1 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n4 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n3 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n1 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n2 4\n4 5\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 3\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n6 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 1\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 2\n5 6\n6 3\n\n2 2\n1 2\n2 2\n\n6 8\n1 3\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n4 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n3 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n1 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n2 4\n4 5\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n3 6\n6 1\n4 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 1\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n4 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n4 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 6\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 3\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n5 1\n2 3\n3 4\n4 2\n5 1\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n3 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n5 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 3\n5 4\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 2\n5 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 2\n3 6\n6 1\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 5\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 2\n3 6\n6 1\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 1\n5 5\n",
"3\n\n6 7\n1 2\n1 3\n4 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n1 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 1\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n4 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n4 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 5\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n3 4\n4 1\n5 4\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n3 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n4 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 2\n2 3\n5 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n4 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n2 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 3\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 6\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n1 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 4\n1 5\n2 6\n6 1\n2 3\n5 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n4 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n5 6\n6 6\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 2\n5 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 4\n4 1\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n4 6\n6 1\n3 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n4 4\n6 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 3\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n3 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 4\n4 1\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 1\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n1 3\n6 4\n1 2\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n3 6\n6 1\n2 3\n4 4\n6 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n1 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 3\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 1\n6 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 6\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 1\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n3 4\n3 1\n3 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n1 2\n5 4\n",
"3\n\n6 7\n2 2\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 3\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n6 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n2 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n1 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 3\n1 5\n3 6\n6 1\n4 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 4\n4 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 5\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 1\n5 5\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 3\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n3 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 1\n2 3\n3 4\n4 2\n5 3\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 1\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n1 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n1 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n5 6\n6 6\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n4 1\n2 3\n2 6\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n2 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n3 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 4\n4 1\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 1\n4 3\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 1\n6 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 4\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n1 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n1 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n2 2\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n3 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 4\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 3\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 2\n1 3\n4 2\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n3 4\n3 1\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n4 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 3\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n2 2\n1 3\n4 2\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n3 4\n6 3\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n2 2\n1 3\n4 2\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n5 4\n3 1\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n4 2\n1 5\n2 6\n6 1\n2 3\n3 3\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n1 5\n5 4\n3 1\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n4 2\n1 5\n2 6\n6 1\n2 3\n3 3\n4 2\n5 4\n",
"3\n\n6 7\n1 5\n1 3\n1 5\n5 4\n3 1\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n4 2\n1 5\n2 6\n6 1\n2 3\n3 3\n4 2\n5 4\n",
"3\n\n6 7\n1 5\n1 3\n1 5\n5 4\n3 1\n4 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n4 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 4\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n2 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 4\n3 6\n5 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n1 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 5\n3 1\n3 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n1 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n3 6\n6 1\n4 3\n2 1\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 1\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 4\n2 3\n3 4\n2 2\n5 2\n",
"3\n\n6 7\n1 3\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n5 1\n2 3\n3 4\n4 4\n5 1\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 1\n5 6\n6 6\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n1 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 2\n5 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n3 4\n6 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n5 4\n4 2\n5 5\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 2\n3 6\n6 1\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n1 4\n5 2\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 1\n5 5\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 3\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n4 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n3 4\n4 1\n5 4\n",
"3\n\n6 7\n1 3\n2 5\n2 5\n2 4\n3 1\n1 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n3 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 3\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 6\n1 5\n2 6\n2 1\n2 3\n2 4\n4 1\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n4 1\n2 3\n2 4\n4 3\n2 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n5 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 4\n4 1\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 3\n1 5\n4 6\n6 2\n3 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n3 6\n6 1\n4 3\n2 4\n4 3\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n3 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 6\n4 1\n5 4\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n2 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n4 3\n2 1\n4 3\n5 4\n",
"3\n\n6 7\n1 3\n1 3\n3 5\n2 4\n6 4\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n3 4\n3 1\n3 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n1 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 6\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 5\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n3 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n2 4\n4 1\n5 5\n",
"3\n\n6 7\n1 4\n1 3\n2 5\n2 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 2\n\n6 8\n1 2\n2 5\n2 6\n6 1\n6 3\n2 4\n6 3\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n3 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 4\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 5\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n3 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n4 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 2\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 5\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n3 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n1 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n2 5\n2 4\n3 1\n5 6\n6 4\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 4\n2 3\n3 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n5 1\n3 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n2 3\n3 4\n4 2\n5 1\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n2 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n6 5\n2 4\n6 2\n4 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n5 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 1\n5 6\n6 6\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n3 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n1 6\n6 1\n2 3\n3 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n2 5\n3 4\n5 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n3 4\n4 2\n5 3\n",
"3\n\n6 7\n1 2\n1 3\n1 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n2 3\n2 4\n4 2\n5 4\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n6 2\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 1\n4 3\n4 4\n3 4\n5 4\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 1\n5 6\n6 3\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n2 5\n2 6\n2 1\n2 3\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n2 3\n3 5\n2 4\n6 2\n5 6\n6 3\n\n2 2\n1 2\n2 2\n\n6 8\n1 3\n1 5\n2 6\n2 1\n2 2\n2 4\n4 2\n5 2\n",
"3\n\n6 7\n1 2\n1 3\n3 5\n2 4\n3 1\n3 6\n6 2\n\n2 2\n1 2\n2 1\n\n6 8\n1 2\n1 5\n2 6\n6 2\n1 3\n3 4\n4 2\n5 1\n"
],
"output": [
"\n0 0 1 2 0 1 \n0 0 \n0 0 2 1 1 0 \n",
"0 0 1 2 0 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 1 2 1 1 1\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 0 1\n0 0\n0 0 2 1 1 0\n",
"0 0 0 1 0 0\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 2 0\n0 0\n0 0 2 2 1 0\n",
"0 0 0 2 2 1\n0 0\n0 1 2 1 1 1\n",
"0 1 0 2 2 0\n0 0\n0 0 2 2 1 0\n",
"0 1 0 1 2 0\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 2 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 1 1\n",
"0 1 1 2 2 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 0 1\n0 0\n0 0 1 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 1 2 1 1 0\n",
"0 0 1 2 0 1\n0 0\n0 0 2 2 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 1 0 0 0\n",
"0 1 1 2 0 1\n0 0\n0 0 0 0 0 0\n",
"0 1 0 4 4 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 0 1\n",
"0 1 1 2 2 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 1 1 2\n",
"0 1 2 1 1 1\n0 0\n0 0 2 1 1 2\n",
"0 1 1 2 1 1\n0 0\n0 0 2 1 1 2\n",
"0 1 1 2 1 1\n0 0\n0 0 1 2 0 3\n",
"0 0 0 2 2 2\n0 0\n0 1 2 1 1 1\n",
"0 1 0 2 2 0\n0 0\n0 0 4 0 0 0\n",
"0 1 1 1 4 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 1 0 1 1 0\n",
"0 1 0 1 4 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 0 1 1 0 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 3 4 1\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 2 2\n0 0\n0 1 2 2 1 1\n",
"0 1 0 2 2 0\n0 0\n0 0 2 2 2 0\n",
"0 0 1 2 0 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 1 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 0 1\n0 0\n0 0 1 2 0 0\n",
"0 1 1 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 3 0 4 4 2\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 4 1\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 0 0\n0 0\n0 0 2 1 1 2\n",
"0 1 1 2 1 1\n0 1\n0 0 1 2 0 3\n",
"0 1 1 1 4 1\n0 0\n0 1 2 0 0 0\n",
"0 1 0 2 1 0\n0 0\n0 1 0 1 1 0\n",
"0 1 1 1 4 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 1 2 0\n0 0\n0 0 2 2 2 0\n",
"0 1 0 2 1 0\n0 0\n0 2 0 1 1 0\n",
"0 0 0 2 0 0\n0 0\n0 0 2 1 1 0\n",
"0 0 1 2 0 1\n0 0\n0 0 2 0 0 0\n",
"0 1 0 2 2 1\n0 0\n0 2 2 2 1 2\n",
"0 1 1 2 0 1\n0 0\n0 1 2 0 0 0\n",
"0 0 0 1 0 0\n0 0\n0 0 2 2 1 0\n",
"0 1 1 2 0 1\n0 0\n0 1 2 1 1 0\n",
"0 1 2 2 2 2\n0 0\n0 0 1 2 0 3\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 0 2\n",
"0 1 1 3 4 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 2 2 0\n0 0\n0 0 2 2 1 0\n",
"0 2 1 3 3 2\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 1 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 2 1 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 2 0 0 0\n",
"0 2 0 3 3 0\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 1 1\n0 0\n0 0 1 1 2 0\n",
"0 2 0 3 3 0\n0 0\n0 0 0 0 0 0\n",
"0 1 1 2 1 1\n0 0\n0 0 0 0 2 0\n",
"0 0 1 0 0 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 3 1 1 0\n",
"0 0 0 2 2 0\n0 0\n0 0 1 0 0 0\n",
"0 0 0 2 2 1\n0 0\n0 1 2 2 1 1\n",
"0 0 0 2 2 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 2 1\n0 1\n0 1 1 1 0 1\n",
"0 1 1 2 2 1\n0 0\n0 0 2 0 0 2\n",
"0 1 0 2 2 0\n0 0\n0 1 1 0 0 0\n",
"0 1 0 2 2 0\n0 1\n0 0 2 1 1 0\n",
"0 0 0 2 2 1\n0 0\n0 1 2 0 0 1\n",
"0 3 0 4 4 2\n0 0\n0 0 0 1 1 2\n",
"0 1 1 2 0 1\n0 0\n0 0 2 0 0 0\n",
"0 1 0 2 2 1\n0 0\n0 2 3 2 1 2\n",
"0 1 1 2 0 1\n0 0\n0 1 0 0 0 0\n",
"0 0 0 1 0 0\n0 0\n0 0 3 2 1 0\n",
"0 1 2 2 2 2\n0 0\n0 0 3 2 0 1\n",
"0 1 0 1 2 0\n0 0\n0 0 4 0 0 0\n",
"0 1 1 1 4 1\n0 0\n0 0 3 0 1 0\n",
"0 1 1 2 2 0\n0 0\n0 0 2 2 2 0\n",
"0 1 0 2 0 0\n0 0\n0 0 2 1 1 2\n",
"0 1 1 2 1 1\n0 0\n0 1 2 2 1 1\n",
"0 0 0 2 2 1\n0 0\n0 0 2 0 0 1\n",
"0 1 1 2 0 1\n0 0\n0 3 0 0 0 0\n",
"0 0 0 1 0 0\n0 0\n0 0 3 2 2 0\n",
"0 1 1 2 2 0\n0 0\n0 0 2 3 2 0\n",
"0 0 0 2 3 0\n0 0\n0 0 1 0 0 0\n",
"0 0 0 3 2 1\n0 0\n0 0 2 0 0 1\n",
"0 0 0 1 0 0\n0 0\n0 0 4 3 2 0\n",
"0 1 0 2 2 1\n0 0\n0 1 1 3 0 1\n",
"0 1 1 2 2 0\n0 0\n0 0 0 3 2 0\n",
"0 0 0 1 2 0\n0 0\n0 0 1 0 0 0\n",
"0 0 0 1 0 0\n0 0\n0 0 3 3 2 0\n",
"0 0 0 2 2 0\n0 0\n0 0 2 1 2 0\n",
"0 0 0 1 0 0\n0 0\n0 1 2 1 1 1\n",
"0 1 1 2 0 1\n0 0\n0 1 1 1 0 0\n",
"0 1 1 2 3 1\n0 1\n0 0 2 1 1 2\n",
"0 0 0 2 2 0\n0 0\n0 1 2 1 1 1\n",
"0 0 0 3 2 3\n0 0\n0 1 2 2 1 1\n",
"0 0 0 4 0 0\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 1 1\n0 0\n0 0 2 0 0 0\n",
"0 1 1 2 4 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 1 4 1\n0 0\n0 1 1 1 1 1\n",
"0 1 0 2 1 0\n0 0\n0 2 0 0 0 0\n",
"0 1 1 2 2 0\n0 0\n0 0 3 2 1 0\n",
"0 1 1 2 0 1\n0 0\n0 0 1 1 2 0\n",
"0 1 1 2 1 1\n0 0\n0 0 0 0 1 0\n",
"0 0 0 2 2 0\n0 0\n0 0 4 0 0 0\n",
"0 1 1 2 0 1\n0 0\n0 1 1 1 1 0\n",
"0 0 0 2 0 0\n0 0\n0 0 2 1 2 2\n",
"0 1 0 1 2 0\n0 0\n0 0 1 0 0 0\n",
"0 1 0 2 0 0\n0 1\n0 0 2 1 1 2\n",
"0 1 1 2 2 1\n0 0\n0 1 2 0 0 2\n",
"0 1 1 1 2 1\n0 0\n0 0 2 2 1 0\n",
"0 0 0 3 4 1\n0 0\n0 0 2 0 0 1\n",
"0 1 1 1 0 1\n0 0\n0 0 4 3 2 0\n",
"0 1 0 1 4 1\n0 0\n0 0 3 3 2 0\n",
"0 1 0 2 1 1\n0 1\n0 0 2 0 0 0\n",
"0 1 1 2 2 1\n0 0\n0 0 2 2 0 0\n",
"0 1 0 1 2 0\n0 0\n0 0 1 1 1 0\n",
"0 1 1 1 2 1\n0 1\n0 0 2 2 1 0\n",
"0 1 1 3 2 1\n0 0\n0 0 2 2 0 0\n",
"0 1 1 1 4 1\n0 0\n0 1 1 1 1 2\n",
"0 1 0 1 1 1\n0 1\n0 0 2 0 0 0\n",
"0 1 1 1 4 1\n0 0\n0 3 1 2 1 4\n",
"0 1 1 1 1 1\n0 0\n0 3 1 2 1 4\n",
"0 1 0 1 1 1\n0 1\n0 0 4 0 0 0\n",
"0 3 0 1 1 2\n0 1\n0 0 4 0 0 0\n",
"0 4 0 2 1 3\n0 1\n0 0 4 0 0 0\n",
"0 4 0 2 1 3\n0 1\n0 0 2 0 0 0\n",
"0 0 0 2 2 0\n0 0\n0 0 3 0 1 0\n",
"0 1 1 2 0 1\n0 0\n0 0 2 1 2 0\n",
"0 1 2 1 1 2\n0 0\n0 1 2 1 1 0\n",
"0 1 1 1 2 1\n0 0\n0 0 2 1 1 0\n",
"0 0 0 4 2 3\n0 0\n0 1 2 2 1 1\n",
"0 1 0 2 1 0\n0 0\n0 0 0 0 0 0\n",
"0 1 0 2 2 1\n0 0\n0 0 2 2 0 2\n",
"0 1 0 2 2 1\n0 0\n0 1 2 3 1 2\n",
"0 3 0 4 2 0\n0 0\n0 0 4 0 0 0\n",
"0 1 0 2 2 1\n0 0\n0 1 2 3 0 2\n",
"0 0 0 2 0 0\n0 0\n0 0 1 1 1 2\n",
"0 1 1 2 1 1\n0 0\n0 0 2 3 1 0\n",
"0 1 1 2 1 1\n0 0\n0 0 2 1 1 0\n",
"0 2 0 3 3 0\n0 0\n0 0 1 0 0 0\n",
"0 1 1 1 1 1\n0 0\n0 0 0 0 2 0\n",
"0 0 0 2 2 0\n0 1\n0 0 1 0 0 0\n",
"0 0 0 1 2 3\n0 0\n0 1 2 2 1 1\n",
"0 0 0 2 2 1\n0 1\n0 1 2 0 0 1\n",
"0 2 0 3 3 1\n0 0\n0 0 0 1 1 2\n",
"0 1 2 2 2 2\n0 0\n0 0 3 0 0 1\n",
"0 1 1 2 2 1\n0 0\n0 0 2 0 1 2\n",
"0 0 0 2 1 3\n0 0\n0 0 2 0 0 1\n",
"0 1 1 2 0 1\n0 0\n0 3 1 2 1 3\n",
"0 0 0 1 0 0\n0 0\n0 0 0 0 2 0\n",
"0 0 0 3 2 1\n0 0\n0 1 2 0 0 1\n",
"0 0 0 1 4 0\n0 0\n0 0 4 3 2 0\n",
"0 3 1 3 2 2\n0 0\n0 0 2 1 1 0\n",
"0 0 0 3 3 3\n0 0\n0 1 2 2 1 1\n",
"0 1 1 1 4 1\n0 0\n0 1 2 1 1 1\n",
"0 1 1 2 0 2\n0 0\n0 0 1 1 2 0\n",
"0 0 0 3 4 1\n0 0\n0 0 2 0 1 1\n",
"0 0 0 1 0 0\n0 1\n0 0 3 2 2 0\n",
"0 1 1 2 0 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 2 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 1 1\n0 0\n0 0 2 1 1 2\n",
"0 0 0 2 2 1\n0 0\n0 1 2 1 1 1\n",
"0 1 0 2 2 0\n0 0\n0 0 2 1 1 0\n",
"0 1 1 1 4 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 3 1\n0 0\n0 0 2 2 1 0\n",
"0 1 1 2 2 1\n0 0\n0 0 2 2 1 0\n",
"0 0 0 2 2 2\n0 0\n0 1 2 1 1 1\n",
"0 1 1 2 2 1\n0 0\n0 0 2 2 1 0\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 1 1\n",
"0 1 1 2 0 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 0 1\n",
"0 1 0 2 2 0\n0 0\n0 0 4 0 0 0\n",
"0 1 1 1 4 1\n0 0\n0 0 2 1 1 0\n",
"0 0 0 2 0 0\n0 0\n0 0 2 1 1 2\n",
"0 1 0 2 2 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 0 1\n0 0\n0 1 2 1 1 0\n",
"0 0 1 2 0 1\n0 0\n0 0 1 1 1 0\n",
"0 1 0 2 1 1\n0 0\n0 0 2 1 1 0\n",
"0 1 1 2 2 1\n0 0\n0 0 2 2 1 0\n",
"0 0 0 2 0 0\n0 0\n0 0 2 1 1 2\n",
"0 1 1 2 1 1\n0 1\n0 0 1 2 0 3\n",
"0 1 0 2 2 1\n0 0\n0 1 1 1 0 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n cities in Berland. The city numbered 1 is the capital. Some pairs of cities are connected by a one-way road of length 1.
Before the trip, Polycarp for each city found out the value of d_i — the shortest distance from the capital (the 1-st city) to the i-th city.
Polycarp begins his journey in the city with number s and, being in the i-th city, chooses one of the following actions:
1. Travel from the i-th city to the j-th city if there is a road from the i-th city to the j-th and d_i < d_j;
2. Travel from the i-th city to the j-th city if there is a road from the i-th city to the j-th and d_i ≥ d_j;
3. Stop traveling.
Since the government of Berland does not want all people to come to the capital, so Polycarp no more than once can take the second action from the list. in other words, he can perform the second action 0 or 1 time during his journey. Polycarp, on the other hand, wants to be as close to the capital as possible.
<image>
For example, if n = 6 and the cities are connected, as in the picture above, then Polycarp could have made the following travels (not all possible options):
* 2 → 5 → 1 → 2 → 5;
* 3 → 6 → 2;
* 1 → 3 → 6 → 2 → 5.
Polycarp wants for each starting city i to find out how close he can get to the capital. More formally: he wants to find the minimal value of d_j that Polycarp can get from the city i to the city j according to the rules described above.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
Each test case is preceded by an empty line.
The first line of each test case contains two integers n (2 ≤ n ≤ 2 ⋅ 10^5) and m (1 ≤ m ≤ 2 ⋅ 10^5) — number of cities and roads, respectively.
This is followed by m lines describing the roads. Each road is characterized by two integers u and v (1 ≤ u, v ≤ n, u ≠ v) — the numbers of cities connected by a one-way road.
It is guaranteed that the sums of n and m over all test cases do not exceed 2 ⋅ 10^5.
It is guaranteed that for each pair of different cities (u, v) there is at most one road from u to v (but a pair of roads from u to v and from v to u — is valid).
It is guaranteed that there is a path from the capital to all cities.
Output
For each test case, on a separate line output n numbers, the i-th of which is equal to the minimum possible distance from the capital to the city where Polycarp ended his journey.
Example
Input
3
6 7
1 2
1 3
2 5
2 4
5 1
3 6
6 2
2 2
1 2
2 1
6 8
1 2
1 5
2 6
6 1
2 3
3 4
4 2
5 4
Output
0 0 1 2 0 1
0 0
0 0 2 1 1 0
### Input:
3
6 7
1 2
1 3
2 5
2 4
5 1
3 6
6 2
2 2
1 2
2 1
6 8
1 2
1 5
2 6
6 1
2 3
3 4
4 2
5 4
### Output:
0 0 1 2 0 1
0 0
0 0 2 1 1 0
### Input:
3
6 7
1 2
1 3
2 5
2 4
5 1
3 6
6 2
2 2
1 2
2 1
6 8
1 2
1 5
2 6
6 1
2 3
2 4
4 2
5 4
### Output:
0 0 1 2 0 1
0 0
0 0 2 1 1 0
### Code:
import sys
from sys import stdin
from collections import deque
def NC_Dij(lis,start):
ret = [float("inf")] * len(lis)
ret[start] = 0
q = deque([start])
plis = [i for i in range(len(lis))]
while len(q) > 0:
now = q.popleft()
for nex in lis[now]:
if ret[nex] > ret[now] + 1:
ret[nex] = ret[now] + 1
plis[nex] = now
q.append(nex)
return ret,plis
tt = int(stdin.readline())
for loop in range(tt):
stdin.readline()
n,m = map(int,stdin.readline().split())
lis = [ [] for i in range(n) ]
for i in range(m):
u,v = map(int,stdin.readline().split())
u -= 1
v -= 1
lis[u].append(v)
dlis,tmp = NC_Dij(lis,0)
dind = []
for i in range(n):
dind.append((dlis[i],i))
dind.sort()
dind.reverse()
ans = [None] * n
for nd,ind in dind:
now = nd
for nex in lis[ind]:
if dlis[nex] > nd:
now = min(now,ans[nex])
else:
now = min(now,dlis[nex])
ans[ind] = now
print (*ans)
|
1499_B. Binary Removals_28598
|
You are given a string s, consisting only of characters '0' or '1'. Let |s| be the length of s.
You are asked to choose some integer k (k > 0) and find a sequence a of length k such that:
* 1 ≤ a_1 < a_2 < ... < a_k ≤ |s|;
* a_{i-1} + 1 < a_i for all i from 2 to k.
The characters at positions a_1, a_2, ..., a_k are removed, the remaining characters are concatenated without changing the order. So, in other words, the positions in the sequence a should not be adjacent.
Let the resulting string be s'. s' is called sorted if for all i from 2 to |s'| s'_{i-1} ≤ s'_i.
Does there exist such a sequence a that the resulting string s' is sorted?
Input
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.
Then the descriptions of t testcases follow.
The only line of each testcase contains a string s (2 ≤ |s| ≤ 100). Each character is either '0' or '1'.
Output
For each testcase print "YES" if there exists a sequence a such that removing the characters at positions a_1, a_2, ..., a_k and concatenating the parts without changing the order produces a sorted string.
Otherwise, print "NO".
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).
Example
Input
5
10101011011
0000
11111
110
1100
Output
YES
YES
YES
YES
NO
Note
In the first testcase you can choose a sequence a=[1,3,6,9]. Removing the underlined letters from "10101011011" will produce a string "0011111", which is sorted.
In the second and the third testcases the sequences are already sorted.
In the fourth testcase you can choose a sequence a=[3]. s'= "11", which is sorted.
In the fifth testcase there is no way to choose a sequence a such that s' is sorted.
|
for q in range(int(input())):
n=input()
s=0
s1=0
p=0
l=len(n)
for i in range(l-1,0,-1):
if(n[i]=='0' and n[i-1]=='0' ):
s=1
p=i-1
break
for i in range(p,0,-1):
if(n[i]=='1' and n[i-1]=='1'):
s1=1
break
if(s1==1):
print("NO")
else:
print("YES")
|
{
"input": [
"5\n10101011011\n0000\n11111\n110\n1100\n",
"9\n11\n11\n11\n11\n11\n11\n11\n11\n11\n",
"1\n0000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100\n",
"1\n0000011111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111100\n",
"5\n10101011011\n1000\n11111\n110\n1100\n",
"5\n10101011011\n1000\n11111\n110\n0100\n",
"5\n10101011001\n1000\n11111\n110\n0101\n",
"5\n10101011001\n1001\n11111\n110\n1100\n",
"5\n10101011011\n0011\n11000\n101\n1100\n",
"5\n10010011011\n1011\n11100\n111\n1010\n",
"5\n10000011000\n1011\n11001\n111\n1000\n",
"1\n0000011111111111111111111011111111111111111111111111111111111111111111101111111111111111111111111100\n",
"1\n0000011111111111111111011011111111111111111111111111111111111111111111101111111111111111111111111100\n",
"5\n10101011011\n1000\n11111\n110\n0101\n",
"1\n0000011111011111111111011011111111111111111111111111111111111111111111101111111111111111111111111100\n",
"1\n0000011111011111111111011011111111111111011111111111111111111111111111101111111111111111111111111100\n",
"5\n10101011001\n1000\n11111\n110\n0100\n",
"1\n0000011111011111111111011011111111111111011111111111111111111111111101101111111111111111111111111100\n",
"5\n10101011001\n1001\n11111\n110\n0100\n",
"1\n0000011111011111111111011011111111111111011111111111111111111111111101101111111111111111101111111100\n",
"1\n0000011111011111111111011011111111111110011111111111111111111111111101101111111111111111101111111100\n",
"5\n10101011001\n1001\n11111\n110\n1110\n",
"1\n0000011111011111111111011011111111111110011111111111101111111111111101101111111111111111101111111100\n",
"5\n10101011001\n1101\n11111\n110\n1110\n",
"1\n0000011111011111111111001011111111111110011111111111101111111111111101101111111111111111101111111100\n",
"5\n10101011001\n1101\n11111\n111\n1110\n",
"1\n0000011111011111111111001011111111111110011111111111101111111111111101101111111111111110101111111100\n",
"5\n10101011011\n1101\n11111\n111\n1110\n",
"1\n0000011111011111111111001011111111111110011111111111101111111111111101001111111111111110101111111100\n",
"5\n10101011011\n1001\n11111\n111\n1110\n",
"1\n0010011111011111111111001011111111111110011111111111101111111111111101001111111111111110101111111100\n",
"5\n10101011011\n1011\n11111\n111\n1110\n",
"1\n0010011111011111111111001011111111111111011111111111101111111111111101001111111111111110101111111100\n",
"5\n10101011011\n1011\n11111\n110\n1110\n",
"1\n0010011111011111111111001011111111111111011111111111101111111111111101001111111111111110001111111100\n",
"5\n10101011011\n1011\n11110\n110\n1110\n",
"1\n0010011111011111111111000011111111111111011111111111101111111111111101001111111111111110001111111100\n",
"5\n10101011011\n1011\n11110\n111\n1110\n",
"1\n0010011111011111111111000011011111111111011111111111101111111111111101001111111111111110001111111100\n",
"5\n10101011011\n1011\n11010\n111\n1110\n",
"1\n0010011111011111111111000011011111111111011111111111101101111111111101001111111111111110001111111100\n",
"5\n10101011011\n1011\n11010\n111\n1100\n",
"1\n0010011111011111111111000011011111111111010111111111101101111111111101001111111111111110001111111100\n",
"5\n10101011011\n1011\n11010\n101\n1100\n",
"1\n0010011111011111111111000011011111111111010111110111101101111111111101001111111111111110001111111100\n",
"5\n10101011011\n0011\n11010\n101\n1100\n",
"1\n0010011111011101111111000011011111111111010111110111101101111111111101001111111111111110001111111100\n",
"1\n0010011101011101111111000011011111111111010111110111101101111111111101001111111111111110001111111100\n",
"5\n00101011011\n0011\n11000\n101\n1100\n",
"1\n0010011101011101111111000011011111111111000111110111101101111111111101001111111111111110001111111100\n",
"5\n00101011011\n0011\n11010\n101\n1100\n",
"1\n0010011101011101110111000011011111111111000111110111101101111111111101001111111111111110001111111100\n",
"5\n00101011011\n0011\n11010\n101\n1101\n",
"1\n0010001101011101110111000011011111111111000111110111101101111111111101001111111111111110001111111100\n",
"5\n00111011011\n0011\n11010\n101\n1101\n",
"1\n0010001101011101110111100011011111111111000111110111101101111111111101001111111111111110001111111100\n",
"5\n00111011011\n0011\n11010\n101\n1111\n",
"1\n0010001101011101110111100011011111111111000111110111101101111111111100001111111111111110001111111100\n",
"5\n00111011011\n0011\n11010\n101\n1110\n",
"1\n1010001101011101110111100011011111111111000111110111101101111111111100001111111111111110001111111100\n",
"5\n00110011011\n0011\n11010\n101\n1110\n",
"1\n1010001101011101110111100011011111111111000111110111101101011111111100001111111111111110001111111100\n",
"5\n00110011011\n0011\n11010\n001\n1110\n",
"1\n1010001101011101110111100011011111111111000111110111101101011111111100000111111111111110001111111100\n",
"5\n00110011011\n0001\n11010\n001\n1110\n",
"1\n1010001101011101110111100011011111111111000111110111101101011111111100000011111111111110001111111100\n",
"5\n00110011011\n0000\n11010\n001\n1110\n",
"1\n1010001101011101110111100011011111111111000111110111101001011111111100000011111111111110001111111100\n",
"5\n00110011011\n0000\n11110\n001\n1110\n",
"1\n1010001101011101110111100011011111111111001111110111101001011111111100000011111111111110001111111100\n",
"5\n00110011011\n0000\n11110\n011\n1110\n",
"1\n1010001101011101110111100011011111111111001111110111101001011111111100000011111101111110001111111100\n",
"5\n00110011011\n0000\n11110\n011\n0110\n",
"1\n1010001101011101110111100011011111111110001111110111101001011111111100000011111101111110001111111100\n",
"5\n00110011011\n0100\n11110\n011\n0110\n",
"1\n1010001101011101110111100011011111111110001111110111101011011111111100000011111101111110001111111100\n",
"5\n10110011011\n0100\n11110\n011\n0110\n",
"1\n1010001101011101110111100011011111111110001111110111101011011111111100000111111101111110001111111100\n",
"5\n10110011011\n0100\n11110\n001\n0110\n",
"1\n1010001101011101110111100011011111111110001111110111101011111111111100000111111101111110001111111100\n",
"5\n11110011011\n0100\n11110\n001\n0110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100000111111101111110001111111100\n",
"5\n11110011011\n0100\n11010\n001\n0110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100000111111101101110001111111100\n",
"5\n11010011011\n0100\n11010\n001\n0110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100010111111101101110001111111100\n",
"5\n11010011111\n0100\n11010\n001\n0110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100010110111101101110001111111100\n",
"5\n11010011111\n0100\n11010\n001\n1110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100010110111101101110101111111100\n",
"5\n11010011111\n0100\n10010\n001\n1110\n",
"1\n1010001101011101110111100011011101111110001111110111101011111111111100010110111101101010101111111100\n",
"5\n11010011111\n0100\n10000\n001\n1110\n",
"1\n1010001101011101110111100011011101111110001111111111101011111111111100010110111101101010101111111100\n",
"5\n11010011111\n0100\n10000\n001\n1111\n",
"1\n1010001101011101110111100011011101111111001111111111101011111111111100010110111101101010101111111100\n",
"5\n11010011111\n0100\n10100\n001\n1111\n",
"1\n1010001101011101110111100011011101110111001111111111101011111111111100010110111101101010101111111100\n",
"5\n11010011111\n0101\n10100\n001\n1111\n",
"1\n1010001101011101110111100011011101110111001111111111101011111111111100110110111101101010101111111100\n",
"5\n11010011111\n0101\n10110\n001\n1111\n",
"1\n1010001101011101010111100011011101110111001111111111101011111111111100110110111101101010101111111100\n",
"5\n11010011011\n0101\n10110\n001\n1111\n",
"1\n1010001101011101010111100011011101110111001111111111101011111111111100111110111101101010101111111100\n",
"5\n11010011011\n0101\n10110\n011\n1111\n",
"1\n1010001101011101010111100011011101110111001111111111111011111111111100111110111101101010101111111100\n",
"5\n11010011011\n0101\n10100\n011\n1111\n",
"1\n1010001101011101010111100011011101110111001111111111111011111111111110111110111101101010101111111100\n",
"5\n11010011011\n0101\n10100\n011\n0111\n",
"1\n1010001101011101010111100011011101110111001111111111110011111111111110111110111101101010101111111100\n",
"5\n11010011011\n0101\n10100\n011\n0110\n",
"1\n1010001101011101010111100001011101110111001111111111110011111111111110111110111101101010101111111100\n",
"5\n11010011011\n0101\n10100\n111\n0110\n",
"1\n1010001101011101010111100001011101110111001110111111110011111111111110111110111101101010101111111100\n",
"5\n11010011011\n0111\n10100\n111\n0110\n",
"1\n1010001101011101010111100001011101110111001110111111110011111111110110111110111101101010101111111100\n",
"5\n11010011011\n1111\n10100\n111\n0110\n",
"1\n0010001101011101010111100001011101110111001110111111110011111111110110111110111101101010101111111100\n",
"5\n10010011011\n1111\n10100\n111\n0110\n",
"1\n0010001101011101010111100011011101110111001110111111110011111111110110111110111101101010101111111100\n",
"5\n10010011011\n1111\n10100\n111\n1110\n",
"1\n0010001101011101010111100011011101110111001110111111110011111111110110111110111100101010101111111100\n",
"5\n10010011011\n1011\n10100\n111\n1110\n",
"1\n0010001101011101010011100011011101110111001110111111110011111111110110111110111100101010101111111100\n",
"5\n10010011011\n1011\n10100\n111\n1010\n",
"1\n0010001101011101010011100011011101110111001110111111110011111111110110111110101100101010101111111100\n",
"1\n0010001101011101010011100010011101110111001110111111110011111111110110111110101100101010101111111100\n",
"5\n10010011011\n1011\n11100\n011\n1010\n",
"1\n0010001101011101010011100110011101110111001110111111110011111111110110111110101100101010101111111100\n",
"5\n10010011011\n1011\n11100\n010\n1010\n",
"1\n0010001101011101010011100110011101110111001110111111110011111111110110111110101100101010101111111000\n",
"5\n10010011011\n1011\n11100\n000\n1010\n",
"1\n0010001101011101010011100110011101110110001110111111110011111111110110111110101100101010101111111000\n",
"5\n10010011011\n1011\n11100\n100\n1010\n",
"1\n0010001101011101010011100110011101110110001110111111110011111011110110111110101100101010101111111000\n",
"5\n10010011011\n1011\n11100\n100\n0010\n",
"1\n0010001101011101010011100110011101110110001110111111111011111011110110111110101100101010101111111000\n",
"5\n10000011011\n1011\n11100\n100\n0010\n",
"1\n0010001101011101010011100110011101110110001110111111111011111011110110111110101100101011101111111000\n",
"5\n10000011010\n1011\n11100\n100\n0010\n",
"1\n0010001100011101010011100110011101110110001110111111111011111011110110111110101100101011101111111000\n",
"5\n10000011010\n1011\n11100\n100\n0011\n",
"1\n0010001100011101010011100110011101110110001110111111111011111011110111111110101100101011101111111000\n",
"5\n10000011010\n1011\n11101\n100\n0011\n",
"1\n0010001100011101010011100110011101110110001110111111111011111011110111111110101100101011101111111001\n",
"5\n10000011010\n1011\n11101\n101\n0011\n",
"1\n0010001100010101010011100110011101110110001110111111111011111011110111111110101100101011101111111001\n",
"5\n10000011010\n0011\n11101\n101\n0011\n",
"1\n0010001100010101010011100110011101110110001110111111111011111011110111111110101100101011101101111001\n",
"5\n10000011000\n0011\n11101\n101\n0011\n",
"1\n0010001100010101010011100110011101110110001110111111111011111011110111111110101100101011101101110001\n",
"5\n10000011000\n0011\n11101\n101\n0001\n",
"1\n0010001100010101010011100110011101110110001110111111111011111011110111111110101100001011101101110001\n",
"5\n10000011000\n0011\n11101\n111\n0001\n",
"1\n0010001100010101010011100110011101110110001110111111111011111011110111110110101100001011101101110001\n",
"5\n10000011010\n0011\n11101\n111\n0001\n",
"1\n0010001100010101010011100110011101110110000110111111111011111011110111110110101100001011101101110001\n",
"5\n10000011010\n0011\n11101\n111\n0000\n",
"1\n0010001100010101010011100110011101111110000110111111111011111011110111110110101100001011101101110001\n",
"5\n10000011000\n0011\n11101\n111\n0000\n",
"1\n0010001100010101010011100110011101111110000110111111111011111001110111110110101100001011101101110001\n",
"5\n10000011000\n0011\n11101\n111\n1000\n",
"1\n0010001100010101010011100110011101111110001110111111111011111001110111110110101100001011101101110001\n",
"5\n10000011000\n1011\n11101\n111\n1000\n",
"1\n0010001100010101010011100110011101111110001110111111111011111001110110110110101100001011101101110001\n",
"5\n10000011010\n1011\n11101\n111\n1000\n",
"1\n0010001100010101010011100110111101111110001110111111111011111001110110110110101100001011101101110001\n",
"1\n0010001100010101010011100110111101111110001110111111111011111001110110110110101101001011101101110001\n",
"5\n10000011000\n1011\n11001\n101\n1000\n",
"1\n0010001100010101010011100110111101111110001110111111111011111001110110110110101101000011101101110001\n",
"5\n10000011000\n1011\n10001\n101\n1000\n",
"1\n0010001100010101010011100110111101111110001110111111111001111001110110110110101101000011101101110001\n",
"5\n10000011000\n1011\n10011\n101\n1000\n",
"1\n0011001100010101010011100110111101111110001110111111111001111001110110110110101101000011101101110001\n",
"5\n11000011000\n1011\n10011\n101\n1000\n",
"1\n0011001100010101010011100110111101111110001110111111111001011001110110110110101101000011101101110001\n",
"5\n11000011000\n1011\n00011\n101\n1000\n",
"1\n0011001100010101010011100110111101011110001110111111111001011001110110110110101101000011101101110001\n",
"5\n11000011000\n1011\n00011\n001\n1000\n",
"1\n0011001100010101010011100110111101011110001110111111011001011001110110110110101101000011101101110001\n",
"5\n11000011000\n1011\n00011\n000\n1000\n",
"1\n0011001100010101010011100110111101011110001110111111011001011001110110110110101001000011101101110001\n",
"5\n11000011100\n1011\n00011\n000\n1000\n",
"1\n0011001100010101010011100110111101011110001110101111011001011001110110110110101001000011101101110001\n",
"5\n11000011100\n1001\n00011\n000\n1000\n",
"1\n0011001100010101010011100110111101011110001110101111011001011101110110110110101001000011101101110001\n",
"5\n11000011100\n0001\n00011\n000\n1000\n",
"1\n0011001100010101010011100110111111011110001110101111011001011101110110110110101001000011101101110001\n",
"5\n11000011110\n0001\n00011\n000\n1000\n",
"1\n0011001100010101010011100110111111011010001110101111011001011101110110110110101001000011101101110001\n",
"5\n11000011110\n0001\n00011\n000\n1001\n",
"1\n0011001100010101010011100110111111011010001110001111011001011101110110110110101001000011101101110001\n",
"5\n11000011110\n0001\n00011\n001\n1001\n",
"1\n0011001100010101010011100110111111001010001110001111011001011101110110110110101001000011101101110001\n",
"5\n11000011110\n0001\n00011\n000\n1101\n",
"1\n0011001100010101010011100110111111001010001110001111011001011101110110110110101101000011101101110001\n",
"5\n11000011110\n0001\n00011\n000\n0101\n",
"1\n0011001100010101010011100110111111001010001110001111011001011101110110110110101100000011101101110001\n",
"5\n11000011110\n0001\n00011\n000\n0001\n",
"1\n0011001100010100010011100110111111001010001110001111011001011101110110110110101100000011101101110001\n",
"5\n11000011110\n0001\n00001\n000\n0001\n",
"1\n0011001100010100010011100110111111001010001111001111011001011101110110110110101100000011101101110001\n",
"5\n11000011110\n0011\n00001\n000\n0001\n"
],
"output": [
"\nYES\nYES\nYES\nYES\nNO\n",
"YES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"YES\nYES\nYES\nYES\nNO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\nYES\nYES\nYES\nNO\n",
"YES\nYES\nNO\nYES\nNO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\nYES\nNO\nYES\nYES\n",
"NO\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nNO\n",
"NO\n",
"YES\nYES\nYES\nYES\nNO\n",
"NO\n",
"YES\nYES\nYES\nYES\nNO\n",
"NO\n",
"NO\n",
"YES\nYES\nNO\nYES\nNO\n",
"NO\n",
"YES\nYES\nYES\nYES\nNO\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nNO\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\nYES\nYES\nYES\nYES\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a string s, consisting only of characters '0' or '1'. Let |s| be the length of s.
You are asked to choose some integer k (k > 0) and find a sequence a of length k such that:
* 1 ≤ a_1 < a_2 < ... < a_k ≤ |s|;
* a_{i-1} + 1 < a_i for all i from 2 to k.
The characters at positions a_1, a_2, ..., a_k are removed, the remaining characters are concatenated without changing the order. So, in other words, the positions in the sequence a should not be adjacent.
Let the resulting string be s'. s' is called sorted if for all i from 2 to |s'| s'_{i-1} ≤ s'_i.
Does there exist such a sequence a that the resulting string s' is sorted?
Input
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.
Then the descriptions of t testcases follow.
The only line of each testcase contains a string s (2 ≤ |s| ≤ 100). Each character is either '0' or '1'.
Output
For each testcase print "YES" if there exists a sequence a such that removing the characters at positions a_1, a_2, ..., a_k and concatenating the parts without changing the order produces a sorted string.
Otherwise, print "NO".
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).
Example
Input
5
10101011011
0000
11111
110
1100
Output
YES
YES
YES
YES
NO
Note
In the first testcase you can choose a sequence a=[1,3,6,9]. Removing the underlined letters from "10101011011" will produce a string "0011111", which is sorted.
In the second and the third testcases the sequences are already sorted.
In the fourth testcase you can choose a sequence a=[3]. s'= "11", which is sorted.
In the fifth testcase there is no way to choose a sequence a such that s' is sorted.
### Input:
5
10101011011
0000
11111
110
1100
### Output:
YES
YES
YES
YES
NO
### Input:
9
11
11
11
11
11
11
11
11
11
### Output:
YES
YES
YES
YES
YES
YES
YES
YES
YES
### Code:
for q in range(int(input())):
n=input()
s=0
s1=0
p=0
l=len(n)
for i in range(l-1,0,-1):
if(n[i]=='0' and n[i-1]=='0' ):
s=1
p=i-1
break
for i in range(p,0,-1):
if(n[i]=='1' and n[i-1]=='1'):
s1=1
break
if(s1==1):
print("NO")
else:
print("YES")
|
1520_G. To Go Or Not To Go?_28602
|
Dima overslept the alarm clock, which was supposed to raise him to school.
Dima wonders if he will have time to come to the first lesson. To do this, he needs to know the minimum time it will take him to get from home to school.
The city where Dima lives is a rectangular field of n × m size. Each cell (i, j) on this field is denoted by one number a_{ij}:
* The number -1 means that the passage through the cell is prohibited;
* The number 0 means that the cell is free and Dima can walk though it.
* The number x (1 ≤ x ≤ 10^9) means that the cell contains a portal with a cost of x. A cell with a portal is also considered free.
From any portal, Dima can go to any other portal, while the time of moving from the portal (i, j) to the portal (x, y) corresponds to the sum of their costs a_{ij} + a_{xy}.
In addition to moving between portals, Dima can also move between unoccupied cells adjacent to one side in time w. In particular, he can enter a cell with a portal and not use it.
Initially, Dima is in the upper-left cell (1, 1), and the school is in the lower right cell (n, m).
Input
The first line contains three integers n, m and w (2 ≤ n, m ≤ 2 ⋅ 10^3, 1 ≤ w ≤ 10^9), where n and m are city size, w is time during which Dima moves between unoccupied cells.
The next n lines each contain m numbers (-1 ≤ a_{ij} ≤ 10^9) — descriptions of cells.
It is guaranteed that the cells (1, 1) and (n, m) are free.
Output
Output the minimum time it will take for Dima to get to school. If he cannot get to school at all, then output "-1".
Example
Input
5 5 1
0 -1 0 1 -1
0 20 0 0 -1
-1 -1 -1 -1 -1
3 0 0 0 0
-1 0 0 0 0
Output
14
Note
Explanation for the first sample:
<image>
|
#!/usr/bin/env python3
import io
import os
from collections import deque
# input = sys.stdin.readline # to read input quickly
from math import inf
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# available on Google, AtCoder Python3, not available on Codeforces
# import numpy as np
# import scipy
M9 = 10**9 + 7 # 998244353
yes, no = "YES", "NO"
d4 = [(1,0),(0,1),(-1,0),(0,-1)]
# d8 = [(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)]
# d6 = [(2,0),(1,1),(-1,1),(-2,0),(-1,-1),(1,-1)] # hexagonal layout
MAXINT = inf
# ---------------------------- template ends here ----------------------------
def solve_(mrr, w, nrows, ncols):
# your solution here
size = nrows*ncols
def dfs(source, size):
# start from zero
stack = deque([source])
dist = [MAXINT]*size
dist[source] = 0
while stack:
loc = stack.popleft()
x,y = divmod(loc, ncols)
for dx,dy in d4:
xx = x+dx
yy = y+dy
new_loc = xx*ncols+yy
if 0 <= xx < nrows and 0 <= yy < ncols and dist[new_loc] == MAXINT and mrr[new_loc] >= 0:
dist[new_loc] = dist[loc] + 1
stack.append(new_loc)
return dist
dist_from_start = dfs(0, size)
dist_from_dest = dfs(size-1, size)
# log(dist_from_start)
# log(dist_from_dest)
tele_from_start = inf
tele_from_dest = inf
for x in range(nrows):
for y in range(ncols):
loc = x*ncols + y
if mrr[loc] > 0:
tele_from_start = min(tele_from_start, mrr[loc] + w * dist_from_start[loc])
tele_from_dest = min(tele_from_dest, mrr[loc] + w * dist_from_dest[loc])
minres = min(dist_from_start[size-1]*w, tele_from_start+tele_from_dest)
if minres == inf:
return -1
return minres
for case_num in [0]: # no loop over test case
# read one line and parse each word as an integer
n,m,w = list(map(int,input().split()))
# lst = list(map(int,input().split()))
# lst = minus_one(lst)
w = float(w)
# read multiple rows
# arr = read_strings(k) # and return as a list of str
mrr = [float(x) for i in range(n) for x in input().split()]
# mrr = read_matrix(n) # and return as a list of list of int
# mrr = minus_one_matrix(mrr)
res = solve_(mrr, w, n, m) # include input here
print(int(res))
|
{
"input": [
"5 5 1\n0 -1 0 1 -1\n0 20 0 0 -1\n-1 -1 -1 -1 -1\n3 0 0 0 0\n-1 0 0 0 0\n",
"2 3 1000000000\n0 0 0\n0 0 0\n",
"10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 0 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n8 4\n0 0\n0 0\n-1 0\n0 0\n0 0\n0 0\n4 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 0 0\n0 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 10 0 0\n",
"10 9 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n-1 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -1 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 0 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 0 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 3\n",
"10 2 2\n0 0\n0 0\n0 -1\n0 10\n-1 3\n0 0\n0 0\n0 0\n0 0\n0 0\n",
"2 5 1\n0 0 0 0 0\n0 0 0 0 0\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 0 0 -1\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 -1\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n0 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 8 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n1 0 0 1\n-1 0 0 -1\n0 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n4 4\n0 0\n0 0\n-1 0\n0 0\n0 0\n0 0\n4 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 0 0\n-1 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 10 0 0\n",
"10 9 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -1 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 0 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 -1 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 3\n",
"2 5 1\n0 -1 0 0 0\n0 0 0 0 0\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 0 0 -1\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 0\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 0 1 0 0 0\n0 0 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 8 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 5 1\n0 3 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 1 10\n0 0 0 0 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n0 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 1\n0 1 -1 0 0 0\n1 0 0 0 -1 0\n",
"10 5 3\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 1 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"5 5 1\n0 -1 0 2 -1\n0 20 0 0 -1\n-1 -1 -1 -1 -1\n3 0 0 0 0\n-1 0 0 0 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 2 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n-1 0 0 2 10\n0 0 0 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 1\n",
"10 4 4\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 1 0 -1\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 -1\n0 0 0 0 1 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 4 4\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 2 0\n0 -1 0 0\n",
"10 4 8\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n1 0 1 1\n-1 0 0 -1\n0 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"5 5 1\n0 -1 -1 1 -1\n0 20 0 0 -1\n-1 -1 -1 -1 -1\n3 0 0 0 0\n-1 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 0\n4 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 0 0\n-1 0 -1 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 10 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -1 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 1 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 -1 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 3\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 0 0 -2\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 0\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n0 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"5 5 1\n0 -1 -1 1 -1\n0 20 0 0 -1\n-1 -1 -1 -1 -1\n3 0 0 0 0\n-1 -1 0 0 0\n",
"10 5 2\n0 3 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 17\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 0\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 1 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 -1 0 0\n0 0 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n0 0 0 0 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 2 2\n0 -1\n-1 17\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 0\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 0 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n-1 17\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 0 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 2 2\n0 -1\n-1 12\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n1 0 0 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 1 10\n0 0 0 0 0\n",
"10 1 2\n0 -1\n-1 12\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n1 0 -1 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n-1 0 0 1 10\n0 0 0 0 0\n",
"10 1 2\n0 -1\n-1 12\n6 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -2\n0 10 0 0 0 0 0 0\n1 0 -1 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 -1\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 -1\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 1\n0 -1 0 2 -1\n-1 0 0 1 10\n0 0 0 0 0\n",
"10 1 2\n0 0\n-1 12\n6 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 4 2\n0 0 0 -1\n0 0 0 -1\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 10\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 0\n0 1 -1 0 0 0\n1 0 0 0 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 -1 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 -1 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 1\n0 1 -1 0 0 0\n1 0 0 0 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n-1 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 1 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 0\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n-1 1 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 0\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 1\n0 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n-1 1 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 1\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 3 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 0 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n8 4\n0 0\n-1 0\n-1 0\n0 0\n0 0\n0 0\n4 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 0 0\n0 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 10 1 0\n",
"10 9 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n-1 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -1 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 1 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 0 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 0 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-2 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 2 2\n0 0\n0 0\n0 -1\n0 10\n-1 3\n0 0\n0 0\n0 0\n0 0\n0 1\n",
"2 5 1\n0 0 0 0 0\n0 0 0 1 0\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 1 0 -1\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 -1\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 -1\n0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 1 0 -1 0 -1\n0 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 8 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 1 0 0\n-1 0 0 -1\n1 0 0 1\n-1 0 0 -1\n0 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 3 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n4 4\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n4 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 1 0\n-1 0 0 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 10 0 0\n",
"10 7 2\n0 0 -1 0 0 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 -1 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 1 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 -1 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 3\n",
"10 6 2\n0 0 0 0 -1 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 0 0 -1\n0 0 -1 0 0 0\n-1 0 0 0 -1 0\n0 -1 0 0 0 0\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 0 1 0 0 0\n0 0 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 1 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 1\n0 -1 8 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n-1 0 0 -1\n1 0 1 1\n-1 0 0 -1\n0 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"5 5 1\n0 -1 -1 1 -1\n0 20 0 0 -1\n-1 -1 -1 0 -1\n3 0 0 0 0\n-1 0 0 0 0\n",
"10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 -1 0 0 0\n",
"10 4 2\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 7 9 0\n0 0 0 0\n-1 0 -1 0\n0 0 -1 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 0 0 -1 0\n0 0 0 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 1 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 0 0 0 -1 0 0\n0 -1 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 0 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 -1 0 0\n0 0 0 0 0 0\n0 0 0 0 0 3\n",
"10 6 2\n0 0 0 0 0 0\n10 0 -1 0 0 0\n0 0 -1 0 0 0\n0 0 -1 0 0 -2\n0 0 -1 0 0 0\n-1 0 0 0 0 0\n0 -1 0 0 0 0\n0 0 0 0 0 0\n-1 -1 0 0 -1 -1\n0 -1 -1 0 0 0\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 -1 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 -1 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n0 0 1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 2 2\n0 -1\n0 17\n4 4\n-1 0\n0 0\n-1 0\n0 0\n-1 0\n0 0\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -2 0 -1 0\n0 0 -1 0 -1 0 0 0 0\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 7 2\n0 0 -1 0 1 0 0\n0 0 0 0 0 0 0\n0 0 0 -1 0 0 0\n-1 -1 0 0 -1 0 0\n0 0 0 0 -1 0 0\n-1 0 0 0 0 0 0\n0 0 0 0 -1 0 0\n-1 0 0 0 0 -1 0\n0 0 0 0 0 0 0\n0 0 0 0 0 0 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n-1 0 0 0 0 0\n0 0 -1 0 0 0\n0 0 0 0 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 1 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 0 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 12 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 -1 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 0 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 3 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 3 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n-1 17\n4 4\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 1 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 0 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 0 0 -1\n9 0 0 0 0 -1\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 0 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 0\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 0\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 -1 0 0\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 1 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 -1 -2 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 -1 0 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 -1 0 0\n0 0 0 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -1 8 0 0 -1 1\n-1 -1 -1 -1 0 -1 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 4 2\n0 1 0 -1\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 1 0 8\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 1 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n-1 12\n4 4\n0 0\n0 0\n-1 0\n0 -1\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -1 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 1 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 0 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n1 0 0 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n-1 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 1 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -2 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 0\n0 0 0 0\n-1 0 0 -1\n1 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 0 0\n0 -1 0 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 10\n0 0 5 6 0\n0 -1 0 2 -1\n0 0 0 1 10\n0 0 0 0 0\n",
"10 1 2\n0 -1\n-1 12\n4 4\n0 0\n0 0\n-1 0\n0 0\n0 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 0 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -1 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 0 0 0\n1 0 0 -1 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -1\n0 10 0 0 0 0 0 0\n1 0 -1 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 1 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n-1 6 0 0 -1 -1 0 0\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 -1 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 1 2\n0 -1\n-1 12\n6 4\n0 0\n-1 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 0\n-1 -1 -1 0 0 0 -1 -1 -1\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 0\n0 0 0 1 0 0\n1 -1 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 8 2\n0 0 0 -1 3 0 2 -2\n1 10 0 0 0 0 0 0\n1 0 -1 -1 0 0 0 0\n0 0 0 -1 0 0 0 0\n0 1 0 -1 0 0 0 0\n0 0 -1 0 0 -1 -1 0\n0 0 0 0 -1 -1 0 0\n-1 0 0 0 1 0 0 0\n7 -1 0 2 0 0 0 0\n0 7 0 0 0 0 0 0\n",
"10 8 2\n0 0 0 0 0 -1 0 -1\n-1 0 0 0 0 0 0 -1\n-1 -1 -1 -1 0 -1 0 0\n0 6 0 0 -1 -1 0 -1\n-1 -1 0 0 0 0 0 0\n-1 0 -1 0 8 0 0 0\n0 0 -2 8 0 0 -1 1\n-1 -1 -1 -1 0 0 1 0\n0 -1 5 -1 0 0 0 9\n0 0 0 0 -1 -1 -1 0\n",
"10 5 1\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 -1 0 0 8\n0 0 5 6 1\n0 -1 0 2 -1\n-1 0 0 1 10\n0 0 0 0 0\n",
"10 1 2\n0 0\n-1 12\n6 7\n0 0\n0 0\n-1 0\n0 0\n-1 0\n0 -1\n4 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n-1 0 -1 -1 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 0 0 -1\n0 0 0 0\n0 0 0 -1\n0 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 5 1\n0 2 1 -1 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 10\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 0 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-2 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 2 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 0\n0 1 -1 0 0 0\n1 0 0 0 -1 3\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n1 0 1 1\n-1 0 0 -1\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 0 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 -1 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 -1 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 0\n0 1 -1 0 0 0\n1 0 0 0 -1 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 2\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 1 -1\n-1 -1 -1 0 -2 -1 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 1 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 0 0 1 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 1\n0 1 -1 0 0 0\n1 0 0 0 -1 0\n",
"10 4 4\n0 0 0 -1\n0 -1 0 -1\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n0 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 -1 0 0\n0 1 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 -1 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -1 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -2 0\n-1 0 0 0 -1 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 6 2\n0 0 0 1 0 0\n-1 -1 0 1 0 -1\n9 0 0 0 0 0\n0 0 0 1 0 -1\n0 -1 0 1 0 0\n1 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 -1 1\n0 1 0 0 0 0\n1 0 0 0 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 0\n0 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 0\n0 1 0 0 1\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 2 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 -1\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 0 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 1 -1\n0 -1 0 -1\n-1 0 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n0 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 2\n0 2 1 0 0\n0 0 0 0 -1\n0 1 0 0 0\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 1 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 1 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 0\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 1\n-1 -1 -1 0 0 0 -1 -1 0\n",
"10 4 2\n0 0 0 -1\n0 -1 0 -1\n-1 1 0 0\n-1 0 0 -1\n0 -1 1 1\n-1 0 0 0\n-1 0 -1 0\n-1 0 0 0\n-1 -1 1 0\n-1 -1 0 0\n",
"10 5 3\n0 4 1 0 0\n0 0 0 0 0\n0 1 0 0 0\n-1 0 0 0 1\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 1 1\n0 -1 0 1 -1\n-1 0 0 1 3\n0 0 0 0 0\n",
"10 8 2\n0 -1 0 -1 -1 0 0 -1 -1\n0 0 -1 0 -1 -1 -1 0 -1\n-1 -1 -1 0 -2 -2 1 0 0\n0 0 0 0 -1 0 0 0 0\n0 -1 -1 0 -1 -1 -1 0 0\n-1 0 -1 0 -2 -2 0 -1 0\n0 0 0 0 -1 0 0 0 -1\n0 0 -1 0 -1 0 0 -1 0\n-1 0 0 0 -1 -1 -1 2 0\n0 -1 -1 0 0 0 -1 -1 0\n",
"10 5 2\n0 3 1 0 0\n0 0 1 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 0 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"10 2 2\n0 -1\n0 10\n8 4\n0 0\n-1 0\n-1 0\n0 0\n-1 0\n0 0\n4 0\n"
],
"output": [
"\n14",
"3000000000",
"16",
"16",
"24",
"-1",
"30",
"10",
"20",
"5",
"28",
"25",
"32",
"24",
"16\n",
"14\n",
"24\n",
"-1\n",
"30\n",
"10\n",
"5\n",
"28\n",
"25\n",
"32\n",
"13\n",
"22\n",
"8\n",
"20\n",
"6\n",
"18\n",
"9\n",
"12\n",
"11\n",
"15\n",
"19\n",
"7\n",
"4\n",
"34\n",
"23\n",
"35\n",
"66\n",
"24\n",
"14\n",
"14\n",
"24\n",
"-1\n",
"30\n",
"10\n",
"28\n",
"32\n",
"24\n",
"14\n",
"13\n",
"14\n",
"-1\n",
"30\n",
"10\n",
"22\n",
"32\n",
"24\n",
"-1\n",
"-1\n",
"10\n",
"22\n",
"24\n",
"8\n",
"-1\n",
"-1\n",
"10\n",
"22\n",
"20\n",
"24\n",
"-1\n",
"-1\n",
"10\n",
"16\n",
"20\n",
"24\n",
"6\n",
"-1\n",
"-1\n",
"10\n",
"16\n",
"32\n",
"6\n",
"-1\n",
"-1\n",
"10\n",
"16\n",
"32\n",
"18\n",
"6\n",
"-1\n",
"-1\n",
"10\n",
"18\n",
"6\n",
"-1\n",
"10\n",
"18\n",
"6\n",
"-1\n",
"22\n",
"18\n",
"-1\n",
"18\n",
"9\n",
"-1\n",
"12\n",
"18\n",
"9\n",
"-1\n",
"18\n",
"9\n",
"-1\n",
"16\n",
"-1\n",
"16\n",
"16\n",
"16\n",
"18\n",
"-1\n",
"30\n",
"14\n",
"5\n",
"28\n",
"25\n",
"14\n",
"22\n",
"16\n",
"14\n",
"24\n",
"30\n",
"10\n",
"28\n",
"25\n",
"32\n",
"24\n",
"8\n",
"13\n",
"24\n",
"-1\n",
"30\n",
"10\n",
"28\n",
"22\n",
"32\n",
"22\n",
"14\n",
"-1\n",
"30\n",
"10\n",
"18\n",
"32\n",
"24\n",
"9\n",
"-1\n",
"-1\n",
"10\n",
"20\n",
"20\n",
"24\n",
"8\n",
"-1\n",
"10\n",
"22\n",
"20\n",
"20\n",
"6\n",
"-1\n",
"-1\n",
"10\n",
"16\n",
"20\n",
"24\n",
"6\n",
"-1\n",
"-1\n",
"10\n",
"16\n",
"32\n",
"-1\n",
"-1\n",
"10\n",
"14\n",
"32\n",
"6\n",
"-1\n",
"-1\n",
"18\n",
"6\n",
"-1\n",
"10\n",
"18\n",
"-1\n",
"22\n",
"9\n",
"-1\n",
"12\n",
"34\n",
"9\n",
"-1\n",
"12\n",
"18\n",
"9\n",
"-1\n",
"10\n",
"9\n",
"-1\n",
"16\n",
"13\n",
"-1\n",
"16\n",
"16\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Dima overslept the alarm clock, which was supposed to raise him to school.
Dima wonders if he will have time to come to the first lesson. To do this, he needs to know the minimum time it will take him to get from home to school.
The city where Dima lives is a rectangular field of n × m size. Each cell (i, j) on this field is denoted by one number a_{ij}:
* The number -1 means that the passage through the cell is prohibited;
* The number 0 means that the cell is free and Dima can walk though it.
* The number x (1 ≤ x ≤ 10^9) means that the cell contains a portal with a cost of x. A cell with a portal is also considered free.
From any portal, Dima can go to any other portal, while the time of moving from the portal (i, j) to the portal (x, y) corresponds to the sum of their costs a_{ij} + a_{xy}.
In addition to moving between portals, Dima can also move between unoccupied cells adjacent to one side in time w. In particular, he can enter a cell with a portal and not use it.
Initially, Dima is in the upper-left cell (1, 1), and the school is in the lower right cell (n, m).
Input
The first line contains three integers n, m and w (2 ≤ n, m ≤ 2 ⋅ 10^3, 1 ≤ w ≤ 10^9), where n and m are city size, w is time during which Dima moves between unoccupied cells.
The next n lines each contain m numbers (-1 ≤ a_{ij} ≤ 10^9) — descriptions of cells.
It is guaranteed that the cells (1, 1) and (n, m) are free.
Output
Output the minimum time it will take for Dima to get to school. If he cannot get to school at all, then output "-1".
Example
Input
5 5 1
0 -1 0 1 -1
0 20 0 0 -1
-1 -1 -1 -1 -1
3 0 0 0 0
-1 0 0 0 0
Output
14
Note
Explanation for the first sample:
<image>
### Input:
5 5 1
0 -1 0 1 -1
0 20 0 0 -1
-1 -1 -1 -1 -1
3 0 0 0 0
-1 0 0 0 0
### Output:
14
### Input:
2 3 1000000000
0 0 0
0 0 0
### Output:
3000000000
### Code:
#!/usr/bin/env python3
import io
import os
from collections import deque
# input = sys.stdin.readline # to read input quickly
from math import inf
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# available on Google, AtCoder Python3, not available on Codeforces
# import numpy as np
# import scipy
M9 = 10**9 + 7 # 998244353
yes, no = "YES", "NO"
d4 = [(1,0),(0,1),(-1,0),(0,-1)]
# d8 = [(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)]
# d6 = [(2,0),(1,1),(-1,1),(-2,0),(-1,-1),(1,-1)] # hexagonal layout
MAXINT = inf
# ---------------------------- template ends here ----------------------------
def solve_(mrr, w, nrows, ncols):
# your solution here
size = nrows*ncols
def dfs(source, size):
# start from zero
stack = deque([source])
dist = [MAXINT]*size
dist[source] = 0
while stack:
loc = stack.popleft()
x,y = divmod(loc, ncols)
for dx,dy in d4:
xx = x+dx
yy = y+dy
new_loc = xx*ncols+yy
if 0 <= xx < nrows and 0 <= yy < ncols and dist[new_loc] == MAXINT and mrr[new_loc] >= 0:
dist[new_loc] = dist[loc] + 1
stack.append(new_loc)
return dist
dist_from_start = dfs(0, size)
dist_from_dest = dfs(size-1, size)
# log(dist_from_start)
# log(dist_from_dest)
tele_from_start = inf
tele_from_dest = inf
for x in range(nrows):
for y in range(ncols):
loc = x*ncols + y
if mrr[loc] > 0:
tele_from_start = min(tele_from_start, mrr[loc] + w * dist_from_start[loc])
tele_from_dest = min(tele_from_dest, mrr[loc] + w * dist_from_dest[loc])
minres = min(dist_from_start[size-1]*w, tele_from_start+tele_from_dest)
if minres == inf:
return -1
return minres
for case_num in [0]: # no loop over test case
# read one line and parse each word as an integer
n,m,w = list(map(int,input().split()))
# lst = list(map(int,input().split()))
# lst = minus_one(lst)
w = float(w)
# read multiple rows
# arr = read_strings(k) # and return as a list of str
mrr = [float(x) for i in range(n) for x in input().split()]
# mrr = read_matrix(n) # and return as a list of list of int
# mrr = minus_one_matrix(mrr)
res = solve_(mrr, w, n, m) # include input here
print(int(res))
|
176_C. Playing with Superglue_28607
|
Two players play a game. The game is played on a rectangular board with n × m squares. At the beginning of the game two different squares of the board have two chips. The first player's goal is to shift the chips to the same square. The second player aims to stop the first one with a tube of superglue.
We'll describe the rules of the game in more detail.
The players move in turns. The first player begins.
With every move the first player chooses one of his unglued chips, and shifts it one square to the left, to the right, up or down. It is not allowed to move a chip beyond the board edge. At the beginning of a turn some squares of the board may be covered with a glue. The first player can move the chip to such square, in this case the chip gets tightly glued and cannot move any longer.
At each move the second player selects one of the free squares (which do not contain a chip or a glue) and covers it with superglue. The glue dries long and squares covered with it remain sticky up to the end of the game.
If, after some move of the first player both chips are in the same square, then the first player wins. If the first player cannot make a move (both of his chips are glued), then the second player wins. Note that the situation where the second player cannot make a move is impossible — he can always spread the glue on the square from which the first player has just moved the chip.
We will further clarify the case where both chips are glued and are in the same square. In this case the first player wins as the game ends as soon as both chips are in the same square, and the condition of the loss (the inability to move) does not arise.
You know the board sizes and the positions of the two chips on it. At the beginning of the game all board squares are glue-free. Find out who wins if the players play optimally.
Input
The first line contains six integers n, m, x1, y1, x2, y2 — the board sizes and the coordinates of the first and second chips, correspondingly (1 ≤ n, m ≤ 100; 2 ≤ n × m; 1 ≤ x1, x2 ≤ n; 1 ≤ y1, y2 ≤ m). The numbers in the line are separated by single spaces.
It is guaranteed that the chips are located in different squares.
Output
If the first player wins, print "First" without the quotes. Otherwise, print "Second" without the quotes.
Examples
Input
1 6 1 2 1 6
Output
First
Input
6 5 4 3 2 1
Output
First
Input
10 10 1 1 10 10
Output
Second
|
n,m,X,Y,x,y=map(int,input().split())
a=[abs(X-x),abs(Y-y)]
a.sort()
print("First" if a[1]<5 and a[0]+a[1]<7 else "Second")
# Made By Mostafa_Khaled
|
{
"input": [
"6 5 4 3 2 1\n",
"10 10 1 1 10 10\n",
"1 6 1 2 1 6\n",
"24 32 6 2 7 4\n",
"45 62 28 48 28 50\n",
"100 32 71 12 71 22\n",
"57 85 29 40 29 69\n",
"95 28 50 12 50 13\n",
"5 4 1 1 5 4\n",
"100 100 1 1 100 100\n",
"51 76 50 5 45 76\n",
"37 100 33 13 32 30\n",
"47 91 36 61 32 63\n",
"28 7 17 5 11 6\n",
"1 2 1 1 1 2\n",
"89 51 76 1 25 51\n",
"60 100 28 80 26 85\n",
"5 5 1 1 5 5\n",
"10 10 3 4 3 5\n",
"5 5 1 1 5 3\n",
"61 39 14 30 14 37\n",
"21 18 16 6 15 17\n",
"97 94 96 2 7 93\n",
"50 50 1 1 4 5\n",
"10 10 7 7 3 4\n",
"41 64 10 21 29 50\n",
"8 33 2 21 8 23\n",
"77 99 56 1 3 99\n",
"3 5 1 1 3 5\n",
"30 47 9 32 3 35\n",
"47 95 27 70 23 70\n",
"39 46 21 22 30 35\n",
"48 53 24 37 21 42\n",
"73 95 58 11 11 24\n",
"18 18 11 12 13 16\n",
"10 10 1 1 5 4\n",
"41 34 27 7 20 8\n",
"10 5 10 1 4 5\n",
"73 27 40 8 45 13\n",
"24 97 21 54 19 55\n",
"15 11 12 5 8 9\n",
"5 4 1 4 5 1\n",
"5 5 1 1 4 5\n",
"64 91 52 64 49 67\n",
"76 7 24 4 26 6\n",
"18 72 2 71 3 71\n",
"31 80 28 70 24 75\n",
"10 10 1 1 3 5\n",
"33 13 12 1 12 6\n",
"21 68 2 13 6 57\n",
"11 97 2 29 1 76\n",
"30 85 9 45 8 49\n",
"4 4 1 4 4 1\n",
"10 10 1 1 5 3\n",
"5 5 1 1 5 4\n",
"100 94 1 30 100 30\n",
"89 100 54 1 55 100\n",
"7 41 3 5 3 6\n",
"100 100 1 1 3 5\n",
"44 99 10 5 8 92\n",
"84 43 71 6 77 26\n",
"6 2 6 1 1 2\n",
"48 11 33 8 24 8\n",
"28 14 21 2 20 5\n",
"96 54 9 30 9 47\n",
"50 50 1 1 5 2\n",
"71 85 10 14 13 20\n",
"25 32 17 18 20 19\n",
"50 50 1 1 5 4\n",
"28 17 20 10 27 2\n",
"73 88 30 58 30 62\n",
"24 65 23 18 3 64\n",
"100 100 1 1 5 1\n",
"6 6 1 1 6 1\n",
"13 62 10 13 5 15\n",
"24 68 19 14 18 15\n",
"49 34 38 19 38 25\n",
"57 17 12 7 12 10\n",
"80 97 70 13 68 13\n",
"13 25 4 2 7 3\n",
"34 55 7 25 8 30\n",
"30 1 10 1 20 1\n",
"73 64 63 32 68 32\n",
"73 79 17 42 10 67\n",
"40 100 4 1 30 100\n",
"48 86 31 36 23 36\n",
"4 5 1 1 4 5\n",
"51 8 24 3 19 7\n",
"10 10 1 1 6 2\n",
"64 96 4 2 4 80\n",
"10 10 6 1 1 1\n",
"10 10 1 1 4 5\n",
"35 19 4 8 9 11\n",
"25 68 3 39 20 41\n",
"23 90 6 31 9 88\n",
"52 70 26 65 23 65\n",
"20 77 5 49 3 52\n",
"6 6 1 1 1 6\n",
"63 22 54 16 58 19\n",
"87 15 56 8 59 12\n",
"16 97 7 4 15 94\n",
"10 10 1 1 1 6\n",
"89 81 33 18 28 19\n",
"100 100 1 1 2 6\n",
"100 100 1 1 5 4\n",
"36 76 36 49 33 51\n",
"74 88 33 20 39 20\n",
"99 100 24 1 24 100\n",
"14 96 3 80 1 86\n",
"34 39 18 1 17 7\n",
"5 5 1 1 3 5\n",
"96 75 15 10 6 65\n",
"63 54 19 22 23 23\n",
"5 5 1 5 4 1\n",
"100 100 10 10 13 14\n",
"40 43 40 9 38 28\n",
"100 100 1 1 4 5\n",
"15 48 6 42 10 48\n",
"87 13 77 7 70 7\n",
"20 32 6 2 7 4\n",
"45 62 28 48 28 88\n",
"100 32 71 2 71 22\n",
"111 85 29 40 29 69\n",
"95 28 50 12 39 13\n",
"5 7 1 1 5 4\n",
"000 100 1 1 100 100\n",
"51 76 72 5 45 76\n",
"37 100 33 13 34 30\n",
"47 91 12 61 32 63\n",
"28 7 20 5 11 6\n",
"1 2 1 2 1 2\n",
"89 51 76 1 25 27\n",
"60 101 28 80 26 85\n",
"5 2 1 1 5 5\n",
"10 10 3 2 3 5\n",
"35 39 14 30 14 37\n",
"21 18 29 6 15 17\n",
"97 94 96 2 7 79\n",
"80 50 1 1 4 5\n",
"10 10 7 7 3 8\n",
"41 64 0 21 29 50\n",
"8 33 2 21 14 23\n",
"77 99 61 1 3 99\n",
"17 47 9 32 3 35\n",
"47 95 32 70 23 70\n",
"39 46 21 36 30 35\n",
"48 18 24 37 21 42\n",
"73 95 58 11 18 24\n",
"18 36 11 12 13 16\n",
"10 10 1 2 5 4\n",
"41 61 27 7 20 8\n",
"10 5 16 1 4 5\n",
"73 27 40 8 45 2\n",
"24 97 21 54 19 43\n",
"15 11 12 5 8 2\n",
"5 4 0 4 5 1\n",
"5 5 1 0 4 5\n",
"64 91 52 27 49 67\n",
"76 7 24 4 26 5\n",
"18 72 4 71 3 71\n",
"31 80 20 70 24 75\n",
"10 10 1 1 3 6\n",
"33 23 12 1 12 6\n",
"0 68 2 13 6 57\n",
"11 97 2 29 0 76\n",
"30 85 15 45 8 49\n",
"10 12 1 1 5 3\n",
"5 5 1 1 5 6\n",
"100 94 1 30 101 30\n",
"89 100 93 1 55 100\n",
"7 41 3 2 3 6\n",
"100 100 1 1 3 8\n",
"44 99 16 5 8 92\n",
"84 43 128 6 77 26\n",
"6 2 6 2 1 2\n",
"48 11 33 8 39 8\n",
"22 14 21 2 20 5\n",
"96 54 9 30 2 47\n",
"50 89 1 1 5 2\n",
"71 85 11 14 13 20\n",
"25 32 17 18 16 19\n",
"0 50 1 1 5 4\n",
"28 17 20 10 48 2\n",
"24 65 23 34 3 64\n",
"100 110 1 1 5 1\n",
"6 6 1 0 6 1\n",
"13 62 18 13 5 15\n",
"49 34 38 19 38 1\n",
"57 17 12 7 12 11\n",
"80 97 70 2 68 13\n",
"34 55 7 25 8 19\n",
"30 1 5 1 20 1\n"
],
"output": [
"First\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Two players play a game. The game is played on a rectangular board with n × m squares. At the beginning of the game two different squares of the board have two chips. The first player's goal is to shift the chips to the same square. The second player aims to stop the first one with a tube of superglue.
We'll describe the rules of the game in more detail.
The players move in turns. The first player begins.
With every move the first player chooses one of his unglued chips, and shifts it one square to the left, to the right, up or down. It is not allowed to move a chip beyond the board edge. At the beginning of a turn some squares of the board may be covered with a glue. The first player can move the chip to such square, in this case the chip gets tightly glued and cannot move any longer.
At each move the second player selects one of the free squares (which do not contain a chip or a glue) and covers it with superglue. The glue dries long and squares covered with it remain sticky up to the end of the game.
If, after some move of the first player both chips are in the same square, then the first player wins. If the first player cannot make a move (both of his chips are glued), then the second player wins. Note that the situation where the second player cannot make a move is impossible — he can always spread the glue on the square from which the first player has just moved the chip.
We will further clarify the case where both chips are glued and are in the same square. In this case the first player wins as the game ends as soon as both chips are in the same square, and the condition of the loss (the inability to move) does not arise.
You know the board sizes and the positions of the two chips on it. At the beginning of the game all board squares are glue-free. Find out who wins if the players play optimally.
Input
The first line contains six integers n, m, x1, y1, x2, y2 — the board sizes and the coordinates of the first and second chips, correspondingly (1 ≤ n, m ≤ 100; 2 ≤ n × m; 1 ≤ x1, x2 ≤ n; 1 ≤ y1, y2 ≤ m). The numbers in the line are separated by single spaces.
It is guaranteed that the chips are located in different squares.
Output
If the first player wins, print "First" without the quotes. Otherwise, print "Second" without the quotes.
Examples
Input
1 6 1 2 1 6
Output
First
Input
6 5 4 3 2 1
Output
First
Input
10 10 1 1 10 10
Output
Second
### Input:
6 5 4 3 2 1
### Output:
First
### Input:
10 10 1 1 10 10
### Output:
Second
### Code:
n,m,X,Y,x,y=map(int,input().split())
a=[abs(X-x),abs(Y-y)]
a.sort()
print("First" if a[1]<5 and a[0]+a[1]<7 else "Second")
# Made By Mostafa_Khaled
|
220_A. Little Elephant and Problem_28613
|
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
|
def main():
n = int(input())
arr = list(map(int, input().split()))
copy = arr[:]
copy.sort()
missed = 0
for i in range(n):
if arr[i] != copy[i]:
missed += 1
if missed == 2:
print('YES')
elif missed == 0:
print('YES')
else:
print('NO')
main()
|
{
"input": [
"4\n4 3 2 1\n",
"2\n1 2\n",
"3\n3 2 1\n",
"5\n1 4 3 2 1\n",
"6\n3 4 5 6 7 2\n",
"3\n1 3 2\n",
"50\n6 7 8 4 10 3 2 7 1 3 10 3 4 7 2 3 7 4 10 6 8 10 9 6 5 10 9 6 1 8 9 4 3 7 3 10 5 3 10 1 6 10 6 7 10 7 1 5 9 5\n",
"3\n2 3 1\n",
"5\n1 1 3 2 2\n",
"5\n1 4 5 2 3\n",
"5\n100 5 6 10 7\n",
"5\n1 2 5 3 4\n",
"5\n1 3 2 3 3\n",
"20\n38205814 119727790 127848638 189351562 742927936 284688399 318826601 326499046 387938139 395996609 494453625 551393005 561264192 573569187 600766727 606718722 730549586 261502770 751513115 943272321\n",
"6\n1 2 3 4 5 3\n",
"2\n1 1\n",
"5\n3 3 1 5 4\n",
"5\n1 3 3 2 2\n",
"4\n3 2 2 4\n",
"11\n2 2 2 2 2 2 2 2 2 2 1\n",
"6\n6 1 2 3 4 5\n",
"5\n2 3 4 5 1\n",
"2\n2 1\n",
"6\n1 6 2 4 3 5\n",
"4\n3 2 1 1\n",
"4\n3 3 2 2\n",
"5\n2 2 1 3 3\n",
"4\n3 4 1 2\n",
"4\n1 2 1 2\n",
"5\n4 4 1 1 1\n",
"3\n2 1 1\n",
"5\n1 4 2 2 3\n",
"4\n4 2 1 3\n",
"4\n5 12 12 6\n",
"9\n7 7 8 8 10 10 10 10 1000000000\n",
"6\n2 2 2 2 3 2\n",
"4\n2 1 1 1\n",
"10\n1 2 4 4 4 5 5 7 7 10\n",
"4\n2 4 1 5\n",
"9\n3 3 3 2 2 2 1 1 1\n",
"8\n3 6 6 6 6 6 4 9\n",
"4\n4 1 2 3\n",
"9\n1 2 3 5 4 6 7 8 9\n",
"4\n1000000000 1 1000000000 1\n",
"8\n5 5 5 5 5 5 1 1\n",
"6\n1 4 3 6 2 5\n",
"5\n4 1 1 1 1\n",
"10\n4 4 4 4 10 4 4 4 4 4\n",
"6\n4 5 3 4 2 6\n",
"5\n3 3 3 2 2\n",
"9\n1 8 7 7 7 7 7 8 3\n",
"4\n2 2 2 1\n",
"5\n1 2 1 1 2\n",
"5\n5 1 2 3 4\n",
"11\n1 2 3 4 5 1 2 3 4 5 1\n",
"6\n1 2 3 1 2 3\n",
"3\n3 1 2\n",
"5\n1 2 2 1 2\n",
"4\n2 2 1 1\n",
"7\n3 2 1 2 3 5 4\n",
"100\n3 7 7 8 15 25 26 31 37 41 43 43 46 64 65 82 94 102 102 103 107 124 125 131 140 145 146 150 151 160 160 161 162 165 169 175 182 191 201 211 214 216 218 304 224 229 236 241 244 249 252 269 270 271 273 289 285 295 222 307 312 317 319 319 320 321 325 330 340 341 345 347 354 356 366 366 375 376 380 383 386 398 401 407 414 417 423 426 431 438 440 444 446 454 457 458 458 466 466 472\n",
"5\n1 5 4 4 4\n",
"47\n6 277 329 393 410 432 434 505 529 545 650 896 949 1053 1543 1554 1599 1648 1927 1976 1998 2141 2248 2384 2542 2638 2995 3155 3216 3355 3409 3597 3851 3940 4169 4176 4378 4378 4425 4490 4627 4986 5025 5033 5374 5453 5644\n",
"6\n6 1 2 3 4 2\n",
"5\n1 3 3 3 2\n",
"5\n1 2 7 3 5\n",
"10\n4 5 11 12 13 14 16 16 16 18\n",
"4\n4 4 3 3\n",
"4\n4 5 1 1\n",
"10\n1 2 9 4 5 6 7 8 3 10\n",
"128\n1 2 4 6 8 17 20 20 23 33 43 49 49 49 52 73 74 75 82 84 85 87 90 91 102 103 104 105 111 111 401 142 142 152 155 160 175 176 178 181 183 184 187 188 191 193 326 202 202 214 224 225 236 239 240 243 246 247 249 249 257 257 261 264 265 271 277 281 284 284 286 289 290 296 297 303 305 307 307 317 318 320 322 200 332 342 393 349 350 350 369 375 381 381 385 385 387 393 347 397 398 115 402 407 407 408 410 411 411 416 423 426 429 429 430 440 447 449 463 464 466 471 473 480 480 483 497 503\n",
"5\n1 4 3 3 1\n",
"6\n3 4 5 6 9 2\n",
"3\n0 3 2\n",
"50\n6 7 8 4 10 3 2 7 1 3 10 3 4 7 2 3 7 4 10 6 8 10 9 3 5 10 9 6 1 8 9 4 3 7 3 10 5 3 10 1 6 10 6 7 10 7 1 5 9 5\n",
"3\n2 6 1\n",
"5\n1 1 3 2 1\n",
"5\n1 8 5 2 3\n",
"5\n100 5 9 10 7\n",
"5\n2 2 5 3 4\n",
"5\n2 3 2 3 3\n",
"20\n38205814 119727790 127848638 189351562 1085863511 284688399 318826601 326499046 387938139 395996609 494453625 551393005 561264192 573569187 600766727 606718722 730549586 261502770 751513115 943272321\n",
"6\n1 2 3 4 5 1\n",
"2\n1 0\n",
"5\n3 0 1 5 4\n",
"5\n1 3 3 2 3\n",
"4\n1 2 2 4\n",
"11\n2 2 2 3 2 2 2 2 2 2 1\n",
"6\n6 1 4 3 4 5\n",
"5\n0 3 4 5 1\n",
"2\n2 0\n",
"6\n1 6 2 0 3 5\n",
"4\n6 2 1 1\n",
"4\n3 2 2 2\n",
"5\n2 2 0 3 3\n",
"4\n3 4 0 2\n",
"4\n1 2 1 3\n",
"5\n4 4 2 1 1\n",
"3\n2 2 1\n",
"5\n1 5 2 2 3\n",
"4\n4 4 1 3\n",
"4\n5 12 12 10\n",
"9\n7 7 8 8 10 17 10 10 1000000000\n",
"6\n2 2 2 1 3 2\n",
"4\n2 0 1 1\n",
"10\n1 2 1 4 4 5 5 7 7 10\n",
"4\n4 4 1 5\n",
"9\n3 3 3 1 2 2 1 1 1\n",
"8\n6 6 6 6 6 6 4 9\n",
"4\n4 1 3 3\n",
"9\n1 2 3 5 4 6 7 8 10\n",
"4\n1000000000 0 1000000000 1\n",
"8\n5 5 0 5 5 5 1 1\n",
"6\n1 7 3 6 2 5\n",
"5\n4 1 2 1 1\n",
"10\n4 4 0 4 10 4 4 4 4 4\n",
"6\n4 5 1 4 2 6\n",
"5\n3 3 3 0 2\n",
"9\n1 1 7 7 7 7 7 8 3\n",
"5\n1 2 1 0 2\n",
"5\n5 2 2 3 4\n",
"11\n1 2 3 4 5 1 2 3 4 3 1\n",
"6\n1 0 3 1 2 3\n",
"3\n3 2 2\n",
"5\n0 2 2 1 2\n",
"4\n0 2 2 1\n",
"7\n3 3 1 2 3 5 4\n",
"100\n3 7 7 8 15 25 26 31 37 41 43 43 46 64 65 82 94 102 102 103 107 124 125 131 140 145 146 150 151 160 160 161 162 165 169 175 182 191 201 211 214 216 218 304 406 229 236 241 244 249 252 269 270 271 273 289 285 295 222 307 312 317 319 319 320 321 325 330 340 341 345 347 354 356 366 366 375 376 380 383 386 398 401 407 414 417 423 426 431 438 440 444 446 454 457 458 458 466 466 472\n",
"5\n2 5 4 4 4\n",
"47\n6 277 329 28 410 432 434 505 529 545 650 896 949 1053 1543 1554 1599 1648 1927 1976 1998 2141 2248 2384 2542 2638 2995 3155 3216 3355 3409 3597 3851 3940 4169 4176 4378 4378 4425 4490 4627 4986 5025 5033 5374 5453 5644\n",
"5\n1 3 4 3 2\n",
"5\n1 2 7 1 5\n",
"10\n4 5 11 12 13 14 16 16 16 27\n",
"4\n4 5 3 3\n",
"4\n4 5 1 0\n",
"10\n1 2 9 4 5 6 7 8 3 14\n",
"128\n1 2 4 6 8 17 20 20 23 33 43 49 49 49 52 73 74 75 82 84 85 87 90 91 102 103 104 105 111 111 401 142 142 152 155 160 175 176 178 181 183 184 187 188 191 193 326 202 202 214 224 225 236 239 240 243 246 247 249 278 257 257 261 264 265 271 277 281 284 284 286 289 290 296 297 303 305 307 307 317 318 320 322 200 332 342 393 349 350 350 369 375 381 381 385 385 387 393 347 397 398 115 402 407 407 408 410 411 411 416 423 426 429 429 430 440 447 449 463 464 466 471 473 480 480 483 497 503\n",
"4\n0 3 2 1\n",
"2\n2 2\n",
"3\n3 0 1\n",
"5\n1 4 3 0 1\n",
"6\n4 4 5 6 9 2\n",
"3\n0 3 0\n",
"50\n6 7 8 4 10 3 2 7 1 1 10 3 4 7 2 3 7 4 10 6 8 10 9 3 5 10 9 6 1 8 9 4 3 7 3 10 5 3 10 1 6 10 6 7 10 7 1 5 9 5\n",
"3\n4 3 1\n",
"5\n1 1 3 0 1\n",
"5\n0 8 5 2 3\n",
"5\n100 5 1 10 7\n",
"5\n3 2 5 3 4\n",
"5\n2 3 0 3 3\n",
"20\n38205814 195654691 127848638 189351562 1085863511 284688399 318826601 326499046 387938139 395996609 494453625 551393005 561264192 573569187 600766727 606718722 730549586 261502770 751513115 943272321\n",
"6\n1 2 1 4 5 1\n",
"2\n0 0\n",
"5\n3 0 1 5 2\n",
"5\n1 4 3 2 3\n",
"4\n1 4 2 4\n",
"11\n2 2 2 3 2 2 2 2 2 1 1\n",
"6\n6 1 4 3 4 8\n",
"5\n0 1 4 5 1\n",
"6\n1 6 2 0 0 5\n",
"4\n6 2 1 2\n",
"4\n3 2 1 2\n",
"5\n2 3 0 6 3\n",
"4\n2 4 0 2\n",
"4\n1 2 1 5\n",
"5\n4 5 2 1 1\n",
"3\n1 2 1\n"
],
"output": [
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
### Input:
4
4 3 2 1
### Output:
NO
### Input:
2
1 2
### Output:
YES
### Code:
def main():
n = int(input())
arr = list(map(int, input().split()))
copy = arr[:]
copy.sort()
missed = 0
for i in range(n):
if arr[i] != copy[i]:
missed += 1
if missed == 2:
print('YES')
elif missed == 0:
print('YES')
else:
print('NO')
main()
|
244_B. Undoubtedly Lucky Numbers_28617
|
Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x = 4, and y = 7, then numbers 47, 744, 4 are lucky.
Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0 ≤ x, y ≤ 9), that the decimal representation of number a (without leading zeroes) contains only digits x and y.
Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.
Input
The first line contains a single integer n (1 ≤ n ≤ 109) — Polycarpus's number.
Output
Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.
Examples
Input
10
Output
10
Input
123
Output
113
Note
In the first test sample all numbers that do not exceed 10 are undoubtedly lucky.
In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky.
|
def func(num):
if 0 < num <= n:
result.add(num)
num *= 10
func(num+x)
func(num+y)
if __name__ == "__main__":
n = int(input())
result = set()
for x in range(10):
for y in range(10):
func(x)
print(len(result))
|
{
"input": [
"123\n",
"10\n",
"784262\n",
"68\n",
"101\n",
"132\n",
"999999998\n",
"468390\n",
"603356456\n",
"820040584\n",
"2\n",
"909090901\n",
"642678\n",
"999999999\n",
"940\n",
"326806\n",
"4\n",
"6\n",
"1000\n",
"356\n",
"999999997\n",
"102\n",
"8\n",
"64214872\n",
"89\n",
"3\n",
"72\n",
"1\n",
"5\n",
"7\n",
"442198\n",
"1000000000\n",
"9\n",
"142498040\n",
"1106646\n",
"0\n",
"111\n",
"178\n",
"631770\n",
"380204978\n",
"12\n",
"999905083\n",
"538039\n",
"223\n",
"596596\n",
"15\n",
"1100\n",
"128\n",
"415673571\n",
"203\n",
"94963945\n",
"133\n",
"69\n",
"844018\n",
"14\n",
"234298201\n",
"20\n",
"16\n",
"854133\n",
"100\n",
"183\n",
"2382\n",
"626243410\n",
"21\n",
"242459604\n",
"640288\n",
"446\n",
"998397\n",
"11\n",
"114\n",
"330499271\n",
"387\n",
"1726751\n",
"25\n",
"13\n",
"83914\n",
"17\n",
"467680878\n",
"29\n",
"798225\n",
"266\n",
"4401\n",
"35\n",
"280567712\n",
"44530\n",
"688\n",
"1593671\n",
"18\n",
"156\n",
"411029171\n",
"574\n",
"1984115\n",
"30\n",
"24\n",
"127752\n",
"33\n",
"811844381\n",
"36\n",
"249621\n",
"364\n",
"8261\n",
"50\n",
"16665\n",
"744\n",
"2404751\n",
"56\n",
"304531400\n",
"498\n",
"378069871\n"
],
"output": [
"113\n",
"10\n",
"4079\n",
"68\n",
"101\n",
"114\n",
"40742\n",
"3223\n",
"31623\n",
"36407\n",
"2\n",
"38532\n",
"3615\n",
"40743\n",
"331\n",
"2759\n",
"4\n",
"6\n",
"352\n",
"175\n",
"40741\n",
"101\n",
"8\n",
"15759\n",
"89\n",
"3\n",
"72\n",
"1\n",
"5\n",
"7\n",
"3071\n",
"40744\n",
"9\n",
"21671\n",
"4719\n",
"0\n",
"103\n",
"123\n",
"3599\n",
"26711\n",
"12\n",
"40471\n",
"3335\n",
"135\n",
"3543\n",
"15\n",
"356\n",
"113\n",
"27223\n",
"129\n",
"19239\n",
"115\n",
"69\n",
"4175\n",
"14\n",
"23903\n",
"20\n",
"16\n",
"4191\n",
"100\n",
"124\n",
"455\n",
"31895\n",
"21\n",
"23967\n",
"3615\n",
"198\n",
"4599\n",
"11\n",
"106\n",
"25119\n",
"180\n",
"5159\n",
"25\n",
"13\n",
"1911\n",
"17\n",
"28879\n",
"29\n",
"4103\n",
"149\n",
"560\n",
"35\n",
"24415\n",
"1411\n",
"265\n",
"5111\n",
"18\n",
"119\n",
"27095\n",
"233\n",
"5223\n",
"30\n",
"24\n",
"2319\n",
"33\n",
"36327\n",
"36\n",
"2631\n",
"176\n",
"809\n",
"50\n",
"1038\n",
"276\n",
"5615\n",
"56\n",
"24799\n",
"210\n",
"26711\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x = 4, and y = 7, then numbers 47, 744, 4 are lucky.
Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0 ≤ x, y ≤ 9), that the decimal representation of number a (without leading zeroes) contains only digits x and y.
Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.
Input
The first line contains a single integer n (1 ≤ n ≤ 109) — Polycarpus's number.
Output
Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.
Examples
Input
10
Output
10
Input
123
Output
113
Note
In the first test sample all numbers that do not exceed 10 are undoubtedly lucky.
In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky.
### Input:
123
### Output:
113
### Input:
10
### Output:
10
### Code:
def func(num):
if 0 < num <= n:
result.add(num)
num *= 10
func(num+x)
func(num+y)
if __name__ == "__main__":
n = int(input())
result = set()
for x in range(10):
for y in range(10):
func(x)
print(len(result))
|
292_B. Network Topology_28623
|
This problem uses a simplified network topology model, please read the problem statement carefully and use it as a formal document as you develop the solution.
Polycarpus continues working as a system administrator in a large corporation. The computer network of this corporation consists of n computers, some of them are connected by a cable. The computers are indexed by integers from 1 to n. It's known that any two computers connected by cable directly or through other computers
Polycarpus decided to find out the network's topology. A network topology is the way of describing the network configuration, the scheme that shows the location and the connections of network devices.
Polycarpus knows three main network topologies: bus, ring and star. A bus is the topology that represents a shared cable with all computers connected with it. In the ring topology the cable connects each computer only with two other ones. A star is the topology where all computers of a network are connected to the single central node.
Let's represent each of these network topologies as a connected non-directed graph. A bus is a connected graph that is the only path, that is, the graph where all nodes are connected with two other ones except for some two nodes that are the beginning and the end of the path. A ring is a connected graph, where all nodes are connected with two other ones. A star is a connected graph, where a single central node is singled out and connected with all other nodes. For clarifications, see the picture.
<image> (1) — bus, (2) — ring, (3) — star
You've got a connected non-directed graph that characterizes the computer network in Polycarpus' corporation. Help him find out, which topology type the given network is. If that is impossible to do, say that the network's topology is unknown.
Input
The first line contains two space-separated integers n and m (4 ≤ n ≤ 105; 3 ≤ m ≤ 105) — the number of nodes and edges in the graph, correspondingly. Next m lines contain the description of the graph's edges. The i-th line contains a space-separated pair of integers xi, yi (1 ≤ xi, yi ≤ n) — the numbers of nodes that are connected by the i-the edge.
It is guaranteed that the given graph is connected. There is at most one edge between any two nodes. No edge connects a node with itself.
Output
In a single line print the network topology name of the given graph. If the answer is the bus, print "bus topology" (without the quotes), if the answer is the ring, print "ring topology" (without the quotes), if the answer is the star, print "star topology" (without the quotes). If no answer fits, print "unknown topology" (without the quotes).
Examples
Input
4 3
1 2
2 3
3 4
Output
bus topology
Input
4 4
1 2
2 3
3 4
4 1
Output
ring topology
Input
4 3
1 2
1 3
1 4
Output
star topology
Input
4 4
1 2
2 3
3 1
1 4
Output
unknown topology
|
n,m=map(int,input().split())
arr=[0]*(n+1)
for w in range(m):
a,b=map(int,input().split())
arr[a]+=1
arr[b]+=1
c1=0
c2=0
cs=0
for i in range(1,n+1):
if arr[i]==1:
c1+=1
if arr[i]==2:
c2+=1
if arr[i]==n-1:
cs+=1
if c1==2 and c2==n-2:
print("bus topology")
elif c2==n:
print("ring topology")
elif c1==n-1 and cs==1:
print("star topology")
else:
print("unknown topology")
|
{
"input": [
"4 3\n1 2\n2 3\n3 4\n",
"4 4\n1 2\n2 3\n3 4\n4 1\n",
"4 4\n1 2\n2 3\n3 1\n1 4\n",
"4 3\n1 2\n1 3\n1 4\n",
"4 4\n1 2\n2 3\n3 4\n4 2\n",
"10 9\n10 6\n3 4\n8 9\n8 4\n6 1\n2 9\n5 1\n7 5\n10 3\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 5\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"6 6\n1 2\n2 3\n3 1\n4 5\n5 6\n6 1\n",
"4 3\n2 4\n1 3\n4 1\n",
"5 4\n4 2\n5 2\n1 2\n2 3\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 4\n7 5\n9 6\n8 1\n2 9\n",
"5 4\n1 2\n3 5\n1 4\n5 4\n",
"5 9\n5 3\n4 5\n3 1\n3 2\n2 1\n2 5\n1 5\n1 4\n4 2\n",
"4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n",
"4 4\n1 2\n2 3\n2 4\n3 4\n",
"5 5\n3 4\n5 2\n2 1\n5 4\n3 1\n",
"10 9\n10 1\n10 2\n10 3\n10 4\n10 5\n10 6\n10 7\n10 8\n10 9\n",
"4 4\n2 4\n4 1\n1 3\n2 3\n",
"6 5\n1 2\n1 3\n1 4\n4 5\n4 6\n",
"10 9\n1 4\n4 10\n4 9\n8 4\n4 7\n4 5\n4 2\n4 6\n4 3\n",
"4 3\n1 2\n2 4\n3 2\n",
"5 4\n1 2\n1 3\n1 4\n4 5\n",
"4 4\n3 2\n2 4\n4 1\n1 2\n",
"6 6\n1 2\n4 3\n3 1\n4 5\n5 6\n6 1\n",
"4 3\n1 4\n2 4\n3 2\n",
"4 3\n1 4\n2 4\n3 4\n",
"4 4\n1 4\n2 3\n2 4\n3 1\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 4\n7 5\n9 6\n8 1\n4 9\n",
"4 4\n1 4\n2 3\n2 4\n3 4\n",
"5 5\n3 4\n5 1\n2 1\n5 4\n3 1\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"6 6\n1 2\n2 3\n3 1\n4 5\n5 2\n6 1\n",
"4 4\n1 2\n2 3\n2 4\n3 3\n",
"4 4\n1 3\n2 3\n3 4\n4 1\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n3 4\n",
"6 6\n1 2\n2 3\n3 2\n4 5\n5 2\n6 1\n",
"4 4\n1 2\n2 3\n2 4\n1 3\n",
"6 6\n1 2\n2 1\n3 1\n4 5\n5 6\n6 1\n",
"5 4\n4 1\n5 2\n1 2\n2 3\n",
"10 10\n1 4\n3 6\n10 9\n5 8\n2 10\n3 4\n7 5\n9 6\n8 1\n2 9\n",
"5 9\n5 3\n4 5\n3 1\n3 2\n2 1\n2 5\n1 5\n1 4\n3 2\n",
"4 4\n2 4\n4 1\n1 2\n2 3\n",
"6 5\n2 2\n1 3\n1 4\n4 5\n4 6\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 4\n7 9\n9 6\n8 1\n4 9\n",
"6 6\n1 2\n2 3\n3 1\n4 4\n5 2\n6 1\n",
"4 4\n1 2\n2 3\n2 4\n3 1\n",
"10 14\n3 1\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n3 4\n",
"4 4\n1 2\n2 3\n2 4\n1 1\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 4\n7 9\n9 6\n8 2\n4 9\n",
"4 4\n1 2\n2 3\n3 4\n3 1\n",
"10 14\n5 1\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n3 4\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 5\n7 10\n9 5\n7 1\n5 10\n3 4\n",
"6 6\n1 2\n2 3\n3 1\n4 5\n5 6\n6 2\n",
"4 3\n2 4\n2 3\n4 1\n",
"4 3\n1 2\n2 3\n1 4\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 5\n7 5\n9 6\n8 1\n4 9\n",
"5 5\n3 4\n5 1\n2 1\n5 4\n4 1\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n4 2\n3 4\n",
"10 10\n1 4\n3 6\n10 9\n5 8\n2 10\n3 1\n7 5\n9 6\n8 1\n2 9\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n",
"10 10\n1 4\n4 6\n10 7\n5 8\n2 10\n3 4\n7 9\n9 6\n8 1\n4 9\n",
"10 14\n3 1\n7 2\n6 3\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n3 4\n",
"4 4\n1 2\n4 3\n2 4\n1 1\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 4\n7 3\n9 6\n8 2\n4 9\n",
"10 14\n5 1\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n1 10\n9 5\n7 1\n8 2\n3 4\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 4\n4 1\n2 1\n7 10\n9 5\n7 1\n4 2\n3 4\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 1\n7 5\n9 6\n8 1\n2 9\n",
"10 10\n1 4\n4 6\n10 7\n5 8\n2 10\n3 4\n7 9\n9 6\n8 2\n4 9\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 2\n2 5\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"5 4\n4 2\n5 1\n1 2\n2 3\n",
"4 3\n1 2\n2 4\n3 4\n",
"6 6\n1 2\n4 3\n3 1\n4 5\n5 5\n6 1\n",
"10 14\n3 2\n7 2\n1 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"4 4\n1 2\n2 3\n2 4\n4 3\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n2 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n3 4\n",
"6 5\n3 2\n1 3\n1 4\n4 5\n4 6\n",
"4 3\n1 3\n2 4\n3 2\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n3 5\n7 9\n9 6\n8 1\n4 9\n",
"10 14\n3 1\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n8 2\n1 4\n",
"5 5\n3 4\n5 1\n2 1\n5 4\n1 1\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 4\n6 3\n4 1\n2 1\n7 10\n9 5\n7 1\n4 2\n3 4\n",
"10 10\n1 7\n4 6\n10 7\n5 8\n2 10\n3 4\n7 9\n9 6\n8 1\n4 9\n",
"4 4\n1 3\n4 3\n2 4\n1 1\n",
"10 14\n5 1\n7 2\n6 4\n8 1\n3 9\n3 6\n6 3\n4 1\n2 1\n1 10\n9 5\n7 1\n8 2\n3 4\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n6 1\n7 5\n9 6\n8 1\n2 9\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 6\n6 3\n4 4\n2 5\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"4 3\n1 3\n2 4\n3 4\n",
"10 10\n1 1\n3 6\n10 7\n5 8\n2 10\n3 5\n7 9\n9 6\n8 1\n4 9\n",
"4 4\n1 4\n2 3\n2 1\n3 1\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 4\n6 3\n4 1\n2 1\n7 10\n9 5\n7 2\n4 2\n3 4\n",
"10 14\n5 1\n7 2\n6 4\n8 1\n3 9\n3 6\n6 3\n4 1\n2 1\n1 10\n9 10\n7 1\n8 2\n3 4\n",
"10 10\n1 4\n3 6\n10 7\n5 8\n2 10\n6 1\n9 5\n9 6\n8 1\n2 9\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 7\n5 6\n6 3\n4 4\n2 5\n7 10\n9 5\n7 1\n8 10\n3 4\n",
"10 10\n1 1\n3 6\n10 7\n5 8\n2 10\n3 5\n7 9\n9 6\n1 1\n4 9\n",
"10 14\n3 2\n7 2\n6 4\n8 1\n3 9\n5 4\n6 3\n7 1\n2 1\n7 10\n9 5\n7 2\n4 2\n3 4\n",
"10 14\n5 1\n7 2\n6 4\n8 1\n3 9\n3 6\n6 3\n4 1\n2 1\n1 10\n6 10\n7 1\n8 2\n3 4\n"
],
"output": [
"bus topology\n",
"ring topology\n",
"unknown topology\n",
"star topology\n",
"unknown topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"star topology\n",
"ring topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"ring topology\n",
"star topology\n",
"ring topology\n",
"unknown topology\n",
"star topology\n",
"star topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"star topology\n",
"ring topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"bus topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n",
"unknown topology\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This problem uses a simplified network topology model, please read the problem statement carefully and use it as a formal document as you develop the solution.
Polycarpus continues working as a system administrator in a large corporation. The computer network of this corporation consists of n computers, some of them are connected by a cable. The computers are indexed by integers from 1 to n. It's known that any two computers connected by cable directly or through other computers
Polycarpus decided to find out the network's topology. A network topology is the way of describing the network configuration, the scheme that shows the location and the connections of network devices.
Polycarpus knows three main network topologies: bus, ring and star. A bus is the topology that represents a shared cable with all computers connected with it. In the ring topology the cable connects each computer only with two other ones. A star is the topology where all computers of a network are connected to the single central node.
Let's represent each of these network topologies as a connected non-directed graph. A bus is a connected graph that is the only path, that is, the graph where all nodes are connected with two other ones except for some two nodes that are the beginning and the end of the path. A ring is a connected graph, where all nodes are connected with two other ones. A star is a connected graph, where a single central node is singled out and connected with all other nodes. For clarifications, see the picture.
<image> (1) — bus, (2) — ring, (3) — star
You've got a connected non-directed graph that characterizes the computer network in Polycarpus' corporation. Help him find out, which topology type the given network is. If that is impossible to do, say that the network's topology is unknown.
Input
The first line contains two space-separated integers n and m (4 ≤ n ≤ 105; 3 ≤ m ≤ 105) — the number of nodes and edges in the graph, correspondingly. Next m lines contain the description of the graph's edges. The i-th line contains a space-separated pair of integers xi, yi (1 ≤ xi, yi ≤ n) — the numbers of nodes that are connected by the i-the edge.
It is guaranteed that the given graph is connected. There is at most one edge between any two nodes. No edge connects a node with itself.
Output
In a single line print the network topology name of the given graph. If the answer is the bus, print "bus topology" (without the quotes), if the answer is the ring, print "ring topology" (without the quotes), if the answer is the star, print "star topology" (without the quotes). If no answer fits, print "unknown topology" (without the quotes).
Examples
Input
4 3
1 2
2 3
3 4
Output
bus topology
Input
4 4
1 2
2 3
3 4
4 1
Output
ring topology
Input
4 3
1 2
1 3
1 4
Output
star topology
Input
4 4
1 2
2 3
3 1
1 4
Output
unknown topology
### Input:
4 3
1 2
2 3
3 4
### Output:
bus topology
### Input:
4 4
1 2
2 3
3 4
4 1
### Output:
ring topology
### Code:
n,m=map(int,input().split())
arr=[0]*(n+1)
for w in range(m):
a,b=map(int,input().split())
arr[a]+=1
arr[b]+=1
c1=0
c2=0
cs=0
for i in range(1,n+1):
if arr[i]==1:
c1+=1
if arr[i]==2:
c2+=1
if arr[i]==n-1:
cs+=1
if c1==2 and c2==n-2:
print("bus topology")
elif c2==n:
print("ring topology")
elif c1==n-1 and cs==1:
print("star topology")
else:
print("unknown topology")
|
363_B. Fence_28631
|
There is a fence in front of Polycarpus's home. The fence consists of n planks of the same width which go one after another from left to right. The height of the i-th plank is hi meters, distinct planks can have distinct heights.
<image> Fence for n = 7 and h = [1, 2, 6, 1, 1, 7, 1]
Polycarpus has bought a posh piano and is thinking about how to get it into the house. In order to carry out his plan, he needs to take exactly k consecutive planks from the fence. Higher planks are harder to tear off the fence, so Polycarpus wants to find such k consecutive planks that the sum of their heights is minimal possible.
Write the program that finds the indexes of k consecutive planks with minimal total height. Pay attention, the fence is not around Polycarpus's home, it is in front of home (in other words, the fence isn't cyclic).
Input
The first line of the input contains integers n and k (1 ≤ n ≤ 1.5·105, 1 ≤ k ≤ n) — the number of planks in the fence and the width of the hole for the piano. The second line contains the sequence of integers h1, h2, ..., hn (1 ≤ hi ≤ 100), where hi is the height of the i-th plank of the fence.
Output
Print such integer j that the sum of the heights of planks j, j + 1, ..., j + k - 1 is the minimum possible. If there are multiple such j's, print any of them.
Examples
Input
7 3
1 2 6 1 1 7 1
Output
3
Note
In the sample, your task is to find three consecutive planks with the minimum sum of heights. In the given case three planks with indexes 3, 4 and 5 have the required attribute, their total height is 8.
|
n,k=map(int,input().split())
A = list(map(int,input().split()))
B = [0]
for i in range(k):
B[0]+=A[i]
for i in range(1,n-k+1):
B.append(B[i-1]-A[i-1]+A[i+k-1])
print(B.index(min(B))+1)
|
{
"input": [
"7 3\n1 2 6 1 1 7 1\n",
"2 1\n10 20\n",
"3 1\n1 2 3\n",
"10 2\n3 1 4 1 4 6 2 1 4 6\n",
"2 2\n20 10\n",
"4 1\n1 5 2 2\n",
"6 3\n1 2 1 3 1 1\n",
"8 3\n1 1 1 1 2 60 90 1\n",
"6 3\n56 56 56 2 1 2\n",
"3 3\n1 2 3\n",
"5 2\n100 100 100 1 1\n",
"10 4\n1 1 1 4 4 4 4 4 4 3\n",
"10 5\n1 2 3 1 2 2 3 1 4 5\n",
"3 2\n1 2 3\n",
"3 1\n2 1 3\n",
"4 2\n4 6 7 4\n",
"4 2\n10 1 2 3\n",
"3 2\n3 2 1\n",
"2 1\n20 1\n",
"1 1\n100\n",
"3 1\n3 2 1\n",
"4 2\n9 8 11 7\n",
"2 1\n10 29\n",
"10 1\n3 1 4 1 4 6 2 1 4 6\n",
"6 3\n56 56 98 2 1 2\n",
"3 1\n3 2 0\n",
"10 2\n3 1 4 1 4 6 2 1 3 8\n",
"6 2\n1 2 1 3 1 1\n",
"3 1\n1 4 3\n",
"2 2\n6 10\n",
"4 1\n2 5 2 2\n",
"6 3\n2 2 1 3 1 1\n",
"8 3\n1 1 1 1 4 60 90 1\n",
"3 3\n0 2 3\n",
"5 2\n000 100 100 1 1\n",
"10 4\n0 1 1 4 4 4 4 4 4 3\n",
"3 2\n1 2 0\n",
"4 2\n4 1 7 4\n",
"4 2\n10 2 2 3\n",
"3 2\n3 3 1\n",
"2 1\n20 2\n",
"4 2\n9 8 11 3\n",
"7 5\n1 2 6 1 1 7 1\n",
"2 1\n19 29\n",
"3 1\n1 7 3\n",
"10 1\n3 1 4 1 4 6 2 1 3 6\n",
"4 1\n2 2 2 2\n",
"8 1\n1 1 1 1 4 60 90 1\n",
"6 3\n56 8 98 2 1 2\n",
"3 3\n0 2 0\n",
"5 2\n000 100 100 2 1\n",
"10 4\n0 1 1 4 8 4 4 4 4 3\n",
"3 2\n1 2 -1\n",
"2 1\n13 2\n",
"4 2\n9 8 17 3\n",
"7 5\n1 2 6 0 1 7 1\n",
"3 1\n1 3 3\n",
"10 1\n3 1 4 1 4 6 2 1 3 8\n",
"6 3\n56 14 98 2 1 2\n",
"10 4\n0 1 1 4 8 4 4 1 4 3\n",
"3 2\n1 4 -1\n",
"4 2\n9 8 16 3\n",
"3 1\n1 3 5\n",
"6 3\n84 14 98 2 1 2\n",
"10 7\n0 1 1 4 8 4 4 1 4 3\n",
"4 2\n10 8 16 3\n",
"3 1\n2 3 5\n",
"10 2\n3 1 4 1 4 6 2 0 3 8\n",
"6 3\n84 14 114 2 1 2\n",
"4 2\n11 8 16 3\n",
"3 1\n2 1 5\n",
"6 3\n84 14 196 2 1 2\n",
"4 2\n11 10 16 3\n",
"3 1\n2 1 7\n",
"2 1\n3 20\n",
"10 2\n3 1 4 1 4 6 2 1 6 6\n",
"2 2\n20 12\n",
"8 3\n1 1 1 1 2 60 85 1\n",
"3 3\n2 2 3\n",
"5 2\n100 100 100 1 2\n",
"10 4\n0 2 1 4 4 4 4 4 4 3\n",
"10 5\n1 2 3 1 3 2 3 1 4 5\n",
"2 2\n1 2 3\n",
"2 1\n2 1 3\n",
"3 2\n10 1 2 3\n",
"2 1\n37 1\n",
"4 2\n9 8 6 7\n",
"7 3\n1 2 6 1 1 7 2\n",
"2 1\n10 53\n",
"2 1\n1 4 3\n",
"10 1\n3 1 4 1 4 6 2 2 4 6\n",
"2 2\n6 9\n",
"6 3\n2 2 1 1 1 1\n",
"8 3\n1 1 1 1 4 60 140 1\n",
"6 3\n56 56 98 2 0 2\n",
"3 3\n-1 2 3\n",
"5 2\n000 100 000 1 1\n",
"10 4\n0 1 1 4 4 3 4 4 4 3\n",
"4 2\n6 1 7 4\n",
"4 2\n12 2 2 3\n",
"3 2\n3 6 1\n",
"2 1\n20 0\n",
"4 2\n9 5 11 3\n",
"7 5\n1 2 6 1 0 7 1\n",
"4 1\n2 2 2 4\n",
"8 1\n1 1 1 1 4 9 90 1\n",
"6 3\n56 8 98 3 1 2\n",
"5 4\n000 100 100 2 1\n",
"10 4\n0 1 0 4 8 4 4 4 4 3\n",
"2 1\n2 2\n",
"4 2\n9 10 11 3\n",
"6 3\n56 14 98 2 0 2\n",
"10 4\n0 1 1 4 8 4 1 1 4 3\n",
"3 2\n0 4 -1\n",
"4 4\n9 8 16 3\n",
"10 2\n3 1 4 1 4 8 2 1 3 8\n",
"6 6\n84 14 98 2 1 2\n",
"4 2\n10 8 11 3\n",
"3 1\n2 3 2\n",
"6 3\n84 14 114 2 0 2\n"
],
"output": [
"3\n",
"1\n",
"1\n",
"7\n",
"1\n",
"1\n",
"1\n",
"1\n",
"4\n",
"1\n",
"4\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"3\n",
"1\n",
"1\n",
"2\n",
"4\n",
"3\n",
"7\n",
"5\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"4\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"4\n",
"1\n",
"4\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"4\n",
"1\n",
"2\n",
"1\n",
"1\n",
"4\n",
"1\n",
"1\n",
"1\n",
"7\n",
"4\n",
"1\n",
"2\n",
"4\n",
"3\n",
"2\n",
"1\n",
"7\n",
"1\n",
"1\n",
"1\n",
"4\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"1\n",
"1\n",
"2\n",
"1\n",
"3\n",
"1\n",
"4\n",
"1\n",
"3\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"4\n",
"1\n",
"1\n",
"1\n",
"3\n",
"4\n",
"1\n",
"2\n",
"1\n",
"7\n",
"1\n",
"3\n",
"1\n",
"4\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There is a fence in front of Polycarpus's home. The fence consists of n planks of the same width which go one after another from left to right. The height of the i-th plank is hi meters, distinct planks can have distinct heights.
<image> Fence for n = 7 and h = [1, 2, 6, 1, 1, 7, 1]
Polycarpus has bought a posh piano and is thinking about how to get it into the house. In order to carry out his plan, he needs to take exactly k consecutive planks from the fence. Higher planks are harder to tear off the fence, so Polycarpus wants to find such k consecutive planks that the sum of their heights is minimal possible.
Write the program that finds the indexes of k consecutive planks with minimal total height. Pay attention, the fence is not around Polycarpus's home, it is in front of home (in other words, the fence isn't cyclic).
Input
The first line of the input contains integers n and k (1 ≤ n ≤ 1.5·105, 1 ≤ k ≤ n) — the number of planks in the fence and the width of the hole for the piano. The second line contains the sequence of integers h1, h2, ..., hn (1 ≤ hi ≤ 100), where hi is the height of the i-th plank of the fence.
Output
Print such integer j that the sum of the heights of planks j, j + 1, ..., j + k - 1 is the minimum possible. If there are multiple such j's, print any of them.
Examples
Input
7 3
1 2 6 1 1 7 1
Output
3
Note
In the sample, your task is to find three consecutive planks with the minimum sum of heights. In the given case three planks with indexes 3, 4 and 5 have the required attribute, their total height is 8.
### Input:
7 3
1 2 6 1 1 7 1
### Output:
3
### Input:
2 1
10 20
### Output:
1
### Code:
n,k=map(int,input().split())
A = list(map(int,input().split()))
B = [0]
for i in range(k):
B[0]+=A[i]
for i in range(1,n-k+1):
B.append(B[i-1]-A[i-1]+A[i+k-1])
print(B.index(min(B))+1)
|
387_A. George and Sleep_28635
|
George woke up and saw the current time s on the digital clock. Besides, George knows that he has slept for time t.
Help George! Write a program that will, given time s and t, determine the time p when George went to bed. Note that George could have gone to bed yesterday relatively to the current time (see the second test sample).
Input
The first line contains current time s as a string in the format "hh:mm". The second line contains time t in the format "hh:mm" — the duration of George's sleep. It is guaranteed that the input contains the correct time in the 24-hour format, that is, 00 ≤ hh ≤ 23, 00 ≤ mm ≤ 59.
Output
In the single line print time p — the time George went to bed in the format similar to the format of the time in the input.
Examples
Input
05:50
05:44
Output
00:06
Input
00:00
01:00
Output
23:00
Input
00:01
00:00
Output
00:01
Note
In the first sample George went to bed at "00:06". Note that you should print the time only in the format "00:06". That's why answers "0:06", "00:6" and others will be considered incorrect.
In the second sample, George went to bed yesterday.
In the third sample, George didn't do to bed at all.
|
def tmins():
sh, sm = map(int, input().split(':'))
return 60 * sh + sm
t = tmins() - tmins()
if t < 0:
t += 60*24
print('%02d:%02d' % (t//60, t%60))
|
{
"input": [
"00:01\n00:00\n",
"05:50\n05:44\n",
"00:00\n01:00\n",
"12:33\n23:33\n",
"10:05\n00:00\n",
"09:09\n00:00\n",
"13:04\n09:58\n",
"01:00\n00:00\n",
"03:48\n00:41\n",
"12:21\n21:12\n",
"12:44\n12:44\n",
"00:00\n00:01\n",
"12:59\n00:45\n",
"05:55\n07:12\n",
"22:22\n22:23\n",
"23:44\n23:55\n",
"07:55\n05:53\n",
"21:30\n02:00\n",
"13:43\n17:23\n",
"19:30\n09:30\n",
"23:59\n23:59\n",
"12:53\n08:37\n",
"00:00\n13:12\n",
"12:00\n23:59\n",
"22:22\n22:22\n",
"20:53\n10:23\n",
"03:23\n08:52\n",
"00:00\n23:59\n",
"07:43\n12:27\n",
"23:24\n23:23\n",
"10:00\n01:00\n",
"21:00\n01:00\n",
"23:24\n00:28\n",
"19:30\n02:00\n",
"10:10\n01:01\n",
"21:21\n12:21\n",
"13:08\n00:42\n",
"23:30\n00:00\n",
"16:04\n10:28\n",
"00:00\n00:00\n",
"21:21\n23:06\n",
"03:38\n23:46\n",
"12:39\n22:21\n",
"07:12\n05:55\n",
"09:10\n00:01\n",
"21:10\n13:50\n",
"05:44\n06:00\n",
"12:33\n23:23\n",
"10:05\n00:01\n",
"00:10\n00:00\n",
"12:44\n21:44\n",
"00:00\n10:00\n",
"12:59\n01:45\n",
"22:22\n22:13\n",
"08:55\n05:53\n",
"21:40\n02:00\n",
"13:43\n16:23\n",
"22:59\n23:59\n",
"12:53\n08:38\n",
"00:00\n13:21\n",
"22:34\n00:28\n",
"21:21\n22:11\n",
"12:39\n22:22\n",
"07:12\n15:55\n",
"09:10\n01:00\n",
"05:44\n05:00\n",
"10:00\n00:00\n",
"10:05\n00:02\n",
"00:11\n00:00\n",
"12:45\n21:44\n",
"00:10\n10:00\n",
"08:54\n05:53\n",
"22:59\n22:59\n",
"19:32\n22:22\n",
"05:44\n04:00\n",
"10:10\n00:00\n",
"11:00\n00:00\n",
"08:54\n04:53\n",
"19:33\n22:22\n",
"11:00\n10:00\n",
"10:00\n00:01\n",
"00:15\n00:00\n",
"01:01\n00:00\n",
"12:20\n21:12\n",
"23:44\n22:55\n",
"03:19\n09:30\n",
"00:21\n23:59\n",
"00:00\n23:58\n",
"10:00\n01:01\n",
"21:00\n00:10\n",
"23:24\n02:08\n",
"19:03\n02:00\n",
"00:10\n01:01\n",
"03:32\n00:00\n",
"22:21\n23:06\n",
"17:12\n05:55\n",
"00:00\n00:10\n",
"01:10\n00:00\n",
"02:59\n01:45\n",
"08:55\n15:53\n",
"10:00\n13:21\n",
"12:34\n00:28\n",
"12:12\n22:11\n",
"10:04\n00:02\n",
"05:44\n00:40\n",
"10:10\n00:01\n",
"10:10\n01:00\n",
"00:15\n10:00\n",
"12:20\n21:13\n",
"22:12\n23:22\n",
"23:54\n22:55\n",
"22:12\n21:22\n",
"21:31\n12:22\n",
"04:32\n00:00\n",
"17:12\n05:54\n",
"09:01\n10:00\n",
"01:10\n00:01\n",
"10:00\n13:20\n",
"20:04\n00:02\n",
"00:10\n00:02\n",
"00:15\n00:01\n",
"04:33\n00:00\n",
"01:00\n10:00\n",
"10:10\n10:00\n",
"19:33\n22:23\n",
"10:00\n10:00\n",
"00:01\n00:01\n",
"22:22\n23:22\n",
"22:22\n21:22\n",
"23:25\n23:23\n",
"21:21\n12:22\n",
"09:10\n10:00\n",
"22:22\n22:12\n",
"07:12\n16:55\n",
"06:44\n05:00\n",
"10:01\n00:01\n",
"00:10\n00:01\n",
"01:10\n01:01\n",
"22:21\n22:12\n",
"11:10\n01:01\n"
],
"output": [
"00:01\n",
"00:06\n",
"23:00\n",
"13:00\n",
"10:05\n",
"09:09\n",
"03:06\n",
"01:00\n",
"03:07\n",
"15:09\n",
"00:00\n",
"23:59\n",
"12:14\n",
"22:43\n",
"23:59\n",
"23:49\n",
"02:02\n",
"19:30\n",
"20:20\n",
"10:00\n",
"00:00\n",
"04:16\n",
"10:48\n",
"12:01\n",
"00:00\n",
"10:30\n",
"18:31\n",
"00:01\n",
"19:16\n",
"00:01\n",
"09:00\n",
"20:00\n",
"22:56\n",
"17:30\n",
"09:09\n",
"09:00\n",
"12:26\n",
"23:30\n",
"05:36\n",
"00:00\n",
"22:15\n",
"03:52\n",
"14:18\n",
"01:17\n",
"09:09\n",
"07:20\n",
"23:44\n",
"13:10\n",
"10:04\n",
"00:10\n",
"15:00\n",
"14:00\n",
"11:14\n",
"00:09\n",
"03:02\n",
"19:40\n",
"21:20\n",
"23:00\n",
"04:15\n",
"10:39\n",
"22:06\n",
"23:10\n",
"14:17\n",
"15:17\n",
"08:10\n",
"00:44\n",
"10:00\n",
"10:03\n",
"00:11\n",
"15:01\n",
"14:10\n",
"03:01\n",
"00:00\n",
"21:10\n",
"01:44\n",
"10:10\n",
"11:00\n",
"04:01\n",
"21:11\n",
"01:00\n",
"09:59\n",
"00:15\n",
"01:01\n",
"15:08\n",
"00:49\n",
"17:49\n",
"00:22\n",
"00:02\n",
"08:59\n",
"20:50\n",
"21:16\n",
"17:03\n",
"23:09\n",
"03:32\n",
"23:15\n",
"11:17\n",
"23:50\n",
"01:10\n",
"01:14\n",
"17:02\n",
"20:39\n",
"12:06\n",
"14:01\n",
"10:02\n",
"05:04\n",
"10:09\n",
"09:10\n",
"14:15\n",
"15:07\n",
"22:50\n",
"00:59\n",
"00:50\n",
"09:09\n",
"04:32\n",
"11:18\n",
"23:01\n",
"01:09\n",
"20:40\n",
"20:02\n",
"00:08\n",
"00:14\n",
"04:33\n",
"15:00\n",
"00:10\n",
"21:10\n",
"00:00\n",
"00:00\n",
"23:00\n",
"01:00\n",
"00:02\n",
"08:59\n",
"23:10\n",
"00:10\n",
"14:17\n",
"01:44\n",
"10:00\n",
"00:09\n",
"00:09\n",
"00:09\n",
"10:09\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
George woke up and saw the current time s on the digital clock. Besides, George knows that he has slept for time t.
Help George! Write a program that will, given time s and t, determine the time p when George went to bed. Note that George could have gone to bed yesterday relatively to the current time (see the second test sample).
Input
The first line contains current time s as a string in the format "hh:mm". The second line contains time t in the format "hh:mm" — the duration of George's sleep. It is guaranteed that the input contains the correct time in the 24-hour format, that is, 00 ≤ hh ≤ 23, 00 ≤ mm ≤ 59.
Output
In the single line print time p — the time George went to bed in the format similar to the format of the time in the input.
Examples
Input
05:50
05:44
Output
00:06
Input
00:00
01:00
Output
23:00
Input
00:01
00:00
Output
00:01
Note
In the first sample George went to bed at "00:06". Note that you should print the time only in the format "00:06". That's why answers "0:06", "00:6" and others will be considered incorrect.
In the second sample, George went to bed yesterday.
In the third sample, George didn't do to bed at all.
### Input:
00:01
00:00
### Output:
00:01
### Input:
05:50
05:44
### Output:
00:06
### Code:
def tmins():
sh, sm = map(int, input().split(':'))
return 60 * sh + sm
t = tmins() - tmins()
if t < 0:
t += 60*24
print('%02d:%02d' % (t//60, t%60))
|
457_B. Distributed Join_28642
|
Piegirl was asked to implement two table join operation for distributed database system, minimizing the network traffic.
Suppose she wants to join two tables, A and B. Each of them has certain number of rows which are distributed on different number of partitions. Table A is distributed on the first cluster consisting of m partitions. Partition with index i has ai rows from A. Similarly, second cluster containing table B has n partitions, i-th one having bi rows from B.
In one network operation she can copy one row from any partition to any other partition. At the end, for each row from A and each row from B there should be a partition that has both rows. Determine the minimal number of network operations to achieve this.
Input
First line contains two integer numbers, m and n (1 ≤ m, n ≤ 105). Second line contains description of the first cluster with m space separated integers, ai (1 ≤ ai ≤ 109). Similarly, third line describes second cluster with n space separated integers, bi (1 ≤ bi ≤ 109).
Output
Print one integer — minimal number of copy operations.
Examples
Input
2 2
2 6
3 100
Output
11
Input
2 3
10 10
1 1 1
Output
6
Note
In the first example it makes sense to move all the rows to the second partition of the second cluster which is achieved in 2 + 6 + 3 = 11 operations
In the second example Piegirl can copy each row from B to the both partitions of the first cluster which needs 2·3 = 6 copy operations.
|
n, m = list(map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))
A.sort(reverse=True)
B.sort(reverse=True)
sumA = sum(A)
sumB = sum(B)
ansA = sumB
ansB = sumA
for i in range(1, n):
ansA += min(A[i],sumB)
for i in range(1, m):
ansB += min(B[i], sumA)
print(min(ansA,ansB))
|
{
"input": [
"2 2\n2 6\n3 100\n",
"2 3\n10 10\n1 1 1\n",
"10 10\n269584761 865524829 265226347 963092340 261501474 16861445 221090297 746538035 842020225 649641719\n49728483 423679832 107851851 179960003 345895125 400584885 460489835 377856735 506736683 676996548\n",
"3 4\n337369924 278848730 654933675\n866361693 732544605 890800310 350303294\n",
"8 8\n808147225 623333304 535665685 469385259 122918604 200681823 800211367 286974812\n85215517 983921829 274028967 567054904 144473212 964018990 177471567 73882806\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 589361337 319325955 938498114 249892107 138299026\n57775135 470751607 454623764 556600014 141039336 225043834 692497485 517610562 635337211 56258907\n",
"10 10\n933168403 835157665 823216696 818565876 448948583 884328249 809244579 473034231 407137956 871269623\n653126539 145998557 644003076 138712151 839886312 479712343 709513279 138285801 858528549 643830064\n",
"6 5\n4689556 6609945 15705705 10301912 11245669 5844638\n440894622 898226832 22060902 222576920 53133033\n",
"5 6\n574664105 497253985 200935113 926362846 223381305\n34188719 14075259 27219005 9682257 14352213 11696423\n",
"20 30\n81 67 100 83 97 97 58 54 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 180 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 64 170 143 143 126 12 175 84\n",
"1 1\n1889\n2867\n",
"5 4\n556840201 669601415 674042771 93322040 157280418\n253115131 933556803 294280580 169051325\n",
"6 5\n45936257 8169878 14134346 26323055 65863745 50728147\n997339869 2970526 163305525 839524148 193404120\n",
"5 6\n7780674 1861750 4491902 10256124 14362475\n1809567 5616386 1771573 2099536 1113026 3938402\n",
"5 7\n473347111 640932948 320036306 595696211 365475226\n347859328 553364017 687935743 145411543 689180757 696504973 783694820\n",
"5 6\n284534195 993347068 628813225 512761241 835859363\n61567950 7311163 14322159 100466429 66443161 48573213\n",
"10 10\n510955240 684852706 455356451 284505713 595775142 646334608 563116339 941123613 818750895 516673753\n382626402 204542396 341363992 234231105 75079663 683639780 624391764 265169060 686304227 280991725\n",
"2 2\n888381664 866366630\n170399907 404233949\n",
"10 10\n326151338 981287141 830123412 482457331 77554645 351237238 663827505 549778905 967488359 954617100\n238752550 787656851 393452025 837732771 522417885 876998499 195063055 325140429 546151936 403260186\n",
"6 5\n40192277 37957130 22509015 95257198 6210193 16850057\n76289330 265203569 184343840 163207736 126924648\n",
"10 10\n269584761 865524829 265226347 963092340 261501474 16861445 221090297 746538035 842020225 649641719\n49728483 423679832 107851851 179960003 345895125 400584885 460489835 377856735 403077618 676996548\n",
"3 4\n337369924 278848730 18889610\n866361693 732544605 890800310 350303294\n",
"8 8\n808147225 623333304 535665685 469385259 122918604 200681823 800211367 286974812\n14713330 983921829 274028967 567054904 144473212 964018990 177471567 73882806\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 589361337 319325955 938498114 249892107 138299026\n57775135 470751607 454623764 556600014 141039336 225043834 692497485 517610562 635337211 67151601\n",
"10 10\n933168403 308417110 823216696 818565876 448948583 884328249 809244579 473034231 407137956 871269623\n653126539 145998557 644003076 138712151 839886312 479712343 709513279 138285801 858528549 643830064\n",
"20 30\n81 67 100 83 97 97 58 54 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 108 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 64 170 143 143 126 12 175 84\n",
"5 4\n556840201 669601415 674042771 90966172 157280418\n253115131 933556803 294280580 169051325\n",
"6 5\n45936257 8169878 14134346 26323055 65863745 50728147\n997339869 4160924 163305525 839524148 193404120\n",
"5 7\n473347111 640932948 320036306 595696211 151648404\n347859328 553364017 687935743 145411543 689180757 696504973 783694820\n",
"5 6\n284534195 993347068 628813225 512761241 835859363\n61567950 7311163 14322159 70462813 66443161 48573213\n",
"10 10\n510955240 684852706 455356451 284505713 595775142 646334608 563116339 941123613 818750895 516673753\n382626402 204542396 341363992 234231105 75079663 683639780 624391764 265169060 686304227 76939693\n",
"2 2\n888381664 866366630\n170399907 723034416\n",
"10 10\n189739384 981287141 830123412 482457331 77554645 351237238 663827505 549778905 967488359 954617100\n238752550 787656851 393452025 837732771 522417885 876998499 195063055 325140429 546151936 403260186\n",
"6 5\n40192277 37957130 22509015 95257198 6210193 16850057\n76289330 265203569 184343840 282294387 126924648\n",
"2 3\n10 10\n1 1 2\n",
"10 10\n269584761 865524829 265226347 963092340 261501474 16861445 221090297 746538035 842020225 649641719\n49728483 423679832 107851851 301306305 345895125 400584885 460489835 377856735 403077618 676996548\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 589361337 319325955 938498114 271204268 138299026\n57775135 470751607 454623764 556600014 141039336 225043834 692497485 517610562 635337211 67151601\n",
"10 10\n933168403 308417110 823216696 818565876 448948583 884328249 809244579 473034231 407137956 871269623\n1302355559 145998557 644003076 138712151 839886312 479712343 709513279 138285801 858528549 643830064\n",
"20 30\n81 67 100 83 97 97 58 54 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 108 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 64 170 143 143 126 12 175 165\n",
"5 4\n12962215 669601415 674042771 90966172 157280418\n253115131 933556803 294280580 169051325\n",
"5 7\n905166376 640932948 320036306 595696211 151648404\n347859328 553364017 687935743 145411543 689180757 696504973 783694820\n",
"10 10\n510955240 684852706 455356451 284505713 595775142 646334608 563116339 941123613 818750895 516673753\n382626402 395268973 341363992 234231105 75079663 683639780 624391764 265169060 686304227 76939693\n",
"10 10\n189739384 981287141 830123412 482457331 77554645 351237238 663827505 549778905 967488359 954617100\n238752550 787656851 393452025 837732771 522417885 876998499 380725999 325140429 546151936 403260186\n",
"6 5\n40192277 37957130 22509015 95257198 7950428 16850057\n76289330 265203569 184343840 282294387 126924648\n",
"2 3\n10 10\n0 1 2\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 589361337 319325955 938498114 271204268 105888757\n57775135 470751607 454623764 556600014 141039336 225043834 692497485 517610562 635337211 67151601\n",
"10 10\n933168403 308417110 823216696 818565876 448948583 884328249 809244579 473034231 407137956 871269623\n1302355559 145998557 644003076 138712151 839886312 235562434 709513279 138285801 858528549 643830064\n",
"20 30\n81 67 100 83 97 97 58 54 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 108 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 81 170 143 143 126 12 175 165\n",
"5 4\n12962215 669601415 674042771 90966172 157280418\n340301928 933556803 294280580 169051325\n",
"6 5\n45936257 10273743 14134346 26323055 65863745 50728147\n1904649320 4160924 163305525 839524148 193404120\n",
"5 7\n905166376 640932948 97971905 595696211 151648404\n347859328 553364017 687935743 145411543 689180757 696504973 783694820\n",
"10 10\n510955240 684852706 455356451 284505713 595775142 215459005 563116339 941123613 818750895 516673753\n382626402 395268973 341363992 234231105 75079663 683639780 624391764 265169060 686304227 76939693\n",
"10 10\n81598156 981287141 830123412 482457331 77554645 351237238 663827505 549778905 967488359 954617100\n238752550 787656851 393452025 837732771 522417885 876998499 380725999 325140429 546151936 403260186\n",
"6 5\n40192277 37957130 22509015 95257198 7950428 16850057\n57089894 265203569 184343840 282294387 126924648\n",
"2 3\n10 10\n0 1 0\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 589361337 319325955 938498114 271204268 105888757\n57775135 470751607 454623764 556600014 141039336 225043834 853643640 517610562 635337211 67151601\n",
"10 10\n933168403 308417110 823216696 818565876 448948583 884328249 775152756 473034231 407137956 871269623\n1302355559 145998557 644003076 138712151 839886312 235562434 709513279 138285801 858528549 643830064\n",
"20 30\n81 67 100 83 128 97 58 54 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 108 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 81 170 143 143 126 12 175 165\n",
"5 4\n12962215 669601415 674042771 90966172 202082930\n340301928 933556803 294280580 169051325\n",
"6 5\n45936257 10273743 14134346 26323055 65863745 50728147\n1904649320 4160924 163305525 839524148 247355749\n",
"5 7\n905166376 640932948 97971905 595696211 151648404\n347859328 553364017 687935743 145411543 689180757 489370467 783694820\n",
"10 10\n510955240 684852706 455356451 284505713 595775142 86948838 563116339 941123613 818750895 516673753\n382626402 395268973 341363992 234231105 75079663 683639780 624391764 265169060 686304227 76939693\n",
"10 10\n81598156 981287141 830123412 482457331 77554645 351237238 663827505 549778905 967488359 954617100\n238752550 787656851 393452025 459495943 522417885 876998499 380725999 325140429 546151936 403260186\n",
"6 5\n18103190 37957130 22509015 95257198 7950428 16850057\n57089894 265203569 184343840 282294387 126924648\n",
"10 10\n458278487 288667180 648471199 581765640 758405216 1053306108 319325955 938498114 271204268 105888757\n57775135 470751607 454623764 556600014 141039336 225043834 853643640 517610562 635337211 67151601\n",
"10 10\n933168403 308417110 823216696 818565876 448948583 884328249 775152756 473034231 407137956 871269623\n1302355559 188479284 644003076 138712151 839886312 235562434 709513279 138285801 858528549 643830064\n",
"20 30\n81 67 100 83 128 97 58 84 72 78 59 64 55 85 75 58 79 91 64 84\n116 13 114 108 17 123 64 185 170 54 138 142 89 191 78 152 49 5 121 66 163 171 81 170 143 143 126 12 175 165\n",
"5 4\n12962215 669601415 674042771 90966172 202082930\n240658326 933556803 294280580 169051325\n",
"6 5\n45936257 8169878 14134346 26323055 65863745 50728147\n1904649320 4160924 163305525 839524148 193404120\n",
"5 6\n284534195 1227211727 628813225 512761241 835859363\n61567950 7311163 14322159 70462813 66443161 48573213\n"
],
"output": [
"11\n",
"6\n",
"7667769112\n",
"3220361921\n",
"6133464042\n",
"7840004002\n",
"11622500129\n",
"238386210\n",
"556069380\n",
"4628\n",
"1889\n",
"2867533881\n",
"781991027\n",
"40738940\n",
"5515744163\n",
"1479270495\n",
"8854660961\n",
"1149267712\n",
"10329862020\n",
"769741424\n",
"7564110047\n",
"2255628086\n",
"6062961855\n",
"7850896696\n",
"11095759574\n",
"4556\n",
"2865178013\n",
"783181425\n",
"5301917341\n",
"1343402295\n",
"8650608929\n",
"1759800953\n",
"10193450066\n",
"825509558\n",
"8\n",
"7685456349\n",
"7872208857\n",
"11375801438\n",
"4637\n",
"2321300027\n",
"5612265050\n",
"8841335506\n",
"10379113010\n",
"828990028\n",
"6\n",
"7839798588\n",
"11131651529\n",
"4654\n",
"2408486824\n",
"787389155\n",
"5390200649\n",
"8410459903\n",
"10270971782\n",
"809790592\n",
"2\n",
"8000944743\n",
"11097559706\n",
"4685\n",
"2453289336\n",
"807244328\n",
"5183066143\n",
"8281949736\n",
"9892734954\n",
"765612418\n",
"8350081520\n",
"11140040433\n",
"4715\n",
"2353645734\n",
"783181425\n",
"1343402295\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Piegirl was asked to implement two table join operation for distributed database system, minimizing the network traffic.
Suppose she wants to join two tables, A and B. Each of them has certain number of rows which are distributed on different number of partitions. Table A is distributed on the first cluster consisting of m partitions. Partition with index i has ai rows from A. Similarly, second cluster containing table B has n partitions, i-th one having bi rows from B.
In one network operation she can copy one row from any partition to any other partition. At the end, for each row from A and each row from B there should be a partition that has both rows. Determine the minimal number of network operations to achieve this.
Input
First line contains two integer numbers, m and n (1 ≤ m, n ≤ 105). Second line contains description of the first cluster with m space separated integers, ai (1 ≤ ai ≤ 109). Similarly, third line describes second cluster with n space separated integers, bi (1 ≤ bi ≤ 109).
Output
Print one integer — minimal number of copy operations.
Examples
Input
2 2
2 6
3 100
Output
11
Input
2 3
10 10
1 1 1
Output
6
Note
In the first example it makes sense to move all the rows to the second partition of the second cluster which is achieved in 2 + 6 + 3 = 11 operations
In the second example Piegirl can copy each row from B to the both partitions of the first cluster which needs 2·3 = 6 copy operations.
### Input:
2 2
2 6
3 100
### Output:
11
### Input:
2 3
10 10
1 1 1
### Output:
6
### Code:
n, m = list(map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))
A.sort(reverse=True)
B.sort(reverse=True)
sumA = sum(A)
sumB = sum(B)
ansA = sumB
ansB = sumA
for i in range(1, n):
ansA += min(A[i],sumB)
for i in range(1, m):
ansB += min(B[i], sumA)
print(min(ansA,ansB))
|
479_E. Riding in a Lift_28646
|
Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.
Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.
Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).
Input
The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).
Output
Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).
Examples
Input
5 2 4 1
Output
2
Input
5 2 4 2
Output
2
Input
5 3 4 1
Output
0
Note
Two sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.
Notes to the samples:
1. In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|.
2. In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.
3. In the third sample there are no sought sequences, because you cannot choose the floor for the first trip.
|
def solve(n, st, k):
MOD = int(1e9 + 7)
prev = [0] * (n + 1)
current = [0] * (n + 1)
prefix_sum = [0] * (n + 1)
prev[st] = 1
for times in range(k):
prefix_sum[0] = 0
for i in range(1, n + 1):
prefix_sum[i] = prefix_sum[i - 1] + prev[i]
if prefix_sum[i] >= MOD:
prefix_sum[i] -= MOD
for i in range(1, n + 1):
current[i] = prefix_sum[n] - prefix_sum[i >> 1] - prev[i]
while current[i] < 0: current[i] += MOD
while current[i] >= MOD: current[i] -= MOD
prev, current = current, prev
return sum(prev) % MOD
def main():
n, a, b, k = [int(i) for i in input().split()]
if a > b:
print(solve(n - b, a - b, k))
else:
print(solve(b - 1, b - a, k))
main()
|
{
"input": [
"5 3 4 1\n",
"5 2 4 1\n",
"5 2 4 2\n",
"500 1 500 500\n",
"300 300 1 300\n",
"5000 1 5000 5000\n",
"232 195 193 322\n",
"5000 5000 1 5000\n",
"2 2 1 1\n",
"500 499 500 500\n",
"1000 500 1 2000\n",
"3 2 3 1\n",
"300 1 300 300\n",
"500 498 500 499\n",
"500 500 498 5000\n",
"2 1 2 1\n",
"2 1 2 5000\n",
"5000 5000 4999 5000\n",
"5000 2081 3619 5000\n",
"300 299 300 300\n",
"50 5 2 50\n",
"500 500 498 4999\n",
"5000 1 100 3\n",
"100 3 30 5000\n",
"22 9 18 3\n",
"5000 2500 1 5000\n",
"5000 2314 1234 5000\n",
"1000 500 1 1000\n",
"400 11 12 400\n",
"5000 1031 4782 5000\n",
"1000 213 480 1\n",
"4998 2 4 5000\n",
"5000 4998 5000 5000\n",
"5000 1 2500 5000\n",
"2332 2204 558 3722\n",
"50 25 21 50\n",
"2032 1050 1339 2334\n",
"150 150 1 150\n",
"5 1 2 1\n",
"5 3 2 2\n",
"10 1 10 2\n",
"500 436 412 500\n",
"1000 1 500 1000\n",
"222 187 134 500\n",
"100 1 30 500\n",
"50 48 41 2\n",
"10 1 4 4999\n",
"300 300 299 300\n",
"4999 1 2 4999\n",
"5 4 2 1\n",
"5000 100 1 5000\n",
"3999 2 10 5000\n",
"500 498 500 500\n",
"2000 500 1 2000\n",
"443 144 6 223\n",
"4943 944 1747 2213\n",
"4988 3629 4106 4488\n",
"5000 3000 2000 5000\n",
"5000 4999 5000 5000\n",
"5000 2 5000 5000\n",
"232 34 49 234\n",
"488 96 473 488\n",
"10 1 3 4\n",
"5000 1031 4737 5000\n",
"35 9 10 35\n",
"2222 1206 1425 2222\n",
"4999 2500 1 4999\n",
"500 1 500 521\n",
"458 195 193 322\n",
"1000 500 2 2000\n",
"50 5 2 79\n",
"569 500 498 4999\n",
"5000 1 100 5\n",
"22 8 18 3\n",
"5000 3372 1 5000\n",
"5000 697 1234 5000\n",
"1000 500 1 1001\n",
"400 11 12 201\n",
"5000 1196 4782 5000\n",
"1001 213 480 1\n",
"3407 2204 558 3722\n",
"52 25 21 50\n",
"2032 1050 1339 4462\n",
"20 1 10 2\n",
"500 436 412 995\n",
"1000 1 988 1000\n",
"222 208 134 500\n",
"100 1 6 500\n",
"50 48 20 2\n",
"9 1 4 4999\n",
"3999 3 10 5000\n",
"500 498 108 500\n",
"2000 500 1 466\n",
"443 192 6 223\n",
"4943 944 1762 2213\n",
"5000 1345 2000 5000\n",
"5000 1 5000 2189\n",
"232 65 49 234\n",
"840 96 473 488\n",
"35 9 5 35\n",
"4999 2500 2 4999\n",
"458 142 193 322\n",
"1000 120 2 2000\n",
"50 5 2 86\n",
"22 8 18 5\n",
"5000 185 1234 5000\n",
"1000 500 1 1101\n",
"5000 1196 1419 5000\n",
"3407 2204 558 1716\n",
"52 25 5 50\n",
"2032 1050 340 4462\n",
"10 3 2 2\n",
"300 300 299 202\n",
"7 4 2 1\n",
"10 1 3 7\n",
"5 2 1 1\n",
"5 2 1 2\n",
"905 1 500 521\n",
"5000 2 100 5\n",
"400 11 12 108\n"
],
"output": [
"0\n",
"2\n",
"2\n",
"521515914\n",
"396536590\n",
"233993486\n",
"12938181\n",
"233993486\n",
"0\n",
"0\n",
"744846473\n",
"0\n",
"396536590\n",
"113017568\n",
"0\n",
"0\n",
"0\n",
"0\n",
"557114846\n",
"0\n",
"923222599\n",
"0\n",
"483642\n",
"831733342\n",
"1964\n",
"898026985\n",
"546628648\n",
"921282926\n",
"0\n",
"981271392\n",
"478\n",
"2\n",
"701940824\n",
"968861072\n",
"659576072\n",
"317551605\n",
"439644037\n",
"954984546\n",
"0\n",
"0\n",
"44\n",
"724363905\n",
"594673663\n",
"769809644\n",
"627243445\n",
"44\n",
"2\n",
"0\n",
"0\n",
"2\n",
"363556022\n",
"343196694\n",
"973540182\n",
"288043610\n",
"362569369\n",
"12879261\n",
"349016655\n",
"82819894\n",
"0\n",
"233993486\n",
"984852735\n",
"212471726\n",
"0\n",
"917351304\n",
"0\n",
"402572650\n",
"694314934\n",
"114877708\n",
"457178613\n",
"39612085\n",
"426832774\n",
"944509926\n",
"101594622\n",
"1964\n",
"233993486\n",
"217751851\n",
"350139480\n",
"0\n",
"981271392\n",
"478\n",
"298061514\n",
"888035755\n",
"82018442\n",
"44\n",
"872851446\n",
"342630861\n",
"769809644\n",
"718837056\n",
"616\n",
"2\n",
"343196694\n",
"525373178\n",
"495072669\n",
"498217749\n",
"478886423\n",
"946052176\n",
"372801080\n",
"839027175\n",
"212471726\n",
"770378295\n",
"951312587\n",
"43264982\n",
"632823646\n",
"165562285\n",
"215424\n",
"427443322\n",
"670858217\n",
"659951113\n",
"388222744\n",
"949561472\n",
"211216783\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"0\n",
"114877708\n",
"101594622\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.
Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.
Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).
Input
The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).
Output
Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).
Examples
Input
5 2 4 1
Output
2
Input
5 2 4 2
Output
2
Input
5 3 4 1
Output
0
Note
Two sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.
Notes to the samples:
1. In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|.
2. In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.
3. In the third sample there are no sought sequences, because you cannot choose the floor for the first trip.
### Input:
5 3 4 1
### Output:
0
### Input:
5 2 4 1
### Output:
2
### Code:
def solve(n, st, k):
MOD = int(1e9 + 7)
prev = [0] * (n + 1)
current = [0] * (n + 1)
prefix_sum = [0] * (n + 1)
prev[st] = 1
for times in range(k):
prefix_sum[0] = 0
for i in range(1, n + 1):
prefix_sum[i] = prefix_sum[i - 1] + prev[i]
if prefix_sum[i] >= MOD:
prefix_sum[i] -= MOD
for i in range(1, n + 1):
current[i] = prefix_sum[n] - prefix_sum[i >> 1] - prev[i]
while current[i] < 0: current[i] += MOD
while current[i] >= MOD: current[i] -= MOD
prev, current = current, prev
return sum(prev) % MOD
def main():
n, a, b, k = [int(i) for i in input().split()]
if a > b:
print(solve(n - b, a - b, k))
else:
print(solve(b - 1, b - a, k))
main()
|
527_C. Glass Carving_28652
|
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm × h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.
In order not to waste time, he decided to practice the technique of carving. To do this, he makes vertical and horizontal cuts through the entire sheet. This process results in making smaller rectangular fragments of glass. Leonid does not move the newly made glass fragments. In particular, a cut divides each fragment of glass that it goes through into smaller fragments.
After each cut Leonid tries to determine what area the largest of the currently available glass fragments has. Since there appear more and more fragments, this question takes him more and more time and distracts him from the fascinating process.
Leonid offers to divide the labor — he will cut glass, and you will calculate the area of the maximum fragment after each cut. Do you agree?
Input
The first line contains three integers w, h, n (2 ≤ w, h ≤ 200 000, 1 ≤ n ≤ 200 000).
Next n lines contain the descriptions of the cuts. Each description has the form H y or V x. In the first case Leonid makes the horizontal cut at the distance y millimeters (1 ≤ y ≤ h - 1) from the lower edge of the original sheet of glass. In the second case Leonid makes a vertical cut at distance x (1 ≤ x ≤ w - 1) millimeters from the left edge of the original sheet of glass. It is guaranteed that Leonid won't make two identical cuts.
Output
After each cut print on a single line the area of the maximum available glass fragment in mm2.
Examples
Input
4 3 4
H 2
V 2
V 3
V 1
Output
8
4
4
2
Input
7 6 5
H 4
V 3
V 5
H 2
V 1
Output
28
16
12
6
4
Note
Picture for the first sample test:
<image> Picture for the second sample test: <image>
|
w,h,n=map(int,input().split())
l=[-1]*(w+1)
r=[-1]*(w+1)
t=[-1]*(h+1)
b=[-1]*(h+1)
l[0]=0
b[0]=0
t[h]=h
r[w]=w
V=[0]*(n)
H=[0]*(n)
for i in range(n):
line,index=input().split()
index=int(index)
if line=="V":
r[index]=w
V[i]=index
else:
t[index]=h
H[i]=index
left=0
mxw=0
for i in range(1,w+1):
if r[i]!=-1:
l[i]=left
r[left]=i
mxw=max(mxw,i-left)
left=i
bottom=0
mxh=0
for i in range(1,h+1):
if t[i]!=-1:
b[i]=bottom
t[bottom]=i
mxh=max(mxh,i-bottom)
bottom=i
ans=[0]*(n)
ans[n-1]=mxh*mxw
for i in range(n-1,0,-1):
if V[i]!=0:
mxw=max(mxw,r[V[i]]-l[V[i]])
r[l[V[i]]]=r[V[i]]
l[r[V[i]]]=l[V[i]]
else:
mxh=max(mxh,t[H[i]]-b[H[i]])
b[t[H[i]]]=b[H[i]]
t[b[H[i]]]=t[H[i]]
ans[i-1]=mxh*mxw
for i in range(n):
print(ans[i])
|
{
"input": [
"4 3 4\nH 2\nV 2\nV 3\nV 1\n",
"7 6 5\nH 4\nV 3\nV 5\nH 2\nV 1\n",
"5 15 10\nH 8\nH 9\nV 1\nH 2\nH 6\nH 4\nH 1\nV 2\nH 13\nV 3\n",
"200000 200000 1\nH 1\n",
"2 2 2\nH 1\nV 1\n",
"2 2 1\nH 1\n",
"2 2 2\nV 1\nH 1\n",
"2 2 1\nV 1\n",
"2 4 1\nH 2\n",
"15 5 10\nV 13\nV 10\nV 3\nH 2\nV 9\nV 7\nV 2\nH 1\nV 4\nH 3\n",
"10 10 10\nV 6\nH 8\nV 4\nV 8\nH 2\nH 5\nV 9\nH 7\nH 3\nV 7\n",
"2 3 1\nH 1\n",
"200000 108415 1\nH 1\n",
"3 2 1\nH 1\n",
"2 6 1\nH 2\n",
"2 3 1\nH 2\n",
"200000 108415 1\nH 2\n",
"5 15 10\nH 8\nH 9\nV 1\nH 2\nH 6\nH 3\nH 1\nV 2\nH 13\nV 3\n",
"2 3 2\nV 1\nH 1\n",
"4 2 1\nV 1\n",
"200000 88688 1\nH 1\n",
"3 3 2\nV 1\nH 1\n",
"5 15 10\nH 8\nH 10\nV 1\nH 2\nH 6\nH 4\nH 1\nV 2\nH 13\nV 3\n",
"5 2 1\nH 1\n",
"2 12 1\nH 2\n",
"200000 160942 1\nH 1\n",
"4 12 1\nH 2\n",
"4 15 1\nH 2\n",
"200000 200000 1\nH 2\n",
"4 2 2\nH 1\nV 1\n",
"10 10 10\nV 6\nH 8\nV 3\nV 8\nH 2\nH 5\nV 9\nH 7\nH 3\nV 7\n",
"7 6 5\nH 5\nV 3\nV 5\nH 2\nV 1\n",
"4 6 1\nH 2\n",
"200000 98691 1\nH 2\n",
"9 2 1\nH 1\n",
"4 13 1\nH 2\n",
"4 24 1\nH 2\n",
"200000 55054 1\nH 2\n",
"4 3 2\nH 1\nV 1\n",
"4 4 1\nH 1\n",
"200000 98691 1\nH 4\n",
"5 30 10\nH 8\nH 9\nV 1\nH 2\nH 5\nH 3\nH 1\nV 2\nH 13\nV 3\n",
"4 10 1\nH 2\n",
"4 24 1\nH 1\n",
"174568 55054 1\nH 2\n",
"7 4 1\nH 1\n",
"200000 98691 1\nH 7\n",
"7 7 1\nH 1\n",
"3 7 1\nH 2\n",
"6 7 1\nH 1\n",
"2 4 1\nH 1\n",
"4 2 1\nH 1\n",
"6 2 1\nH 1\n",
"4 3 1\nH 1\n",
"3 3 1\nH 1\n",
"5 15 10\nH 8\nH 9\nV 1\nH 2\nH 5\nH 3\nH 1\nV 2\nH 13\nV 3\n",
"3 6 1\nH 2\n",
"4 7 1\nH 2\n"
],
"output": [
"8\n4\n4\n2\n",
"28\n16\n12\n6\n4\n",
"40\n40\n32\n24\n24\n24\n24\n18\n12\n8\n",
"39999800000\n",
"2\n1\n",
"2\n",
"2\n1\n",
"2\n",
"4\n",
"65\n50\n35\n21\n18\n12\n12\n12\n9\n6\n",
"60\n48\n32\n32\n24\n12\n12\n12\n8\n8\n",
"4\n",
"21682800000\n",
"3\n",
"8\n",
"4\n",
"21682600000\n",
"40\n40\n32\n24\n24\n24\n24\n18\n12\n8\n",
"3\n2\n",
"6\n",
"17737400000\n",
"6\n4\n",
"40\n40\n32\n24\n20\n20\n20\n15\n9\n6\n",
"5\n",
"20\n",
"32188200000\n",
"40\n",
"52\n",
"39999600000\n",
"4\n3\n",
"60\n48\n32\n24\n18\n9\n9\n9\n6\n6\n",
"35\n20\n15\n9\n6\n",
"16\n",
"19737800000\n",
"9\n",
"44\n",
"88\n",
"11010400000\n",
"8\n6\n",
"12\n",
"19737400000\n",
"110\n105\n84\n84\n84\n84\n84\n63\n51\n34\n",
"32\n",
"92\n",
"9610317536\n",
"21\n",
"19736800000\n",
"42\n",
"15\n",
"36\n",
"6\n",
"4\n",
"6\n",
"8\n",
"6\n",
"40\n40\n32\n24\n24\n24\n24\n18\n12\n8\n",
"12\n",
"20\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm × h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.
In order not to waste time, he decided to practice the technique of carving. To do this, he makes vertical and horizontal cuts through the entire sheet. This process results in making smaller rectangular fragments of glass. Leonid does not move the newly made glass fragments. In particular, a cut divides each fragment of glass that it goes through into smaller fragments.
After each cut Leonid tries to determine what area the largest of the currently available glass fragments has. Since there appear more and more fragments, this question takes him more and more time and distracts him from the fascinating process.
Leonid offers to divide the labor — he will cut glass, and you will calculate the area of the maximum fragment after each cut. Do you agree?
Input
The first line contains three integers w, h, n (2 ≤ w, h ≤ 200 000, 1 ≤ n ≤ 200 000).
Next n lines contain the descriptions of the cuts. Each description has the form H y or V x. In the first case Leonid makes the horizontal cut at the distance y millimeters (1 ≤ y ≤ h - 1) from the lower edge of the original sheet of glass. In the second case Leonid makes a vertical cut at distance x (1 ≤ x ≤ w - 1) millimeters from the left edge of the original sheet of glass. It is guaranteed that Leonid won't make two identical cuts.
Output
After each cut print on a single line the area of the maximum available glass fragment in mm2.
Examples
Input
4 3 4
H 2
V 2
V 3
V 1
Output
8
4
4
2
Input
7 6 5
H 4
V 3
V 5
H 2
V 1
Output
28
16
12
6
4
Note
Picture for the first sample test:
<image> Picture for the second sample test: <image>
### Input:
4 3 4
H 2
V 2
V 3
V 1
### Output:
8
4
4
2
### Input:
7 6 5
H 4
V 3
V 5
H 2
V 1
### Output:
28
16
12
6
4
### Code:
w,h,n=map(int,input().split())
l=[-1]*(w+1)
r=[-1]*(w+1)
t=[-1]*(h+1)
b=[-1]*(h+1)
l[0]=0
b[0]=0
t[h]=h
r[w]=w
V=[0]*(n)
H=[0]*(n)
for i in range(n):
line,index=input().split()
index=int(index)
if line=="V":
r[index]=w
V[i]=index
else:
t[index]=h
H[i]=index
left=0
mxw=0
for i in range(1,w+1):
if r[i]!=-1:
l[i]=left
r[left]=i
mxw=max(mxw,i-left)
left=i
bottom=0
mxh=0
for i in range(1,h+1):
if t[i]!=-1:
b[i]=bottom
t[bottom]=i
mxh=max(mxh,i-bottom)
bottom=i
ans=[0]*(n)
ans[n-1]=mxh*mxw
for i in range(n-1,0,-1):
if V[i]!=0:
mxw=max(mxw,r[V[i]]-l[V[i]])
r[l[V[i]]]=r[V[i]]
l[r[V[i]]]=l[V[i]]
else:
mxh=max(mxh,t[H[i]]-b[H[i]])
b[t[H[i]]]=b[H[i]]
t[b[H[i]]]=t[H[i]]
ans[i-1]=mxh*mxw
for i in range(n):
print(ans[i])
|
553_A. Kyoya and Colored Balls_28656
|
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen.
Input
The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.
Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).
The total number of balls doesn't exceed 1000.
Output
A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.
Examples
Input
3
2
2
1
Output
3
Input
4
1
2
3
4
Output
1680
Note
In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:
1 2 1 2 3
1 1 2 2 3
2 1 1 2 3
|
#!/usr/bin/python3
import sys
from functools import lru_cache
MOD = 1000000007
cnk = [[1 for i in range(1001)] for j in range(1001)]
for i in range(1, 1001):
for j in range(1, i):
cnk[i][j] = cnk[i - 1][j - 1] + cnk[i - 1][j]
k = int(input())
cs = [int(input()) for i in range(k)]
ans = 1
sm = 0
for c in cs:
sm += c
ans = (ans * cnk[sm - 1][c - 1]) % MOD
print(ans)
|
{
"input": [
"4\n1\n2\n3\n4\n",
"3\n2\n2\n1\n",
"1\n5\n",
"10\n100\n100\n100\n100\n100\n100\n100\n100\n100\n100\n",
"25\n35\n43\n38\n33\n47\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"5\n10\n10\n10\n10\n10\n",
"1\n1\n",
"11\n291\n381\n126\n39\n19\n20\n3\n1\n20\n45\n2\n",
"13\n67\n75\n76\n80\n69\n86\n75\n86\n81\n84\n73\n72\n76\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n22\n26\n24\n17\n18\n21\n22\n21\n23\n17\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"3\n343\n317\n337\n",
"1\n3\n",
"25\n35\n43\n38\n33\n47\n44\n40\n36\n41\n42\n33\n30\n49\n42\n36\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"5\n10\n10\n10\n10\n17\n",
"11\n291\n381\n126\n39\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n75\n86\n81\n84\n73\n72\n76\n",
"4\n1\n2\n3\n2\n",
"11\n291\n381\n126\n66\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n81\n84\n73\n72\n76\n",
"4\n1\n4\n3\n2\n",
"11\n291\n381\n126\n66\n23\n20\n6\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n81\n84\n73\n99\n76\n",
"4\n1\n4\n6\n2\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n81\n84\n19\n99\n76\n",
"4\n1\n4\n6\n3\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n116\n84\n19\n99\n76\n",
"4\n1\n3\n6\n3\n",
"13\n67\n5\n76\n151\n69\n86\n61\n86\n116\n84\n19\n99\n76\n",
"13\n67\n5\n76\n151\n69\n33\n61\n86\n116\n84\n19\n99\n76\n",
"13\n67\n5\n76\n151\n69\n33\n61\n86\n116\n84\n30\n99\n76\n",
"25\n35\n43\n38\n33\n47\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n13\n",
"5\n10\n10\n10\n10\n2\n",
"11\n166\n381\n126\n39\n19\n20\n3\n1\n20\n45\n2\n",
"13\n53\n75\n76\n80\n69\n86\n75\n86\n81\n84\n73\n72\n76\n",
"3\n318\n317\n337\n",
"3\n2\n3\n1\n",
"25\n35\n43\n38\n33\n47\n44\n40\n52\n41\n42\n33\n30\n49\n42\n36\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"5\n10\n11\n10\n10\n17\n",
"11\n291\n381\n36\n39\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n75\n86\n81\n84\n73\n18\n76\n",
"4\n1\n2\n2\n2\n",
"11\n291\n381\n38\n66\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n81\n84\n36\n72\n76\n",
"11\n291\n381\n6\n66\n23\n20\n6\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n51\n61\n86\n81\n84\n73\n99\n76\n",
"4\n2\n4\n6\n2\n",
"13\n67\n5\n76\n80\n20\n86\n61\n86\n81\n84\n19\n99\n76\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n116\n84\n19\n73\n76\n",
"4\n1\n5\n6\n3\n",
"13\n67\n5\n76\n151\n69\n86\n61\n86\n116\n84\n19\n64\n76\n",
"13\n67\n5\n76\n151\n69\n33\n91\n86\n116\n84\n19\n99\n76\n",
"13\n67\n5\n76\n160\n69\n33\n61\n86\n116\n84\n30\n99\n76\n",
"25\n35\n43\n38\n33\n47\n55\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n13\n",
"5\n2\n10\n10\n10\n2\n",
"11\n166\n381\n126\n39\n19\n20\n3\n1\n30\n45\n2\n",
"3\n318\n33\n337\n",
"3\n2\n6\n1\n",
"5\n10\n18\n10\n10\n17\n",
"11\n291\n381\n36\n48\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n75\n86\n81\n161\n73\n18\n76\n",
"4\n2\n2\n2\n2\n",
"11\n291\n381\n38\n66\n23\n40\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n61\n86\n81\n84\n37\n72\n76\n",
"13\n67\n5\n76\n80\n69\n51\n61\n86\n81\n84\n102\n99\n76\n",
"4\n2\n3\n6\n2\n",
"13\n67\n5\n96\n80\n20\n86\n61\n86\n81\n84\n19\n99\n76\n",
"13\n67\n5\n35\n80\n69\n86\n61\n86\n116\n84\n19\n73\n76\n",
"13\n67\n5\n76\n151\n69\n86\n61\n86\n116\n103\n19\n64\n76\n",
"13\n67\n5\n76\n151\n69\n33\n91\n86\n129\n84\n19\n99\n76\n",
"25\n35\n43\n38\n33\n47\n55\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n39\n13\n",
"5\n2\n4\n10\n10\n2\n",
"3\n318\n33\n180\n",
"3\n2\n10\n1\n",
"5\n10\n28\n10\n10\n17\n",
"11\n291\n381\n3\n48\n23\n20\n3\n1\n20\n45\n2\n",
"13\n67\n5\n76\n80\n69\n86\n75\n86\n35\n161\n73\n18\n76\n",
"4\n2\n2\n4\n2\n",
"11\n291\n381\n16\n66\n23\n40\n3\n1\n20\n45\n2\n",
"13\n31\n5\n76\n80\n69\n86\n61\n86\n81\n84\n37\n72\n76\n",
"13\n67\n5\n76\n80\n69\n51\n61\n86\n81\n84\n102\n99\n93\n",
"4\n2\n6\n6\n2\n",
"13\n68\n5\n96\n80\n20\n86\n61\n86\n81\n84\n19\n99\n76\n",
"13\n67\n5\n35\n80\n69\n138\n61\n86\n116\n84\n19\n73\n76\n",
"13\n67\n5\n76\n151\n69\n86\n61\n86\n116\n103\n19\n64\n50\n",
"25\n35\n43\n38\n33\n47\n55\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n21\n42\n46\n42\n39\n13\n",
"5\n2\n4\n12\n10\n2\n",
"3\n305\n33\n180\n",
"3\n2\n10\n2\n",
"5\n10\n28\n10\n10\n15\n",
"3\n2\n1\n1\n",
"1\n2\n",
"1\n4\n",
"1\n6\n",
"1\n7\n"
],
"output": [
"1680\n",
"3\n",
"1\n",
"12520708\n",
"362689152\n",
"425711769\n",
"1\n",
"902382672\n",
"232242896\n",
"295545118\n",
"691446102\n",
"1\n",
"997961972\n",
"741776646\n",
"561962362\n",
"872636499\n",
"140\n",
"957968984\n",
"882010690\n",
"756\n",
"734734213\n",
"248017518\n",
"12096\n",
"67616577\n",
"78624\n",
"906113884\n",
"24948\n",
"410366722\n",
"200911746\n",
"864842422\n",
"78820644\n",
"75782637\n",
"236575578\n",
"269600365\n",
"462623218\n",
"6\n",
"15644367\n",
"200406298\n",
"215626521\n",
"231144888\n",
"48\n",
"296218359\n",
"69577029\n",
"566019161\n",
"667966130\n",
"60060\n",
"395962938\n",
"868686169\n",
"210210\n",
"571867598\n",
"864580062\n",
"398529333\n",
"289252420\n",
"207935858\n",
"71126029\n",
"794427986\n",
"21\n",
"237550644\n",
"33733705\n",
"295312122\n",
"105\n",
"776448978\n",
"421970440\n",
"986468588\n",
"18144\n",
"699726491\n",
"238112626\n",
"988951103\n",
"656673519\n",
"795647390\n",
"774246930\n",
"609120060\n",
"55\n",
"900560572\n",
"526774893\n",
"579369431\n",
"945\n",
"75386802\n",
"839484998\n",
"106624056\n",
"405405\n",
"53320218\n",
"486830189\n",
"699384957\n",
"451426514\n",
"202280253\n",
"59672446\n",
"715\n",
"645711692\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen.
Input
The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.
Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).
The total number of balls doesn't exceed 1000.
Output
A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.
Examples
Input
3
2
2
1
Output
3
Input
4
1
2
3
4
Output
1680
Note
In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:
1 2 1 2 3
1 1 2 2 3
2 1 1 2 3
### Input:
4
1
2
3
4
### Output:
1680
### Input:
3
2
2
1
### Output:
3
### Code:
#!/usr/bin/python3
import sys
from functools import lru_cache
MOD = 1000000007
cnk = [[1 for i in range(1001)] for j in range(1001)]
for i in range(1, 1001):
for j in range(1, i):
cnk[i][j] = cnk[i - 1][j - 1] + cnk[i - 1][j]
k = int(input())
cs = [int(input()) for i in range(k)]
ans = 1
sm = 0
for c in cs:
sm += c
ans = (ans * cnk[sm - 1][c - 1]) % MOD
print(ans)
|
579_F. LCS Again_28659
|
You are given a string S of length n with each character being one of the first m lowercase English letters.
Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.
Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.
Input
The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).
The second line contains string S.
Output
Print the only line containing the answer.
Examples
Input
3 3
aaa
Output
6
Input
3 3
aab
Output
11
Input
1 2
a
Output
1
Input
10 9
abacadefgh
Output
789
Note
For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa.
For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.
For the third sample, the only possible string T is b.
|
def main():
n, m = map(int, input().split())
s = input()
k = sum(s[i] != s[i - 1] for i in range(1, n)) + 1
x = i = 0
while i < n - 1:
if s[i] != s[i + 1]:
j = i
while i + 2 < n and s[i] == s[i + 2]:
i += 1
j = (i - j) + 2
x += j * (j - 1) // 2
i += 1
ans = k * (m * n - n) - x
print(ans)
main()
|
{
"input": [
"3 3\naaa\n",
"10 9\nabacadefgh\n",
"1 2\na\n",
"3 3\naab\n",
"1 26\nz\n",
"100 26\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnefzmqlvtvqqfbfsf\n",
"15 3\nabababababababa\n",
"100 27\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnefzmqlvtvqqfbfsf\n",
"3 6\naab\n",
"10 14\nabacadefgh\n",
"1 2\nb\n",
"3 12\naab\n",
"10 16\nabacadefgh\n",
"1 3\nb\n",
"10 18\nabacadefgh\n",
"10 9\nabacadefhg\n",
"3 2\naab\n",
"3 19\naab\n",
"10 16\nabacadeegh\n",
"10 10\nabacadefgh\n",
"10 19\nhgfedacaba\n",
"3 29\naab\n",
"10 29\nabacadeegh\n",
"10 8\nhgfedacaba\n",
"10 10\naeacacbfgh\n",
"1 26\ny\n",
"100 30\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnefzmqlvtvqqfbfsf\n",
"15 6\nabababababababa\n",
"10 11\nabacadefgh\n",
"100 27\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnffzmqlvtvqqfbfsf\n",
"10 14\nabadadefgh\n",
"1 1\na\n",
"3 10\naab\n",
"10 14\nbbacadefgh\n",
"3 36\naab\n",
"10 8\nabacadeegh\n",
"1 5\nc\n",
"10 21\nhgfedacaba\n",
"3 41\naab\n",
"15 3\nababababababaca\n",
"10 18\nabadadefgh\n",
"15 3\naaabababababaca\n",
"3 14\nbaa\n",
"10 21\nabacadefhh\n",
"10 8\naaacadeffh\n",
"3 13\nbaa\n",
"10 8\nhcfedafaaa\n",
"3 11\ndaa\n",
"3 9\ndaa\n",
"100 34\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnefzmqlvtvqqfbfsf\n",
"3 3\nbab\n",
"3 2\naba\n",
"3 35\naab\n",
"10 16\nabacbdeegh\n",
"10 30\nhgfedacaba\n",
"3 50\naab\n",
"10 29\nabacadedgh\n",
"1 36\ny\n",
"3 8\naab\n",
"10 19\nbbacadefgh\n",
"3 37\nbaa\n",
"10 33\nabacadefgh\n",
"10 24\nhgfedadaba\n",
"3 14\naaa\n",
"3 2\naaa\n",
"10 24\nabacbdeegh\n",
"10 30\nggfedacaba\n",
"10 29\nabacbdedgh\n",
"10 22\nhgfedadaba\n",
"3 9\naaa\n",
"3 4\naaa\n",
"10 22\nabacbdeegh\n",
"3 43\ncaa\n",
"10 13\nhgfedadaba\n",
"3 4\nbaa\n",
"10 22\nababbdeegh\n",
"10 13\nggfedacaba\n",
"10 30\nababbdeegh\n",
"10 13\nggfedacaca\n",
"10 16\nigfedadaba\n",
"10 13\nggfedadaca\n",
"3 43\naaa\n",
"3 25\naaa\n",
"3 15\naaa\n",
"3 7\naaa\n",
"3 5\naab\n",
"10 22\nabacadefgh\n",
"10 14\nhgfedacaaa\n",
"3 49\naab\n",
"15 9\nabababababababa\n",
"10 11\nabacacefgh\n",
"100 35\njysrixyptvsesnapfljeqkytlpeepjopspmkviqdqbdkylvfiawhdjjdvqqvcjmmsgfdmpjwahuwhgsyfcgnffzmqlvtvqqfbfsf\n",
"3 23\naab\n",
"10 18\nhgfedadaaa\n",
"10 21\nbaacadefhh\n",
"10 10\nhffedacaaa\n",
"10 8\nhcfedfaaaa\n",
"3 13\ndba\n",
"10 9\nhgfedacabb\n",
"10 16\nabbcbdeegh\n",
"10 35\nbbacadefgh\n",
"3 26\naab\n",
"10 24\nggfedadaba\n",
"10 42\nabacbdeegh\n",
"10 40\nggfedacaba\n",
"3 45\ncaa\n",
"10 34\nabadadefgh\n"
],
"output": [
"6\n",
"789\n",
"1\n",
"11\n",
"25\n",
"237400\n",
"345\n",
"246900\n",
"29\n",
"1289\n",
"1\n",
"65\n",
"1489\n",
"2\n",
"1689\n",
"789\n",
"5\n",
"107\n",
"1340\n",
"889\n",
"1789\n",
"167\n",
"2510\n",
"689\n",
"887\n",
"25\n",
"275400\n",
"1020\n",
"989\n",
"244301\n",
"1287\n",
"0\n",
"53\n",
"1161\n",
"209\n",
"620\n",
"4\n",
"1989\n",
"239\n",
"369\n",
"1687\n",
"332\n",
"77\n",
"1790\n",
"483\n",
"71\n",
"552\n",
"59\n",
"47\n",
"313400\n",
"15\n",
"6\n",
"203\n",
"1341\n",
"2889\n",
"293\n",
"2788\n",
"35\n",
"41\n",
"1611\n",
"215\n",
"3189\n",
"2287\n",
"39\n",
"3\n",
"2061\n",
"2600\n",
"2789\n",
"2087\n",
"24\n",
"9\n",
"1881\n",
"251\n",
"1187\n",
"17\n",
"1670\n",
"1070\n",
"2310\n",
"1066\n",
"1487\n",
"1068\n",
"126\n",
"72\n",
"42\n",
"18\n",
"23\n",
"2089\n",
"1032\n",
"287\n",
"1695\n",
"987\n",
"319501\n",
"131\n",
"1350\n",
"1592\n",
"623\n",
"484\n",
"106\n",
"711\n",
"1192\n",
"3051\n",
"149\n",
"2058\n",
"3681\n",
"3500\n",
"263\n",
"3287\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a string S of length n with each character being one of the first m lowercase English letters.
Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.
Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.
Input
The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).
The second line contains string S.
Output
Print the only line containing the answer.
Examples
Input
3 3
aaa
Output
6
Input
3 3
aab
Output
11
Input
1 2
a
Output
1
Input
10 9
abacadefgh
Output
789
Note
For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa.
For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.
For the third sample, the only possible string T is b.
### Input:
3 3
aaa
### Output:
6
### Input:
10 9
abacadefgh
### Output:
789
### Code:
def main():
n, m = map(int, input().split())
s = input()
k = sum(s[i] != s[i - 1] for i in range(1, n)) + 1
x = i = 0
while i < n - 1:
if s[i] != s[i + 1]:
j = i
while i + 2 < n and s[i] == s[i + 2]:
i += 1
j = (i - j) + 2
x += j * (j - 1) // 2
i += 1
ans = k * (m * n - n) - x
print(ans)
main()
|
600_E. Lomsat gelral_28661
|
You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.
Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree of some vertex.
The subtree of vertex v is the vertex v and all other vertices that contains vertex v in each path to the root.
For each vertex v find the sum of all dominating colours in the subtree of vertex v.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of vertices in the tree.
The second line contains n integers ci (1 ≤ ci ≤ n), ci — the colour of the i-th vertex.
Each of the next n - 1 lines contains two integers xj, yj (1 ≤ xj, yj ≤ n) — the edge of the tree. The first vertex is the root of the tree.
Output
Print n integers — the sums of dominating colours for each vertex.
Examples
Input
4
1 2 3 4
1 2
2 3
2 4
Output
10 9 3 4
Input
15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13
Output
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
|
import sys
input = sys.stdin.buffer.readline
class SegmentTree:
def __init__(self, n, op, e):
self.n = n
self.op = op
self.e = e
self.size = 2 ** ((n - 1).bit_length())
self.node = [self.e] * (2 * self.size)
def __getitem__(self, i):
return self.node[i + self.size]
def __setitem__(self, i, val):
i += self.size
self.node[i] = val
while i > 1:
i >>= 1
self.node[i] = self.op(self.node[i << 1], self.node[(i << 1) + 1])
def build(self, array):
for i, val in enumerate(array, self.size):
self.node[i] = val
for i in range(self.size - 1, 0, -1):
self.node[i] = self.op(self.node[i << 1], self.node[(i << 1) + 1])
def all_fold(self):
return self.node[1]
def fold(self, l, r):
l, r = l + self.size, r + self.size
vl, vr = self.e, self.e
while l < r:
if l & 1:
vl = self.op(vl, self.node[l])
l += 1
if r & 1:
r -= 1
vr = self.op(self.node[r], vr)
l, r = l >> 1, r >> 1
return self.op(vl, vr)
def topological_sorted(tree, root=None):
n = len(tree)
par = [-1] * n
tp_order = []
for v in range(n):
if par[v] != -1 or (root is not None and v != root):
continue
stack = [v]
while stack:
v = stack.pop()
tp_order.append(v)
for nxt_v in tree[v]:
if nxt_v == par[v]:
continue
par[nxt_v] = v
stack.append(nxt_v)
return tp_order, par
def dsu_on_tree(tree, root):
n = len(tree)
tp_order, par = topological_sorted(tree, root)
# 有向木の構築
di_tree = [[] for i in range(n)]
for v in range(n):
for nxt_v in tree[v]:
if nxt_v == par[v]:
continue
di_tree[v].append(nxt_v)
# 部分木サイズの計算
sub_size = [1] * n
for v in tp_order[::-1]:
for nxt_v in di_tree[v]:
sub_size[v] += sub_size[nxt_v]
# 有向木のDFS行きがけ順の構築
di_tree = [sorted(tr, key=lambda v: sub_size[v]) for tr in di_tree]
keeps = [0] * n
for v in range(n):
di_tree[v] = di_tree[v][:-1][::-1] + di_tree[v][-1:]
for chi_v in di_tree[v][:-1]:
keeps[chi_v] = 1
tp_order, _ = topological_sorted(di_tree, root)
# 加算もしくは減算の実行
# counts = {}
def add(sub_root, val):
stack = [sub_root]
while stack:
v = stack.pop()
vals = st[colors[v]]
st[colors[v]] = (vals[0] + val, vals[1])
# counts[colors[v]] = counts.get(colors[v], 0) + val
for chi_v in di_tree[v]:
stack.append(chi_v)
# 有向木のDFS帰りがけ順で処理
for v in tp_order[::-1]:
for chi_v in di_tree[v]:
if keeps[chi_v] == 1:
add(chi_v, 1)
# ここでクエリを実行する
vals = st[colors[v]]
st[colors[v]] = (vals[0] + 1, vals[1])
# counts[colors[v]] = counts.get(colors[v], 0) + 1
ans[v] = st.all_fold()[1]
if keeps[v] == 1:
add(v, -1)
n = int(input())
colors = list(map(int, input().split()))
edges = [list(map(int, input().split())) for i in range(n - 1)]
tree = [[] for i in range(n)]
for u, v in edges:
u -= 1
v -= 1
tree[u].append(v)
tree[v].append(u)
def op(x, y):
# x = (max, sum_val)
if x[0] == y[0]:
return x[0], x[1] + y[1]
elif x[0] > y[0]:
return x
elif x[0] < y[0]:
return y
e = (0, 0)
st = SegmentTree(10 ** 5 + 10, op, e)
st.build([(0, i) for i in range(10 ** 5 + 10)])
ans = [0] * n
dsu_on_tree(tree, 0)
print(*ans)
|
{
"input": [
"4\n1 2 3 4\n1 2\n2 3\n2 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n3 10\n4 11\n4 12\n4 13\n",
"4\n1 2 3 4\n1 2\n2 3\n1 4\n",
"4\n2 2 3 4\n1 2\n2 3\n2 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n3 10\n4 11\n5 12\n4 13\n",
"4\n1 2 3 4\n1 2\n1 3\n1 4\n",
"4\n3 2 3 4\n1 2\n2 3\n2 4\n",
"4\n1 2 3 4\n1 2\n1 3\n2 4\n",
"4\n1 2 1 4\n1 2\n1 3\n2 4\n",
"4\n1 2 1 4\n1 2\n1 3\n1 4\n",
"4\n1 2 3 3\n1 2\n2 3\n1 4\n",
"4\n2 2 3 3\n1 2\n2 3\n2 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n4 10\n4 11\n5 12\n4 13\n",
"4\n1 2 1 4\n1 2\n2 3\n2 4\n",
"4\n1 4 3 3\n1 2\n2 3\n1 4\n",
"15\n1 2 1 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n4 10\n4 11\n5 12\n4 13\n",
"4\n2 2 3 2\n1 2\n2 3\n2 4\n",
"4\n1 3 3 4\n1 2\n1 3\n1 4\n",
"4\n3 1 3 4\n1 2\n2 3\n2 4\n",
"4\n1 2 2 4\n1 2\n1 3\n1 4\n",
"4\n1 2 3 3\n1 2\n2 3\n2 4\n",
"15\n2 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n4 10\n4 11\n5 12\n4 13\n",
"4\n1 2 1 1\n1 2\n2 3\n2 4\n",
"4\n1 1 3 4\n1 2\n1 3\n1 4\n",
"4\n3 1 3 4\n1 3\n2 3\n2 4\n",
"4\n1 3 2 4\n1 2\n1 3\n1 4\n",
"4\n1 1 3 4\n1 2\n2 3\n1 4\n",
"4\n3 1 3 4\n1 4\n2 3\n2 4\n",
"4\n1 2 4 4\n1 2\n2 3\n1 4\n",
"4\n1 4 3 4\n1 2\n2 3\n1 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n2 15\n2 5\n2 6\n2 7\n3 8\n3 9\n4 10\n4 11\n5 12\n4 13\n",
"4\n3 1 3 4\n1 4\n4 3\n2 4\n",
"4\n1 4 3 4\n1 2\n2 3\n2 4\n",
"4\n1 4 3 1\n1 2\n2 3\n2 4\n",
"4\n1 1 3 4\n1 2\n2 3\n2 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n3 10\n7 11\n4 12\n4 13\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n3 10\n4 11\n8 12\n4 13\n",
"4\n1 1 1 4\n1 2\n1 3\n1 4\n",
"4\n1 1 3 3\n1 2\n2 3\n1 4\n",
"4\n2 2 3 2\n1 2\n4 3\n2 4\n",
"4\n3 1 3 1\n1 2\n2 3\n2 4\n",
"15\n2 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n1 15\n2 5\n2 6\n2 7\n3 8\n3 9\n4 10\n4 11\n1 12\n4 13\n",
"4\n1 2 1 1\n1 2\n2 3\n1 4\n",
"4\n1 1 3 1\n1 2\n1 3\n1 4\n",
"4\n1 3 2 4\n1 2\n2 3\n1 4\n",
"4\n3 1 3 1\n1 4\n2 3\n2 4\n",
"4\n4 2 3 3\n1 2\n2 3\n2 4\n",
"4\n1 3 3 3\n1 2\n2 3\n1 4\n",
"4\n2 2 3 2\n1 2\n1 3\n2 4\n",
"4\n1 3 3 3\n1 3\n2 3\n1 4\n",
"4\n1 2 3 2\n1 2\n1 3\n2 4\n",
"15\n1 2 3 1 2 3 3 1 1 3 2 2 1 2 3\n1 2\n1 3\n1 4\n1 14\n2 15\n2 5\n2 6\n3 7\n3 8\n3 9\n4 10\n4 11\n5 12\n4 13\n"
],
"output": [
"10 9 3 4 \n",
"6 5 4 3 2 3 3 1 1 3 2 2 1 2 3 \n",
"10 5 3 4\n",
"2 9 3 4\n",
"6 2 4 1 2 3 3 1 1 3 2 2 1 2 3\n",
"10 2 3 4\n",
"3 9 3 4\n",
"10 6 3 4\n",
"1 6 1 4\n",
"1 2 1 4\n",
"3 5 3 3\n",
"5 3 3 3\n",
"6 2 1 1 2 3 3 1 1 3 2 2 1 2 3\n",
"1 7 1 4\n",
"3 7 3 3\n",
"1 2 1 1 2 3 3 1 1 3 2 2 1 2 3\n",
"2 2 3 2\n",
"3 3 3 4\n",
"3 8 3 4\n",
"2 2 2 4\n",
"3 3 3 3\n",
"2 2 1 1 2 3 3 1 1 3 2 2 1 2 3\n",
"1 1 1 1\n",
"1 1 3 4\n",
"3 5 8 4\n",
"10 3 2 4\n",
"1 4 3 4\n",
"3 4 3 8\n",
"4 6 4 4\n",
"4 7 3 4\n",
"6 5 1 1 2 3 3 1 1 3 2 2 1 2 3\n",
"3 1 3 8\n",
"4 4 3 4\n",
"1 8 3 1\n",
"1 8 3 4\n",
"6 2 4 1 2 3 5 1 1 3 2 2 1 2 3\n",
"6 5 4 1 2 3 3 3 1 3 2 2 1 2 3\n",
"1 1 1 4\n",
"4 4 3 3\n",
"2 2 3 5\n",
"4 1 3 1\n",
"2 5 1 1 2 3 3 1 1 3 2 2 1 2 3\n",
"1 3 1 1\n",
"1 1 3 1\n",
"10 5 2 4\n",
"4 4 3 1\n",
"3 3 3 3\n",
"3 3 3 3\n",
"2 2 3 2\n",
"3 3 3 3\n",
"2 2 3 2\n",
"6 2 4 1 2 3 3 1 1 3 2 2 1 2 3\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.
Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree of some vertex.
The subtree of vertex v is the vertex v and all other vertices that contains vertex v in each path to the root.
For each vertex v find the sum of all dominating colours in the subtree of vertex v.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of vertices in the tree.
The second line contains n integers ci (1 ≤ ci ≤ n), ci — the colour of the i-th vertex.
Each of the next n - 1 lines contains two integers xj, yj (1 ≤ xj, yj ≤ n) — the edge of the tree. The first vertex is the root of the tree.
Output
Print n integers — the sums of dominating colours for each vertex.
Examples
Input
4
1 2 3 4
1 2
2 3
2 4
Output
10 9 3 4
Input
15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13
Output
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
### Input:
4
1 2 3 4
1 2
2 3
2 4
### Output:
10 9 3 4
### Input:
15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13
### Output:
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
### Code:
import sys
input = sys.stdin.buffer.readline
class SegmentTree:
def __init__(self, n, op, e):
self.n = n
self.op = op
self.e = e
self.size = 2 ** ((n - 1).bit_length())
self.node = [self.e] * (2 * self.size)
def __getitem__(self, i):
return self.node[i + self.size]
def __setitem__(self, i, val):
i += self.size
self.node[i] = val
while i > 1:
i >>= 1
self.node[i] = self.op(self.node[i << 1], self.node[(i << 1) + 1])
def build(self, array):
for i, val in enumerate(array, self.size):
self.node[i] = val
for i in range(self.size - 1, 0, -1):
self.node[i] = self.op(self.node[i << 1], self.node[(i << 1) + 1])
def all_fold(self):
return self.node[1]
def fold(self, l, r):
l, r = l + self.size, r + self.size
vl, vr = self.e, self.e
while l < r:
if l & 1:
vl = self.op(vl, self.node[l])
l += 1
if r & 1:
r -= 1
vr = self.op(self.node[r], vr)
l, r = l >> 1, r >> 1
return self.op(vl, vr)
def topological_sorted(tree, root=None):
n = len(tree)
par = [-1] * n
tp_order = []
for v in range(n):
if par[v] != -1 or (root is not None and v != root):
continue
stack = [v]
while stack:
v = stack.pop()
tp_order.append(v)
for nxt_v in tree[v]:
if nxt_v == par[v]:
continue
par[nxt_v] = v
stack.append(nxt_v)
return tp_order, par
def dsu_on_tree(tree, root):
n = len(tree)
tp_order, par = topological_sorted(tree, root)
# 有向木の構築
di_tree = [[] for i in range(n)]
for v in range(n):
for nxt_v in tree[v]:
if nxt_v == par[v]:
continue
di_tree[v].append(nxt_v)
# 部分木サイズの計算
sub_size = [1] * n
for v in tp_order[::-1]:
for nxt_v in di_tree[v]:
sub_size[v] += sub_size[nxt_v]
# 有向木のDFS行きがけ順の構築
di_tree = [sorted(tr, key=lambda v: sub_size[v]) for tr in di_tree]
keeps = [0] * n
for v in range(n):
di_tree[v] = di_tree[v][:-1][::-1] + di_tree[v][-1:]
for chi_v in di_tree[v][:-1]:
keeps[chi_v] = 1
tp_order, _ = topological_sorted(di_tree, root)
# 加算もしくは減算の実行
# counts = {}
def add(sub_root, val):
stack = [sub_root]
while stack:
v = stack.pop()
vals = st[colors[v]]
st[colors[v]] = (vals[0] + val, vals[1])
# counts[colors[v]] = counts.get(colors[v], 0) + val
for chi_v in di_tree[v]:
stack.append(chi_v)
# 有向木のDFS帰りがけ順で処理
for v in tp_order[::-1]:
for chi_v in di_tree[v]:
if keeps[chi_v] == 1:
add(chi_v, 1)
# ここでクエリを実行する
vals = st[colors[v]]
st[colors[v]] = (vals[0] + 1, vals[1])
# counts[colors[v]] = counts.get(colors[v], 0) + 1
ans[v] = st.all_fold()[1]
if keeps[v] == 1:
add(v, -1)
n = int(input())
colors = list(map(int, input().split()))
edges = [list(map(int, input().split())) for i in range(n - 1)]
tree = [[] for i in range(n)]
for u, v in edges:
u -= 1
v -= 1
tree[u].append(v)
tree[v].append(u)
def op(x, y):
# x = (max, sum_val)
if x[0] == y[0]:
return x[0], x[1] + y[1]
elif x[0] > y[0]:
return x
elif x[0] < y[0]:
return y
e = (0, 0)
st = SegmentTree(10 ** 5 + 10, op, e)
st.build([(0, i) for i in range(10 ** 5 + 10)])
ans = [0] * n
dsu_on_tree(tree, 0)
print(*ans)
|
645_A. Amity Assessment_28667
|
Bessie the cow and her best friend Elsie each received a sliding puzzle on Pi Day. Their puzzles consist of a 2 × 2 grid and three tiles labeled 'A', 'B', and 'C'. The three tiles sit on top of the grid, leaving one grid cell empty. To make a move, Bessie or Elsie can slide a tile adjacent to the empty cell into the empty cell as shown below:
<image>
In order to determine if they are truly Best Friends For Life (BFFLs), Bessie and Elsie would like to know if there exists a sequence of moves that takes their puzzles to the same configuration (moves can be performed in both puzzles). Two puzzles are considered to be in the same configuration if each tile is on top of the same grid cell in both puzzles. Since the tiles are labeled with letters, rotations and reflections are not allowed.
Input
The first two lines of the input consist of a 2 × 2 grid describing the initial configuration of Bessie's puzzle. The next two lines contain a 2 × 2 grid describing the initial configuration of Elsie's puzzle. The positions of the tiles are labeled 'A', 'B', and 'C', while the empty cell is labeled 'X'. It's guaranteed that both puzzles contain exactly one tile with each letter and exactly one empty position.
Output
Output "YES"(without quotes) if the puzzles can reach the same configuration (and Bessie and Elsie are truly BFFLs). Otherwise, print "NO" (without quotes).
Examples
Input
AB
XC
XB
AC
Output
YES
Input
AB
XC
AC
BX
Output
NO
Note
The solution to the first sample is described by the image. All Bessie needs to do is slide her 'A' tile down.
In the second sample, the two puzzles can never be in the same configuration. Perhaps Bessie and Elsie are not meant to be friends after all...
|
def read_ints():
return [int(x) for x in input(' ').split()]
def evaluate(top, bot):
res = 1 if 'X' in top else 2
perm = top + bot
perm = [x for x in perm if x != 'X']
for i in range(len(perm)):
for j in range(i+1, len(perm)):
if perm[i] > perm[j]:
res += 1
return res % 2
def main():
top = input()
bot = input()
x = evaluate(top, bot)
top = input()
bot = input()
y = evaluate(top, bot)
print("YES" if x == y else "NO")
if __name__ == '__main__':
main()
|
{
"input": [
"AB\nXC\nAC\nBX\n",
"AB\nXC\nXB\nAC\n",
"CX\nBA\nAX\nBC\n",
"XB\nAC\nBX\nAC\n",
"BA\nXC\nXB\nAC\n",
"CA\nBX\nCB\nXA\n",
"AC\nBX\nCB\nAX\n",
"BC\nXA\nXC\nAB\n",
"XA\nCB\nBA\nCX\n",
"CA\nXB\nXB\nCA\n",
"AC\nXB\nBA\nCX\n",
"AX\nCB\nBC\nAX\n",
"BA\nXC\nBC\nAX\n",
"CB\nAX\nXA\nBC\n",
"CB\nAX\nCA\nBX\n",
"AX\nCB\nCX\nAB\n",
"AB\nXC\nAB\nCX\n",
"CX\nBA\nBA\nXC\n",
"CX\nAB\nXB\nAC\n",
"CX\nBA\nAC\nXB\n",
"CB\nAX\nXC\nBA\n",
"XC\nAB\nCB\nAX\n",
"CA\nXB\nBA\nXC\n",
"CA\nBX\nBA\nXC\n",
"AC\nBX\nAB\nXC\n",
"XB\nCA\nAX\nCB\n",
"XB\nAC\nCX\nBA\n",
"BX\nCA\nXB\nCA\n",
"AB\nXC\nBX\nAC\n",
"AX\nBC\nAC\nBX\n",
"XC\nBA\nCB\nAX\n",
"XA\nBC\nXB\nCA\n",
"AB\nCX\nAC\nBX\n",
"XC\nBA\nBA\nXC\n",
"CX\nAB\nAX\nCB\n",
"XB\nCA\nCX\nBA\n",
"CB\nXA\nBC\nXA\n",
"XB\nAC\nXC\nBA\n",
"CX\nBA\nXB\nAC\n",
"CX\nBA\nCX\nBA\n",
"BA\nCX\nAC\nBX\n",
"CX\nBA\nCX\nAB\n",
"BC\nAX\nXC\nAB\n",
"BX\nAC\nCX\nBA\n",
"BX\nCA\nXA\nBC\n",
"BC\nAX\nXC\nBA\n",
"CB\nAX\nBA\nXC\n",
"XB\nAC\nCA\nBX\n",
"BC\nAX\nAC\nBX\n",
"BX\nCA\nAC\nBX\n",
"CA\nXB\nBA\nCX\n",
"XC\nBA\nCB\nXA\n",
"CA\nBX\nXC\nBA\n",
"XB\nAC\nXC\nAB\n",
"AB\nCX\nXB\nAC\n",
"CA\nBX\nBX\nCA\n",
"AX\nCB\nBC\nXA\n",
"AX\nCB\nAX\nBC\n",
"AC\nXB\nCX\nBA\n",
"AX\nBC\nAX\nCB\n",
"AX\nCB\nCB\nAX\n",
"XC\nAB\nBC\nXA\n",
"CB\nAX\nCA\nXB\n",
"AB\nCX\nXA\nBC\n",
"XB\nCA\nXC\nBA\n",
"CX\nAB\nXC\nBA\n",
"XA\nBC\nCB\nAX\n",
"BA\nXC\nAC\nXB\n",
"XC\nBA\nAC\nBX\n",
"BA\nCX\nBA\nXC\n",
"AB\nXC\nAX\nCB\n",
"CX\nBA\nBX\nAC\n",
"XB\nCA\nBC\nXA\n",
"XC\nBA\nXC\nAB\n",
"XB\nAC\nAB\nXC\n",
"BA\nXC\nCA\nXB\n",
"CB\nAX\nXB\nAC\n",
"BX\nAC\nAB\nXC\n",
"BC\nXA\nCB\nXA\n",
"XA\nCB\nXA\nBC\n",
"AC\nXB\nCB\nXA\n",
"BA\nCX\nAB\nCX\n",
"XA\nCB\nAB\nXC\n",
"CB\nAX\nBC\nXA\n",
"AB\nCX\nXC\nBA\n",
"XA\nBC\nCX\nAB\n",
"CA\nXB\nAC\nBX\n",
"BX\nCA\nXB\nAC\n",
"XC\nBA\nBX\nCA\n",
"XA\nBC\nBX\nAC\n",
"XC\nBA\nCA\nBX\n",
"CA\nBX\nCB\nAX\n",
"BC\nXA\nBX\nCA\n",
"BC\nXA\nBA\nXC\n",
"AB\nXC\nXC\nAB\n",
"CB\nAX\nCX\nAB\n",
"AX\nBC\nCA\nXB\n",
"CX\nBA\nCA\nXB\n",
"XB\nAC\nCX\nAB\n",
"CB\nAX\nBC\nAX\n",
"CA\nBX\nAC\nXB\n",
"BA\nCX\nCX\nBA\n",
"XB\nCA\nBX\nAC\n",
"CB\nAX\nAX\nBC\n",
"BA\nCX\nXB\nAC\n",
"AC\nBX\nBC\nAX\n",
"XA\nCB\nBA\nXC\n",
"CA\nXB\nBX\nCA\n",
"AX\nCB\nXC\nAB\n",
"CX\nAB\nBX\nAC\n",
"CB\nXA\nXC\nBA\n",
"CA\nBX\nBA\nCX\n",
"XC\nAB\nCB\nXA\n",
"AB\nCX\nAC\nXB\n",
"CX\nAB\nXA\nCB\n",
"XC\nBA\nBX\nAC\n",
"BA\nXC\nAC\nBX\n",
"BX\nAC\nCX\nAB\n",
"BX\nCA\nXA\nCB\n",
"CB\nAX\nAB\nXC\n",
"XB\nAC\nCA\nXB\n",
"BC\nAX\nAC\nXB\n",
"CA\nBX\nXC\nAB\n",
"XB\nCA\nCX\nAB\n",
"BA\nCX\nBX\nAC\n",
"CA\nBX\nXB\nCA\n",
"XA\nBC\nCB\nXA\n",
"CX\nBA\nAC\nBX\n",
"BX\nAC\nBA\nXC\n",
"CB\nXA\nXB\nAC\n",
"BX\nCA\nAB\nXC\n",
"AC\nXB\nCB\nAX\n",
"BA\nCX\nBA\nCX\n",
"BC\nXA\nXB\nCA\n",
"BC\nAX\nCX\nAB\n",
"XA\nBC\nCA\nXB\n",
"BC\nAX\nBC\nAX\n",
"CA\nXB\nAC\nXB\n",
"BA\nCX\nXB\nCA\n",
"AC\nBX\nBC\nXA\n",
"BC\nAX\nAX\nBC\n",
"AX\nCB\nXC\nBA\n",
"BA\nCX\nAC\nXB\n",
"CX\nBA\nBX\nCA\n",
"BX\nAC\nXC\nAB\n",
"CB\nXA\nAB\nXC\n",
"XB\nAC\nAC\nXB\n",
"BC\nAX\nCA\nXB\n",
"CA\nBX\nXB\nAC\n",
"XA\nBC\nBC\nXA\n",
"BX\nAC\nBA\nCX\n",
"CB\nXA\nXB\nCA\n",
"CA\nBX\nAC\nBX\n",
"CA\nBX\nBC\nXA\n",
"XA\nCB\nXC\nBA\n",
"AB\nCX\nCA\nXB\n",
"CX\nBA\nXB\nCA\n",
"BX\nAC\nXC\nBA\n",
"XB\nAC\nAC\nBX\n",
"XA\nCB\nBC\nXA\n",
"XB\nAC\nBA\nCX\n",
"CB\nXA\nBX\nCA\n",
"XC\nBA\nXB\nCA\n",
"BX\nAC\nAC\nBX\n",
"BX\nAC\nAC\nXB\n",
"BX\nAC\nCA\nXB\n",
"BX\nCA\nCA\nXB\n",
"BA\nXC\nXB\nCA\n",
"CA\nBX\nBC\nAX\n",
"XA\nBC\nBA\nCX\n",
"AC\nBX\nBA\nCX\n",
"XA\nCB\nCB\nAX\n",
"BA\nXC\nBC\nXA\n",
"CB\nXA\nCA\nBX\n",
"XA\nCB\nCX\nAB\n",
"AB\nXC\nBA\nCX\n",
"CX\nBA\nAB\nXC\n",
"XC\nAB\nAC\nBX\n",
"BC\nXA\nXC\nBA\n",
"CA\nBX\nAB\nXC\n",
"XB\nCA\nXB\nCA\n",
"AB\nXC\nBX\nCA\n",
"AX\nCB\nAC\nBX\n",
"CX\nBA\nCB\nAX\n",
"CX\nBA\nAX\nCB\n",
"CX\nAB\nCX\nAB\n"
],
"output": [
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bessie the cow and her best friend Elsie each received a sliding puzzle on Pi Day. Their puzzles consist of a 2 × 2 grid and three tiles labeled 'A', 'B', and 'C'. The three tiles sit on top of the grid, leaving one grid cell empty. To make a move, Bessie or Elsie can slide a tile adjacent to the empty cell into the empty cell as shown below:
<image>
In order to determine if they are truly Best Friends For Life (BFFLs), Bessie and Elsie would like to know if there exists a sequence of moves that takes their puzzles to the same configuration (moves can be performed in both puzzles). Two puzzles are considered to be in the same configuration if each tile is on top of the same grid cell in both puzzles. Since the tiles are labeled with letters, rotations and reflections are not allowed.
Input
The first two lines of the input consist of a 2 × 2 grid describing the initial configuration of Bessie's puzzle. The next two lines contain a 2 × 2 grid describing the initial configuration of Elsie's puzzle. The positions of the tiles are labeled 'A', 'B', and 'C', while the empty cell is labeled 'X'. It's guaranteed that both puzzles contain exactly one tile with each letter and exactly one empty position.
Output
Output "YES"(without quotes) if the puzzles can reach the same configuration (and Bessie and Elsie are truly BFFLs). Otherwise, print "NO" (without quotes).
Examples
Input
AB
XC
XB
AC
Output
YES
Input
AB
XC
AC
BX
Output
NO
Note
The solution to the first sample is described by the image. All Bessie needs to do is slide her 'A' tile down.
In the second sample, the two puzzles can never be in the same configuration. Perhaps Bessie and Elsie are not meant to be friends after all...
### Input:
AB
XC
AC
BX
### Output:
No
### Input:
AB
XC
XB
AC
### Output:
Yes
### Code:
def read_ints():
return [int(x) for x in input(' ').split()]
def evaluate(top, bot):
res = 1 if 'X' in top else 2
perm = top + bot
perm = [x for x in perm if x != 'X']
for i in range(len(perm)):
for j in range(i+1, len(perm)):
if perm[i] > perm[j]:
res += 1
return res % 2
def main():
top = input()
bot = input()
x = evaluate(top, bot)
top = input()
bot = input()
y = evaluate(top, bot)
print("YES" if x == y else "NO")
if __name__ == '__main__':
main()
|
697_A. Pineapple Incident_28673
|
Ted has a pineapple. This pineapple is able to bark like a bulldog! At time t (in seconds) it barks for the first time. Then every s seconds after it, it barks twice with 1 second interval. Thus it barks at times t, t + s, t + s + 1, t + 2s, t + 2s + 1, etc.
<image>
Barney woke up in the morning and wants to eat the pineapple, but he can't eat it when it's barking. Barney plans to eat it at time x (in seconds), so he asked you to tell him if it's gonna bark at that time.
Input
The first and only line of input contains three integers t, s and x (0 ≤ t, x ≤ 109, 2 ≤ s ≤ 109) — the time the pineapple barks for the first time, the pineapple barking interval, and the time Barney wants to eat the pineapple respectively.
Output
Print a single "YES" (without quotes) if the pineapple will bark at time x or a single "NO" (without quotes) otherwise in the only line of output.
Examples
Input
3 10 4
Output
NO
Input
3 10 3
Output
YES
Input
3 8 51
Output
YES
Input
3 8 52
Output
YES
Note
In the first and the second sample cases pineapple will bark at moments 3, 13, 14, ..., so it won't bark at the moment 4 and will bark at the moment 3.
In the third and fourth sample cases pineapple will bark at moments 3, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, ..., so it will bark at both moments 51 and 52.
|
t,s,x=(int(z) for z in input().split())
x-=t
if x>=0 and x%s in [0,1] and x!=1:
print("YES")
else:
print("NO")
|
{
"input": [
"3 10 4\n",
"3 8 52\n",
"3 10 3\n",
"3 8 51\n",
"4 2 6\n",
"3 743604 201724\n",
"6947541 698167 6\n",
"688051712 67 51\n",
"29318 787017 587931018\n",
"0 2 1000000000\n",
"0 2 3\n",
"0 2 0\n",
"6 5 3\n",
"556888 514614196 515171084\n",
"6 328006 584834704\n",
"3 3 1000000000\n",
"11 2 0\n",
"83 6 6772861\n",
"21 65767 55245\n",
"456947336 740144 45\n",
"60 317278 109460971\n",
"4363010 696782227 701145238\n",
"3 10 125\n",
"60686899 78474 60704617\n",
"5 3 300000035\n",
"586389 79039 850729874\n",
"1 2 999999937\n",
"1 10 20\n",
"5 1000 1000\n",
"2 2 4\n",
"120 2 1000000000\n",
"8 6728951 860676\n",
"6 3 9\n",
"4 4 0\n",
"0 3 999999998\n",
"351416375 243431 368213115\n",
"723634470 2814619 940360134\n",
"93647 7 451664565\n",
"3 3 4\n",
"5 18553 10908\n",
"1 3 6\n",
"10 5 15\n",
"0 6906451 366041903\n",
"6 52 30\n",
"11750 8 446010134\n",
"54 197366062 197366117\n",
"1 38 902410512\n",
"906385 342131991 685170368\n",
"11 957526890 957526901\n",
"0 79 4000\n",
"5 2 7\n",
"5 6 19\n",
"0 4 0\n",
"74619 213344 6432326\n",
"5 3 8\n",
"0 3 5\n",
"1 2 1000000000\n",
"6431 855039 352662\n",
"1 5 1000000000\n",
"10 5 11\n",
"50 64536 153660266\n",
"10 3 5\n",
"0 2 999999999\n",
"4567998 4 204966403\n",
"1 5 6\n",
"571128 973448796 10\n",
"876884 55420 971613604\n",
"5 3 9\n",
"3 3 5\n",
"5 5 13\n",
"5 2 6\n",
"1 2 3\n",
"3 2 5\n",
"76079 281367 119938421\n",
"582692707 66997 925047377\n",
"3 3 0\n",
"0 2 1\n",
"1 5 103\n",
"3 8 53\n",
"4796601 66897 4860613\n",
"0 10 23\n",
"749399100 103031711 761562532\n",
"9295078 2 6\n",
"5 5 10\n",
"8897216 734348516 743245732\n",
"1 2 4\n",
"0 2 2\n",
"5 2 10\n",
"251132 67561 135026988\n",
"914016 6 914019\n",
"0 215 403\n",
"0 2 900000000\n",
"2 2 1000000000\n",
"33 232603 599417964\n",
"0 10001 0\n",
"3 858900 201724\n",
"0 1 0\n",
"6947541 1148187 6\n",
"358866430 67 51\n",
"29318 787017 594773003\n",
"0 2 -1\n",
"8 5 3\n",
"916562 514614196 515171084\n",
"6 328006 894225749\n",
"3 3 1010000000\n",
"11 4 0\n",
"83 5 6772861\n",
"6 65767 55245\n",
"456947336 1129818 45\n",
"60 140664 109460971\n",
"4363010 99284751 701145238\n",
"3 3 125\n",
"60686899 78474 49081528\n",
"5 4 300000035\n",
"586389 79039 1519525355\n",
"1 3 999999937\n",
"1 17 20\n",
"5 1000 1010\n",
"2 2 5\n",
"148 2 1000000000\n",
"11 6728951 860676\n",
"6 3 17\n",
"4 8 0\n",
"15268430 243431 368213115\n",
"723634470 2814619 986961042\n",
"93647 7 347759567\n",
"3 3 8\n",
"10 18553 10908\n",
"1 3 10\n",
"10 5 2\n",
"1 6906451 366041903\n",
"6 18 30\n",
"6825 8 446010134\n",
"54 8901282 197366117\n",
"2 38 902410512\n",
"906385 673945327 685170368\n",
"11 957526890 994155534\n",
"0 143 4000\n",
"5 2 14\n",
"0 7 0\n",
"74619 213344 706347\n",
"0 2 5\n",
"6431 51302 352662\n",
"10 5 22\n",
"50 64536 243790224\n",
"10 2 5\n",
"4567998 6 204966403\n",
"2 5 6\n",
"571128 1203989025 10\n",
"876884 55420 1152861709\n",
"5 6 9\n",
"3 3 6\n",
"5 5 1\n",
"5 2 0\n",
"1 4 3\n",
"3 2 6\n",
"76079 281367 160106493\n",
"582692707 66997 1470928699\n",
"3 5 0\n",
"0 5 103\n",
"3 8 61\n",
"309365 66897 4860613\n",
"0 10 4\n",
"178769979 103031711 761562532\n",
"8897216 734348516 783259913\n",
"0 2 4\n",
"1 2 2\n",
"3 2 10\n",
"201347 67561 135026988\n",
"1548550 6 914019\n",
"-1 215 403\n",
"0 2 72858658\n",
"4 2 1000000000\n",
"33 232603 908492958\n",
"0 10001 1\n",
"3 10 7\n",
"2 8 52\n",
"5 10 3\n",
"1 8 51\n",
"1 858900 201724\n",
"13656541 1148187 6\n",
"53088652 67 51\n",
"29318 787017 581601530\n"
],
"output": [
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ted has a pineapple. This pineapple is able to bark like a bulldog! At time t (in seconds) it barks for the first time. Then every s seconds after it, it barks twice with 1 second interval. Thus it barks at times t, t + s, t + s + 1, t + 2s, t + 2s + 1, etc.
<image>
Barney woke up in the morning and wants to eat the pineapple, but he can't eat it when it's barking. Barney plans to eat it at time x (in seconds), so he asked you to tell him if it's gonna bark at that time.
Input
The first and only line of input contains three integers t, s and x (0 ≤ t, x ≤ 109, 2 ≤ s ≤ 109) — the time the pineapple barks for the first time, the pineapple barking interval, and the time Barney wants to eat the pineapple respectively.
Output
Print a single "YES" (without quotes) if the pineapple will bark at time x or a single "NO" (without quotes) otherwise in the only line of output.
Examples
Input
3 10 4
Output
NO
Input
3 10 3
Output
YES
Input
3 8 51
Output
YES
Input
3 8 52
Output
YES
Note
In the first and the second sample cases pineapple will bark at moments 3, 13, 14, ..., so it won't bark at the moment 4 and will bark at the moment 3.
In the third and fourth sample cases pineapple will bark at moments 3, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, ..., so it will bark at both moments 51 and 52.
### Input:
3 10 4
### Output:
NO
### Input:
3 8 52
### Output:
YES
### Code:
t,s,x=(int(z) for z in input().split())
x-=t
if x>=0 and x%s in [0,1] and x!=1:
print("YES")
else:
print("NO")
|
762_C. Two strings_28681
|
You are given two strings a and b. You have to remove the minimum possible number of consecutive (standing one after another) characters from string b in such a way that it becomes a subsequence of string a. It can happen that you will not need to remove any characters at all, or maybe you will have to remove all of the characters from b and make it empty.
Subsequence of string s is any such string that can be obtained by erasing zero or more characters (not necessarily consecutive) from string s.
Input
The first line contains string a, and the second line — string b. Both of these strings are nonempty and consist of lowercase letters of English alphabet. The length of each string is no bigger than 105 characters.
Output
On the first line output a subsequence of string a, obtained from b by erasing the minimum number of consecutive characters.
If the answer consists of zero characters, output «-» (a minus sign).
Examples
Input
hi
bob
Output
-
Input
abca
accepted
Output
ac
Input
abacaba
abcdcba
Output
abcba
Note
In the first example strings a and b don't share any symbols, so the longest string that you can get is empty.
In the second example ac is a subsequence of a, and at the same time you can obtain it by erasing consecutive symbols cepted from string b.
|
from sys import stdin
def main():
t = stdin.readline()
s = stdin.readline()
n = len(s) - 1
m = len(t) - 1
post = [-1] * n
ss = n - 1
st = m - 1
while st >= 0 and ss >= 0:
if t[st] == s[ss]:
post[ss] = st
ss -= 1
st -= 1
pre = [-1] * n
ss = 0
st = 0
while st < m and ss < n:
if t[st] == s[ss]:
pre[ss] = st
ss += 1
st += 1
low = 0
high = n
min_ans = n
start = -1
end = -1
while low < high:
mid = (low + high) >> 1
ok = False
if post[mid] != -1:
if mid < min_ans:
min_ans = mid
start = 0
end = mid - 1
ok = True
for i in range(1, n - mid):
if pre[i - 1] != -1 and post[i + mid] != -1 and post[i + mid] > pre[i - 1]:
if mid < min_ans:
min_ans = mid
start = i
end = i + mid - 1
ok = True
if pre[n - mid - 1] != -1:
if mid < min_ans:
min_ans = mid
start = n - mid
end = n - 1
ok = True
if not ok:
low = mid + 1
else:
high = mid
ans = []
for i in range(n):
if start <= i <= end:
continue
ans.append(s[i])
if min_ans == n:
print('-')
else:
print(''.join(ans))
if __name__ == '__main__':
main()
|
{
"input": [
"hi\nbob\n",
"abca\naccepted\n",
"abacaba\nabcdcba\n",
"edbcd\nd\n",
"aa\nzzaa\n",
"aaaaaaaaaaaa\naaa\n",
"aaaaaabbbbbbaaaaaa\naba\n",
"a\naaa\n",
"ab\naba\n",
"aaaaaaaaa\na\n",
"njtdhyqundyedsjyvy\nypjrs\n",
"bacb\nccacacbacbccbbccccaccccccbcbabbbaababa\n",
"caacacaacbaa\nacbbbabacacac\n",
"asdf\ngasdf\n",
"aaaabbbbaaaa\naba\n",
"a\nzazaa\n",
"fdtffutxkujflswyddvhusfcook\nkavkhnhphcvckogqqqqhdmgwjdfenzizrebefsbuhzzwhzvc\n",
"az\naaazazaa\n",
"abbcc\naca\n",
"def\nabcdef\n",
"haddack\nhack\n",
"dedcbaa\ndca\n",
"aaa\naa\n",
"bbacaabbaaa\nacaabcaa\n",
"abxzxzxzzaba\naba\n",
"aba\na\n",
"abab\nab\n",
"aaxyaba\naaba\n",
"abacaba\naa\n",
"asdf\nfasdf\n",
"aaaaaaaaaaaaaaaaaaaa\naaaaaaaa\n",
"npnkmawey\nareakefvowledfriyjejqnnaeqheoh\n",
"abcabbcbcccbccbbcc\nacbcaabbbbcabbbaca\n",
"bababsbs\nabs\n",
"aa\naaab\n",
"aa\naaaa\n",
"aaaaabbbaaaaa\naabbaa\n",
"abcabc\nabc\n",
"abcde\nfabcde\n",
"aaaaabbbbbbaaaaaa\naba\n",
"abbba\naba\n",
"bacbcaacabbaacb\ncbbaaccccbcaacacaabb\n",
"aaaab\naab\n",
"aaaaa\naaaa\n",
"aaaaaaaaa\naaaa\n",
"a\nb\n",
"ac\naacacaacbaaacbbbabacaca\n",
"c\ncbcbcbbacacacbccaaccbcabaaabbaaa\n",
"bbbbaabbababbaaaaababbaaabbbbaaabbbababbbbabaabababaabaaabbbabababbbabababaababaaaaa\nbbabaaaabaaaabbaaabbbabaaabaabbbababbbbbbbbbbabbababbaababbbaaabababababbbbaaababaaaaab\n",
"lctsczqr\nqvkp\n",
"aa\na\n",
"abc\nksdksdsdsnabc\n",
"a\nab\n",
"a\naaaaaaaaa\n",
"b\nabb\n",
"ashfaniosafapisfasipfaspfaspfaspfapsfjpasfshvcmvncxmvnxcvnmcxvnmxcnvmcvxvnxmcvxcmvh\nashish\n",
"acbc\ncacacbac\n",
"zhbt\nztjihmhebkrztefpwty\n",
"aaaaaaa\naaa\n",
"aaaaaaaaaaaa\naaaaaaaaaaaa\n",
"b\ncb\n",
"aaeojkdyuilpdvyewjfrftkpcobhcumwlaoiocbfdtvjkhgda\nmlmarpivirqbxcyhyerjoxlslyfzftrylpjyouypvk\n",
"abcd\nzzhabcd\n",
"uglyqhkpruxoakm\ncixxkpaaoodpuuh\n",
"test\nt\n",
"baababaaaab\nbaababbbbbbb\n",
"a\na\n",
"ofih\nihfsdf\n",
"gkvubrvpbhsfiuyha\nihotmn\n",
"abba\naba\n",
"abcd\nfaaaabbbbccccdddeda\n",
"accac\nbaacccbcccabaabbcacbbcccacbaabaaac\n",
"aaa\naaaaa\n",
"hddddddack\nhackyz\n",
"ababbbbbbbbbbbb\nabbbbb\n",
"babababbaaabb\nabbab\n",
"ccccabccbb\ncbbabcc\n",
"ba\nbb\n",
"aa\naa\n",
"lo\neuhaqdhhzlnkmqnakgwzuhurqlpmdm\n",
"bbaabb\nab\n",
"aac\naaa\n",
"ddbcd\nd\n",
"aa\nzyaa\n",
"aaaaabaaa\na\n",
"njtdhyqundyedsjyvy\nypjqs\n",
"babb\nccacacbacbccbbccccaccccccbcbabbbaababa\n",
"caacacaacbaa\ncacacababbbca\n",
"asdf\ngatdf\n",
"b\nzazaa\n",
"koocfsuhvddywslfjukxtufftdf\nkavkhnhphcvckogqqqqhdmgwjdfenzizrebefsbuhzzwhzvc\n",
"fed\nabcdef\n",
"eedcbaa\ndca\n",
"bbacabbbaaa\nacaabcaa\n",
"baba\nab\n",
"aaxyaba\nbaaa\n",
"fsda\nfasdf\n",
"abcabbcbcccbccbbcc\nacabbbacbbbbaacbca\n",
"bababsbs\nasb\n",
"abcde\nedcbaf\n",
"aaaabbabbbbaaaaaa\naba\n",
"bcaabbacaacbcab\ncbbaaccccbcaacacaabb\n",
"b\nb\n",
"c\ncbcbcbbacacacbccaaccccabaaabbaaa\n",
"bbbbaabbababbaaaaababbaaabbbbaaabbbababbbbabaabababaabaaabbbabababbbabababaababaaaaa\nbbabaaaabaaaabbaaabbbabaaabaabbbababbbbbbbbbbabbababbaababbbaaabababaaabbbbaaababaaaaab\n",
"rqzcstcl\nqvkp\n",
"ashfaniosafapisfasipfaspfaspfaspfapsfjpasfshvcmvncxmvnxcvnmcxvnmxcnvmcvxvnxmcvxcmvh\nasgish\n",
"acbc\nbacacbac\n",
"zhbt\nztjihmhebjrztefpwty\n",
"adghkjvtdfbcoioalwmuchbocpktfrfjweyvdpliuydkjoeaa\nmlmarpivirqbxcyhyerjoxlslyfzftrylpjyouypvk\n",
"mkaoxurpkhqylgu\ncixxkpaaoodpuuh\n",
"tset\nt\n",
"baabaaaabab\nbaababbbbbbb\n",
"ofih\nihfsef\n",
"aaaaaabbbbbbaaaaaa\naca\n",
"a{\naaazazaa\n",
"bbbcc\naca\n",
"abxzxzxzzaba\naca\n",
"aca\na\n",
"abacaca\naa\n",
"npnkeawmy\nareakefvowledfriyjejqnnaeqheoh\n",
"ba\naaaa\n",
"aaaaa\naab\n",
"ad\naacacaacbaaacbbbabacaca\n",
"a\nba\n",
"a\naaaabaaaa\n",
"b\nacb\n",
"aaaaaaa\nbaa\n",
"b\nbb\n",
"abcd\ndcbahzz\n"
],
"output": [
"-",
"ac",
"abcba",
"d",
"aa",
"aaa",
"aba",
"a",
"ab",
"a",
"ys",
"ba",
"aacacac",
"asdf",
"aba",
"a",
"kvc",
"a",
"ac",
"def",
"hack",
"dca",
"aa",
"acaabaa",
"aba",
"a",
"ab",
"aaba",
"aa",
"asdf",
"aaaaaaaa",
"a",
"acbc",
"abs",
"aa",
"aa",
"aabbaa",
"abc",
"abcde",
"aba",
"aba",
"cbcaabb",
"aab",
"aaaa",
"aaaa",
"-",
"a",
"c",
"bbbbbbbabbababbaababbbaaabababababbbbaaababaaaaab",
"q",
"a",
"abc",
"a",
"a",
"b",
"ashish",
"ac",
"zt",
"aaa",
"aaaaaaaaaaaa",
"b",
"ouypvk",
"abcd",
"uh",
"t",
"baababb",
"a",
"ih",
"ih",
"aba",
"a",
"aac",
"aaa",
"hack",
"abbbbb",
"abbab",
"cabcc",
"b",
"aa",
"-",
"ab",
"aa",
"d\n",
"aa\n",
"a\n",
"jqs\n",
"ba\n",
"cacacabaa\n",
"df\n",
"-\n",
"kc\n",
"f\n",
"dca\n",
"acaaaa\n",
"ab\n",
"aaa\n",
"fa\n",
"acabbb\n",
"asb\n",
"e\n",
"aba\n",
"cbbacaabb\n",
"b\n",
"c\n",
"bbbbbbbabbababbaababbbaaabababaaabbbbaaababaaaaab\n",
"q\n",
"asish\n",
"ac\n",
"zt\n",
"mpvk\n",
"uh\n",
"t\n",
"baababb\n",
"ih\n",
"aa\n",
"a\n",
"-\n",
"aa\n",
"a\n",
"aa\n",
"a\n",
"a\n",
"aa\n",
"a\n",
"a\n",
"a\n",
"b\n",
"aa\n",
"b\n",
"d\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given two strings a and b. You have to remove the minimum possible number of consecutive (standing one after another) characters from string b in such a way that it becomes a subsequence of string a. It can happen that you will not need to remove any characters at all, or maybe you will have to remove all of the characters from b and make it empty.
Subsequence of string s is any such string that can be obtained by erasing zero or more characters (not necessarily consecutive) from string s.
Input
The first line contains string a, and the second line — string b. Both of these strings are nonempty and consist of lowercase letters of English alphabet. The length of each string is no bigger than 105 characters.
Output
On the first line output a subsequence of string a, obtained from b by erasing the minimum number of consecutive characters.
If the answer consists of zero characters, output «-» (a minus sign).
Examples
Input
hi
bob
Output
-
Input
abca
accepted
Output
ac
Input
abacaba
abcdcba
Output
abcba
Note
In the first example strings a and b don't share any symbols, so the longest string that you can get is empty.
In the second example ac is a subsequence of a, and at the same time you can obtain it by erasing consecutive symbols cepted from string b.
### Input:
hi
bob
### Output:
-
### Input:
abca
accepted
### Output:
ac
### Code:
from sys import stdin
def main():
t = stdin.readline()
s = stdin.readline()
n = len(s) - 1
m = len(t) - 1
post = [-1] * n
ss = n - 1
st = m - 1
while st >= 0 and ss >= 0:
if t[st] == s[ss]:
post[ss] = st
ss -= 1
st -= 1
pre = [-1] * n
ss = 0
st = 0
while st < m and ss < n:
if t[st] == s[ss]:
pre[ss] = st
ss += 1
st += 1
low = 0
high = n
min_ans = n
start = -1
end = -1
while low < high:
mid = (low + high) >> 1
ok = False
if post[mid] != -1:
if mid < min_ans:
min_ans = mid
start = 0
end = mid - 1
ok = True
for i in range(1, n - mid):
if pre[i - 1] != -1 and post[i + mid] != -1 and post[i + mid] > pre[i - 1]:
if mid < min_ans:
min_ans = mid
start = i
end = i + mid - 1
ok = True
if pre[n - mid - 1] != -1:
if mid < min_ans:
min_ans = mid
start = n - mid
end = n - 1
ok = True
if not ok:
low = mid + 1
else:
high = mid
ans = []
for i in range(n):
if start <= i <= end:
continue
ans.append(s[i])
if min_ans == n:
print('-')
else:
print(''.join(ans))
if __name__ == '__main__':
main()
|
785_D. Anton and School - 2_28685
|
As you probably know, Anton goes to school. One of the school subjects that Anton studies is Bracketology. On the Bracketology lessons students usually learn different sequences that consist of round brackets (characters "(" and ")" (without quotes)).
On the last lesson Anton learned about the regular simple bracket sequences (RSBS). A bracket sequence s of length n is an RSBS if the following conditions are met:
* It is not empty (that is n ≠ 0).
* The length of the sequence is even.
* First <image> charactes of the sequence are equal to "(".
* Last <image> charactes of the sequence are equal to ")".
For example, the sequence "((()))" is an RSBS but the sequences "((())" and "(()())" are not RSBS.
Elena Ivanovna, Anton's teacher, gave him the following task as a homework. Given a bracket sequence s. Find the number of its distinct subsequences such that they are RSBS. Note that a subsequence of s is a string that can be obtained from s by deleting some of its elements. Two subsequences are considered distinct if distinct sets of positions are deleted.
Because the answer can be very big and Anton's teacher doesn't like big numbers, she asks Anton to find the answer modulo 109 + 7.
Anton thought of this task for a very long time, but he still doesn't know how to solve it. Help Anton to solve this task and write a program that finds the answer for it!
Input
The only line of the input contains a string s — the bracket sequence given in Anton's homework. The string consists only of characters "(" and ")" (without quotes). It's guaranteed that the string is not empty and its length doesn't exceed 200 000.
Output
Output one number — the answer for the task modulo 109 + 7.
Examples
Input
)(()()
Output
6
Input
()()()
Output
7
Input
)))
Output
0
Note
In the first sample the following subsequences are possible:
* If we delete characters at the positions 1 and 5 (numbering starts with one), we will get the subsequence "(())".
* If we delete characters at the positions 1, 2, 3 and 4, we will get the subsequence "()".
* If we delete characters at the positions 1, 2, 4 and 5, we will get the subsequence "()".
* If we delete characters at the positions 1, 2, 5 and 6, we will get the subsequence "()".
* If we delete characters at the positions 1, 3, 4 and 5, we will get the subsequence "()".
* If we delete characters at the positions 1, 3, 5 and 6, we will get the subsequence "()".
The rest of the subsequnces are not RSBS. So we got 6 distinct subsequences that are RSBS, so the answer is 6.
|
mod = 10 ** 9 + 7
fact, inv, invfact = [1, 1], [0, 1], [1, 1]
for i in range(2, 200200):
fact.append(fact[-1] * i % mod)
inv.append(inv[mod % i] * (mod - mod // i) % mod)
invfact.append(invfact[-1] * inv[-1] % mod)
def C(n, k):
if k < 0 or k > n:
return 0
return fact[n] * invfact[k] * invfact[n - k] % mod
s = input()
op, cl = 0, s.count(')')
ans = 0
for x in s:
if x == '(':
op += 1
cur = C(cl + op - 1, op)
ans += cur
else:
cl -= 1
print(ans % mod)
|
{
"input": [
")(()()\n",
"()()()\n",
")))\n",
"())(()(())(()()))()()(()((()(())()))(()()(()()(())()()())))()()(()(((((()())(((())(((())((()(()()())()(()())()((((())()()(((()(((()(())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
"((\n",
"()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
"(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
")))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))()))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))())))))))))))))))))))))))))))))))))))))))))))))))\n",
"))())(()()(((()))(()((())(()()(()()(((((()))((()())()())()()()))(((())()(()((())))(())())(((())))(()))())(((()(((())(()()))())))()((((())()()())(((((((())((())()(()(())(())()()(()())()))()()(()))()())()()())())))(()())(())())))(())))))(())())(()((((()()(()\n",
"))\n",
"))(\n",
"))())(()((())()((((()((())(()()()))((()())()(()))))()))()))()))(())))((()))())()(())()))()()())(())(()())())((()())())()())(((((()())((((())()()((()))))())()))(())())())))()())))())()((((()(()(())((()((())))(((())))((()()())()))\n",
"))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
")(())()())(())))\n",
")(()()))((\n",
"((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()\n",
"()(\n",
")())))(((())))())))))))()())(())))))))())))(((())))())()()))(())())((()())(((((()()()())()()()))((()\n",
")))()(())(((((()))\n",
")()\n",
"(()\n",
")(\n",
")())((((((()))()((()))()((()()()((()()()))\n",
"(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((\n",
")((\n",
"(\n",
")\n",
"(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())\n",
"(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
"((((()())))())((((((()(()())(()())()((()()))(((())()()()(())))))()())())))(()()(()))))()(((()(((())()))())())))))(()()()((((((())(()())())()())(()))))()(()))(((()()()))())()(((()(()(((()))(()))()(()))((((((((())))))()))())(())))))()(()(()(((()((()()()())(((())())((()())(((((()()(())()()(()())()()))((()()())(())))))(()()(((()()()))(()())((()))()())))))()))))()(()()()))(()(()))))))(())))))()(()(())()()(\n",
")()))()(()))\n",
"()\n",
"()(())()((((()(((((((())()(())()()((())()))())((()(())()()(((()(((()(()((()()())(()(((()(((()()())((((()())()(()())()()(()((())(((())(((())()(((((()(()()())))()()())(()()(()()(()))())(()((()(()()()))()(())(()(())(\n",
"*(\n",
"())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))\n",
"(((((((((((((((((((((((((((((((((((((((()((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
"))))))))))))))))))))))))))))))))))))))))))))))))())))))))()))))))))))))))))))))))))))))))))))))))))))))))))))))())))))()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
"))())(()((())()((((()((())(()()())))(()())()(()))))()))()))()))(())))((()))())()(())()))()()())(())(()())())((()())())()())(((((()())((((())()()((()))))())()))(())())())))()())))())()((((()(()(())((()((())))(((())))((()()())()))\n",
")))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))\n",
")(())()())()))))\n",
"(()))()(()\n",
")))()(())((((((())\n",
")())((((((())(()((()))()((()()()((()))()))\n",
"((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()(((((((((((((((((((((((((((((((((((((((((((((((((((\n",
")(()))\n",
"()(())()((((()(((((((())()(())()()((())()))())((()(())()()(((()(((()(()((()()())(()(((()(((()()())((((()())()(()())()()(()((())(((())(((())()(((((()(()()())))()()())(()())()()(()))())(()((()(()()()))()(())(()(())(\n",
"()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))\n",
"))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))()))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()((((((((((((((((((((((((((((((((((((((((\n",
")))())()()((())))(((())))((()((())(()(()((((()())())))()())))())())(()))())()))))((()()())((((())()(((((())()())())()((())())()(())(())()()()))())(()())()))((())))(()))()))()))()))))(()())()(())))()()(())((()((((()())((()(())())\n",
")))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))()())))))))))))))))\n",
")(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((\n",
")))))(())((((((())\n",
")(()((((()())(()((()))()((()()()((()))()))\n",
"((()))\n",
"()(())()((((()(((((((())()(())()()((())()))())((()(())()()(((()(((()(()((()()())(()(((()((())()())((((()())()(()())()()(()((())(((())(((())()(((((()(()()())))()()())(()())()()(()))())(()((()(()()()))()(())(()(())(\n",
"()))))))))))))))))))))))))))))()))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))\n",
"))))))))))))))))()()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
"(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()\n",
"))((((((())(()))))\n",
")(()((((()())(()((()))))((()()()((()))()))\n",
"())(()(())(()()))()()(()((()(())()))(()()())()(())()()())))()()(()(((((()())(((())(((())((()(()()())()(()())()((((())()())((()(((()(())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
"))))))))))))))))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))()))))))))))))))))))))))))))))))))))))))()))))))))))))))))))))))))))))(\n",
")))()))((()()()((()))))((()(())()((((()(()\n",
"(()())\n",
"())(()(())(()()))()()(()((()(())()))(()()())()(())()()())))()()(()(((((()())(((())(((())((()(()()())()(()())()((((())()())((()(((())())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
"())())\n",
"())(()(())(()()()()()(()((()(())()))(()()())()(())()()())))()()(()(((((()())(((())(((())((()(()()())()(()())()((((())()())((()(((())())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
")))())\n",
"())(()(())(()()()()()(((((()(())()))(()()())()(())()()())))()()(()(((((()())(((())(((())((()(()()())()(()())()((((())()())((()(((())())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
"())(()(())(()()()()()(((((()(())()))(()()())()(())()()())))()()(()(((((()())(((()))((())((()(()()())()(()())()((((())()())((()(((())())()()((()(()(((()(((()()())(()((())()))())((()()())(()())(((((((()((((()())(()(\n",
"))()))\n",
"()(())()((((()(((((((())()(())()()((())()))())((()(())()()(((()(((()(()((()()())())(((()((())()())((((()())()(()())()()(()((())((()))(((())()(((((()(()()())))()()())(()())()()(()))())(()(((((()()()()()(())(()(())(\n",
"())))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\n",
")))))))))))))))()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))()))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))())))))))))))))))))))))))))))))))))))))))))))))))\n",
"))())(()()(((()))(()((())(()()(()()(((((()))((()())()())()()()))(((())()(()((())))(())())(((())))(()))())(((()(((())(()()))())))()((((())()()())(((((((())((())()(()(())(())()()(()())()))()()(()))()())()()())())))(()())(())())))(())()))(())())(()((((()()(()\n",
"))'\n",
")(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((\n",
"(((\n",
"'(\n",
")*\n",
"))*\n",
"&(\n",
")((())\n",
"))))))\n",
"))())(\n",
"))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((\n"
],
"output": [
"6\n",
"7\n",
"0\n",
"933002737\n",
"0\n",
"199\n",
"407336794\n",
"286866\n",
"546547243\n",
"0\n",
"0\n",
"587599278\n",
"0\n",
"404\n",
"24\n",
"199\n",
"1\n",
"99037306\n",
"256\n",
"1\n",
"2\n",
"0\n",
"4344426\n",
"0\n",
"0\n",
"0\n",
"0\n",
"19899\n",
"211518470\n",
"702597744\n",
"42\n",
"1\n",
"31047720\n",
"0\n",
"549\n",
"893315182\n",
"2053083\n",
"884461294\n",
"16\n",
"521\n",
"26\n",
"91\n",
"15615782\n",
"143\n",
"9\n",
"702530357\n",
"11729\n",
"75\n",
"187576390\n",
"153\n",
"120\n",
"63\n",
"15716746\n",
"19\n",
"658038868\n",
"395735\n",
"19306\n",
"3279\n",
"4641\n",
"24279625\n",
"90720086\n",
"7011\n",
"196442\n",
"13\n",
"35373917\n",
"7\n",
"207351936\n",
"2\n",
"371654780\n",
"116249802\n",
"3\n",
"40084722\n",
"17218\n",
"3282751\n",
"273155769\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"9\n",
"0\n",
"2\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
As you probably know, Anton goes to school. One of the school subjects that Anton studies is Bracketology. On the Bracketology lessons students usually learn different sequences that consist of round brackets (characters "(" and ")" (without quotes)).
On the last lesson Anton learned about the regular simple bracket sequences (RSBS). A bracket sequence s of length n is an RSBS if the following conditions are met:
* It is not empty (that is n ≠ 0).
* The length of the sequence is even.
* First <image> charactes of the sequence are equal to "(".
* Last <image> charactes of the sequence are equal to ")".
For example, the sequence "((()))" is an RSBS but the sequences "((())" and "(()())" are not RSBS.
Elena Ivanovna, Anton's teacher, gave him the following task as a homework. Given a bracket sequence s. Find the number of its distinct subsequences such that they are RSBS. Note that a subsequence of s is a string that can be obtained from s by deleting some of its elements. Two subsequences are considered distinct if distinct sets of positions are deleted.
Because the answer can be very big and Anton's teacher doesn't like big numbers, she asks Anton to find the answer modulo 109 + 7.
Anton thought of this task for a very long time, but he still doesn't know how to solve it. Help Anton to solve this task and write a program that finds the answer for it!
Input
The only line of the input contains a string s — the bracket sequence given in Anton's homework. The string consists only of characters "(" and ")" (without quotes). It's guaranteed that the string is not empty and its length doesn't exceed 200 000.
Output
Output one number — the answer for the task modulo 109 + 7.
Examples
Input
)(()()
Output
6
Input
()()()
Output
7
Input
)))
Output
0
Note
In the first sample the following subsequences are possible:
* If we delete characters at the positions 1 and 5 (numbering starts with one), we will get the subsequence "(())".
* If we delete characters at the positions 1, 2, 3 and 4, we will get the subsequence "()".
* If we delete characters at the positions 1, 2, 4 and 5, we will get the subsequence "()".
* If we delete characters at the positions 1, 2, 5 and 6, we will get the subsequence "()".
* If we delete characters at the positions 1, 3, 4 and 5, we will get the subsequence "()".
* If we delete characters at the positions 1, 3, 5 and 6, we will get the subsequence "()".
The rest of the subsequnces are not RSBS. So we got 6 distinct subsequences that are RSBS, so the answer is 6.
### Input:
)(()()
### Output:
6
### Input:
()()()
### Output:
7
### Code:
mod = 10 ** 9 + 7
fact, inv, invfact = [1, 1], [0, 1], [1, 1]
for i in range(2, 200200):
fact.append(fact[-1] * i % mod)
inv.append(inv[mod % i] * (mod - mod // i) % mod)
invfact.append(invfact[-1] * inv[-1] % mod)
def C(n, k):
if k < 0 or k > n:
return 0
return fact[n] * invfact[k] * invfact[n - k] % mod
s = input()
op, cl = 0, s.count(')')
ans = 0
for x in s:
if x == '(':
op += 1
cur = C(cl + op - 1, op)
ans += cur
else:
cl -= 1
print(ans % mod)
|
807_D. Dynamic Problem Scoring_28689
|
Vasya and Petya take part in a Codeforces round. The round lasts for two hours and contains five problems.
For this round the dynamic problem scoring is used. If you were lucky not to participate in any Codeforces round with dynamic problem scoring, here is what it means. The maximum point value of the problem depends on the ratio of the number of participants who solved the problem to the total number of round participants. Everyone who made at least one submission is considered to be participating in the round.
<image>
Pay attention to the range bounds. For example, if 40 people are taking part in the round, and 10 of them solve a particular problem, then the solvers fraction is equal to 1 / 4, and the problem's maximum point value is equal to 1500.
If the problem's maximum point value is equal to x, then for each whole minute passed from the beginning of the contest to the moment of the participant's correct submission, the participant loses x / 250 points. For example, if the problem's maximum point value is 2000, and the participant submits a correct solution to it 40 minutes into the round, this participant will be awarded with 2000·(1 - 40 / 250) = 1680 points for this problem.
There are n participants in the round, including Vasya and Petya. For each participant and each problem, the number of minutes which passed between the beginning of the contest and the submission of this participant to this problem is known. It's also possible that this participant made no submissions to this problem.
With two seconds until the end of the round, all participants' submissions have passed pretests, and not a single hack attempt has been made. Vasya believes that no more submissions or hack attempts will be made in the remaining two seconds, and every submission will pass the system testing.
Unfortunately, Vasya is a cheater. He has registered 109 + 7 new accounts for the round. Now Vasya can submit any of his solutions from these new accounts in order to change the maximum point values of the problems. Vasya can also submit any wrong solutions to any problems. Note that Vasya can not submit correct solutions to the problems he hasn't solved.
Vasya seeks to score strictly more points than Petya in the current round. Vasya has already prepared the scripts which allow to obfuscate his solutions and submit them into the system from any of the new accounts in just fractions of seconds. However, Vasya doesn't want to make his cheating too obvious, so he wants to achieve his goal while making submissions from the smallest possible number of new accounts.
Find the smallest number of new accounts Vasya needs in order to beat Petya (provided that Vasya's assumptions are correct), or report that Vasya can't achieve his goal.
Input
The first line contains a single integer n (2 ≤ n ≤ 120) — the number of round participants, including Vasya and Petya.
Each of the next n lines contains five integers ai, 1, ai, 2..., ai, 5 ( - 1 ≤ ai, j ≤ 119) — the number of minutes passed between the beginning of the round and the submission of problem j by participant i, or -1 if participant i hasn't solved problem j.
It is guaranteed that each participant has made at least one successful submission.
Vasya is listed as participant number 1, Petya is listed as participant number 2, all the other participants are listed in no particular order.
Output
Output a single integer — the number of new accounts Vasya needs to beat Petya, or -1 if Vasya can't achieve his goal.
Examples
Input
2
5 15 40 70 115
50 45 40 30 15
Output
2
Input
3
55 80 10 -1 -1
15 -1 79 60 -1
42 -1 13 -1 -1
Output
3
Input
5
119 119 119 119 119
0 0 0 0 -1
20 65 12 73 77
78 112 22 23 11
1 78 60 111 62
Output
27
Input
4
-1 20 40 77 119
30 10 73 50 107
21 29 -1 64 98
117 65 -1 -1 -1
Output
-1
Note
In the first example, Vasya's optimal strategy is to submit the solutions to the last three problems from two new accounts. In this case the first two problems will have the maximum point value of 1000, while the last three problems will have the maximum point value of 500. Vasya's score will be equal to 980 + 940 + 420 + 360 + 270 = 2970 points, while Petya will score just 800 + 820 + 420 + 440 + 470 = 2950 points.
In the second example, Vasya has to make a single unsuccessful submission to any problem from two new accounts, and a single successful submission to the first problem from the third new account. In this case, the maximum point values of the problems will be equal to 500, 1500, 1000, 1500, 3000. Vasya will score 2370 points, while Petya will score just 2294 points.
In the third example, Vasya can achieve his goal by submitting the solutions to the first four problems from 27 new accounts. The maximum point values of the problems will be equal to 500, 500, 500, 500, 2000. Thanks to the high cost of the fifth problem, Vasya will manage to beat Petya who solved the first four problems very quickly, but couldn't solve the fifth one.
|
import sys
inf = 10**9 + 7
def solve():
n = int(sys.stdin.readline())
v = [int(vi) for vi in sys.stdin.readline().split()] # Vesya
p = [int(pi) for pi in sys.stdin.readline().split()] # Petya
cnt = [0]*5
for i in range(5):
if v[i] != -1:
cnt[i] += 1
if p[i] != -1:
cnt[i] += 1
for i in range(n - 2):
a = [int(ai) for ai in sys.stdin.readline().split()]
for j in range(5):
if a[j] != -1:
cnt[j] += 1
for i in range(10**5):
if check(n, v, p, cnt, i):
print(i)
return
print(-1)
def check(n, v, p, cnt, m):
tot = n + m
solved = cnt[:]
dif = 0
for i in range(5):
if p[i] != -1 and v[i] > p[i]:
solved[i] += m
for i in range(5):
if solved[i]*2 > tot:
max_score = 500
elif solved[i]*4 > tot:
max_score = 1000
elif solved[i]*8 > tot:
max_score = 1500
elif solved[i]*16 > tot:
max_score = 2000
elif solved[i]*32 > tot:
max_score = 2500
else:
max_score = 3000
if v[i] == p[i] == -1:
pass
elif v[i] == -1:
dif -= max_score * (250 - p[i]) // 250
elif p[i] == -1:
dif += max_score * (250 - v[i]) // 250
else:
dif += max_score * (p[i] - v[i]) // 250
return dif > 0
if __name__ == '__main__':
solve()
|
{
"input": [
"2\n5 15 40 70 115\n50 45 40 30 15\n",
"5\n119 119 119 119 119\n0 0 0 0 -1\n20 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"4\n-1 20 40 77 119\n30 10 73 50 107\n21 29 -1 64 98\n117 65 -1 -1 -1\n",
"3\n55 80 10 -1 -1\n15 -1 79 60 -1\n42 -1 13 -1 -1\n",
"2\n33 15 51 7 101\n41 80 40 13 46\n",
"2\n0 0 0 0 1\n0 0 0 1 0\n",
"4\n66 55 95 78 114\n70 98 8 95 95\n17 47 88 71 18\n23 22 9 104 38\n",
"17\n66 15 -1 42 90\n67 108 104 16 110\n76 -1 -1 -1 96\n108 32 100 91 17\n87 -1 85 10 -1\n70 55 102 15 23\n-1 33 111 105 63\n-1 56 104 68 116\n56 111 102 89 63\n63 -1 68 80 -1\n80 61 -1 81 19\n101 -1 87 -1 89\n92 82 4 105 83\n19 30 114 77 104\n100 99 29 68 82\n98 -1 62 52 -1\n108 -1 -1 50 -1\n",
"9\n57 52 60 56 91\n32 40 107 89 36\n80 0 45 92 119\n62 9 107 24 61\n43 28 4 26 113\n31 91 86 13 95\n4 2 88 38 68\n83 35 57 101 28\n12 40 37 56 73\n",
"3\n20 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"10\n-1 18 44 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n13 75 0 71 42\n116 75 42 79 88\n62 -1 98 114 -1\n68 96 44 61 35\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 98 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n91 104 111 -1 -1\n92 -1 52 -1 11\n118 25 97 1 108\n-1 61 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 19 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 0\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n106 21 96 15 73\n75 66 54 46 107\n108 49 17 34 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 73 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n27 15 51 7 101\n41 80 40 13 46\n",
"4\n66 55 95 78 114\n70 98 8 95 95\n17 47 88 71 18\n7 22 9 104 38\n",
"17\n66 15 -1 42 90\n67 108 104 16 110\n76 -1 -1 -1 96\n108 32 100 91 17\n87 -1 85 10 -1\n70 55 102 15 23\n-1 33 111 105 63\n-1 56 104 68 116\n56 111 102 89 63\n63 -1 68 80 -1\n80 61 -1 81 19\n001 -1 87 -1 89\n92 82 4 105 83\n19 30 114 77 104\n100 99 29 68 82\n98 -1 62 52 -1\n108 -1 -1 50 -1\n",
"9\n57 52 60 56 91\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 86 13 95\n4 2 88 38 68\n83 35 57 101 28\n12 40 37 56 73\n",
"3\n20 65 12 73 77\n78 112 22 23 0\n1 78 60 111 62\n",
"10\n-1 18 44 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n13 75 0 71 42\n116 75 42 79 88\n62 -1 98 114 -1\n47 96 44 61 35\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 135 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n91 104 111 -1 -1\n92 -1 52 -1 11\n118 25 97 1 108\n-1 61 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 19 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 1\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n106 21 96 15 73\n75 66 54 46 107\n108 49 17 34 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 73 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n5 15 40 70 115\n3 45 40 30 15\n",
"4\n-1 20 40 77 119\n30 10 73 50 194\n21 29 -1 64 98\n117 65 -1 -1 -1\n",
"17\n66 15 -1 42 90\n67 108 104 16 110\n76 -1 -1 -1 96\n108 32 100 91 17\n87 -1 85 10 -1\n70 55 102 15 23\n-1 33 111 105 63\n-1 56 104 68 116\n56 111 102 89 63\n63 0 68 80 -1\n80 61 -1 81 19\n001 -1 87 -1 89\n92 82 4 137 83\n19 30 114 77 104\n100 99 29 68 82\n98 -1 62 52 -1\n108 -1 -1 50 -1\n",
"10\n-1 18 34 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n24 75 0 71 42\n116 75 42 79 88\n62 -1 105 114 -1\n47 96 44 61 28\n",
"2\n0 0 0 0 1\n0 0 0 1 -1\n",
"5\n119 119 119 119 119\n0 0 -1 0 -1\n20 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"3\n55 80 10 -1 -1\n15 -1 79 117 -1\n42 -1 13 -1 -1\n",
"2\n15 15 51 7 101\n41 80 40 13 46\n",
"2\n0 0 0 0 1\n0 -1 0 1 -1\n",
"4\n66 55 95 78 114\n70 98 13 95 95\n17 47 88 71 18\n7 22 9 104 38\n",
"17\n66 15 -1 42 90\n67 108 104 16 110\n76 -1 -1 -1 96\n108 32 100 91 17\n87 -1 85 10 -1\n70 55 102 15 23\n-1 33 111 105 63\n-1 56 104 68 116\n56 111 102 89 63\n63 -1 68 80 -1\n80 61 -1 81 19\n001 -1 87 -1 89\n92 82 4 137 83\n19 30 114 77 104\n100 99 29 68 82\n98 -1 62 52 -1\n108 -1 -1 50 -1\n",
"9\n57 52 60 56 91\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 23 13 95\n4 2 88 38 68\n83 35 57 101 28\n12 40 37 56 73\n",
"3\n20 65 12 73 77\n78 112 22 23 0\n1 78 60 110 62\n",
"10\n-1 18 44 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n13 75 0 71 42\n116 75 42 79 88\n62 -1 105 114 -1\n47 96 44 61 35\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 135 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n91 104 111 -1 -1\n92 -1 52 -1 11\n118 25 97 1 108\n-1 78 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 19 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 1\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n106 21 96 15 73\n75 66 54 46 107\n108 49 17 48 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 73 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n3 15 40 70 115\n3 45 40 30 15\n",
"5\n119 119 119 119 119\n0 1 -1 0 -1\n20 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"4\n-1 20 40 77 119\n30 10 73 22 194\n21 29 -1 64 98\n117 65 -1 -1 -1\n",
"3\n55 80 10 -1 -1\n15 -1 79 62 -1\n42 -1 13 -1 -1\n",
"2\n16 15 51 7 101\n41 80 40 13 46\n",
"2\n0 0 0 -1 1\n0 -1 0 1 -1\n",
"4\n66 55 95 78 114\n70 98 13 95 95\n17 47 88 71 18\n7 36 9 104 38\n",
"9\n57 52 60 56 91\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 23 13 95\n4 2 88 38 68\n83 35 57 101 28\n12 40 54 56 73\n",
"3\n20 65 12 73 77\n78 112 39 23 0\n1 78 60 110 62\n",
"10\n-1 18 44 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n13 75 0 71 42\n116 75 42 79 88\n62 -1 105 114 -1\n47 96 44 61 28\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 135 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n116 104 111 -1 -1\n92 -1 52 -1 11\n118 25 97 1 108\n-1 78 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 19 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 1\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n106 21 96 15 73\n75 66 54 46 107\n108 49 17 48 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 111 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n4 15 40 70 115\n3 45 40 30 15\n",
"5\n119 187 119 119 119\n0 1 -1 0 -1\n20 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"4\n-1 20 40 77 119\n30 10 73 22 194\n21 37 -1 64 98\n117 65 -1 -1 -1\n",
"2\n16 15 79 7 101\n41 80 40 13 46\n",
"2\n0 -1 0 -1 1\n0 -1 0 1 -1\n",
"4\n66 55 95 78 114\n70 98 13 126 95\n17 47 88 71 18\n7 36 9 104 38\n",
"17\n66 15 -1 42 90\n67 108 104 16 110\n76 -1 -1 -1 96\n108 32 100 91 17\n87 -1 85 10 -1\n70 55 102 15 23\n0 33 111 105 63\n-1 56 104 68 116\n56 111 102 89 63\n63 0 68 80 -1\n80 61 -1 81 19\n001 -1 87 -1 89\n92 82 4 137 83\n19 30 114 77 104\n100 99 29 68 82\n98 -1 62 52 -1\n108 -1 -1 50 -1\n",
"9\n57 52 60 56 91\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 23 13 95\n4 2 70 38 68\n83 35 57 101 28\n12 40 54 56 73\n",
"3\n20 65 12 117 77\n78 112 39 23 0\n1 78 60 110 62\n",
"10\n-1 18 44 61 115\n-1 34 12 40 114\n-1 86 100 119 58\n-1 4 36 8 91\n1 58 85 13 82\n-1 9 85 109 -1\n24 75 0 71 42\n116 75 42 79 88\n62 -1 105 114 -1\n47 96 44 61 28\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 135 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n116 104 111 -1 -1\n92 -1 52 -1 5\n118 25 97 1 108\n-1 78 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 19 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 1\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n93 21 96 15 73\n75 66 54 46 107\n108 49 17 48 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 111 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n4 15 56 70 115\n3 45 40 30 15\n",
"5\n119 187 119 119 119\n0 1 -1 0 -1\n6 65 12 73 77\n78 112 22 23 11\n1 78 60 111 62\n",
"4\n-1 20 40 77 119\n30 10 73 22 194\n21 37 -1 25 98\n117 65 -1 -1 -1\n",
"2\n16 15 79 7 101\n74 80 40 13 46\n",
"2\n0 -1 0 -1 1\n-1 -1 0 1 -1\n",
"4\n66 55 95 78 114\n70 98 13 171 95\n17 47 88 71 18\n7 36 9 104 38\n",
"9\n57 52 60 56 93\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 23 13 95\n4 2 70 38 68\n83 35 57 101 28\n12 40 54 56 73\n",
"3\n20 65 12 117 18\n78 112 39 23 0\n1 78 60 110 62\n",
"26\n3 -1 71 -1 42\n85 72 48 38 -1\n-1 -1 66 24 -1\n46 -1 60 99 107\n53 106 51 -1 104\n-1 17 135 54 -1\n44 107 66 65 102\n47 40 62 34 5\n-1 10 -1 98 -1\n-1 69 47 85 75\n12 62 -1 15 -1\n48 63 72 32 99\n116 104 111 -1 -1\n92 -1 52 -1 5\n118 25 97 1 108\n-1 78 97 37 -1\n87 47 -1 -1 21\n79 87 73 82 70\n90 108 22 25 57\n37 -1 51 8 119\n64 -1 -1 38 82\n42 61 63 25 27\n82 -1 15 82 15\n-1 89 73 95 -1\n4 8 -1 70 116\n89 21 65 -1 88\n",
"19\n78 100 74 31 2\n27 45 72 63 1\n42 114 31 106 79\n88 119 118 69 90\n68 14 90 104 70\n93 21 96 15 73\n75 66 54 46 107\n108 49 17 48 90\n76 112 49 56 76\n34 43 5 57 67\n47 43 114 011 109\n79 118 69 22 19\n31 74 21 84 79\n1 64 88 97 79\n115 14 119 101 28\n55 9 43 67 10\n33 40 26 10 11\n92 0 60 14 48\n58 57 8 12 118\n",
"2\n4 15 56 70 152\n3 45 40 30 15\n",
"5\n119 187 119 119 119\n0 1 -1 0 -1\n6 65 12 73 77\n78 112 22 23 11\n0 78 60 111 62\n",
"4\n-1 20 40 123 119\n30 10 73 22 194\n21 37 -1 25 98\n117 65 -1 -1 -1\n",
"2\n16 27 79 7 101\n74 80 40 13 46\n",
"2\n-1 -1 0 -1 1\n-1 -1 0 1 -1\n",
"4\n66 55 95 78 114\n70 113 13 171 95\n17 47 88 71 18\n7 36 9 104 38\n",
"9\n57 52 60 56 93\n32 40 107 89 36\n80 0 45 92 119\n62 12 107 24 61\n43 28 4 26 113\n31 91 23 13 95\n4 2 70 38 68\n83 16 57 101 28\n12 40 54 56 73\n",
"3\n20 65 12 117 18\n78 112 39 19 0\n1 78 60 110 62\n"
],
"output": [
"2\n",
"27\n",
"-1\n",
"3\n",
"0\n",
"2\n",
"4\n",
"5\n",
"9\n",
"3\n",
"62\n",
"10\n",
"133\n",
"0\n",
"4\n",
"5\n",
"9\n",
"3\n",
"62\n",
"10\n",
"133\n",
"30\n",
"-1\n",
"7\n",
"26\n",
"0\n",
"3\n",
"0\n",
"0\n",
"0\n",
"4\n",
"5\n",
"9\n",
"3\n",
"62\n",
"10\n",
"133\n",
"30\n",
"3\n",
"-1\n",
"3\n",
"0\n",
"0\n",
"4\n",
"9\n",
"0\n",
"62\n",
"10\n",
"133\n",
"30\n",
"3\n",
"-1\n",
"0\n",
"-1\n",
"4\n",
"7\n",
"9\n",
"3\n",
"62\n",
"10\n",
"133\n",
"62\n",
"3\n",
"-1\n",
"0\n",
"0\n",
"0\n",
"9\n",
"0\n",
"10\n",
"133\n",
"-1\n",
"3\n",
"-1\n",
"0\n",
"-1\n",
"0\n",
"9\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vasya and Petya take part in a Codeforces round. The round lasts for two hours and contains five problems.
For this round the dynamic problem scoring is used. If you were lucky not to participate in any Codeforces round with dynamic problem scoring, here is what it means. The maximum point value of the problem depends on the ratio of the number of participants who solved the problem to the total number of round participants. Everyone who made at least one submission is considered to be participating in the round.
<image>
Pay attention to the range bounds. For example, if 40 people are taking part in the round, and 10 of them solve a particular problem, then the solvers fraction is equal to 1 / 4, and the problem's maximum point value is equal to 1500.
If the problem's maximum point value is equal to x, then for each whole minute passed from the beginning of the contest to the moment of the participant's correct submission, the participant loses x / 250 points. For example, if the problem's maximum point value is 2000, and the participant submits a correct solution to it 40 minutes into the round, this participant will be awarded with 2000·(1 - 40 / 250) = 1680 points for this problem.
There are n participants in the round, including Vasya and Petya. For each participant and each problem, the number of minutes which passed between the beginning of the contest and the submission of this participant to this problem is known. It's also possible that this participant made no submissions to this problem.
With two seconds until the end of the round, all participants' submissions have passed pretests, and not a single hack attempt has been made. Vasya believes that no more submissions or hack attempts will be made in the remaining two seconds, and every submission will pass the system testing.
Unfortunately, Vasya is a cheater. He has registered 109 + 7 new accounts for the round. Now Vasya can submit any of his solutions from these new accounts in order to change the maximum point values of the problems. Vasya can also submit any wrong solutions to any problems. Note that Vasya can not submit correct solutions to the problems he hasn't solved.
Vasya seeks to score strictly more points than Petya in the current round. Vasya has already prepared the scripts which allow to obfuscate his solutions and submit them into the system from any of the new accounts in just fractions of seconds. However, Vasya doesn't want to make his cheating too obvious, so he wants to achieve his goal while making submissions from the smallest possible number of new accounts.
Find the smallest number of new accounts Vasya needs in order to beat Petya (provided that Vasya's assumptions are correct), or report that Vasya can't achieve his goal.
Input
The first line contains a single integer n (2 ≤ n ≤ 120) — the number of round participants, including Vasya and Petya.
Each of the next n lines contains five integers ai, 1, ai, 2..., ai, 5 ( - 1 ≤ ai, j ≤ 119) — the number of minutes passed between the beginning of the round and the submission of problem j by participant i, or -1 if participant i hasn't solved problem j.
It is guaranteed that each participant has made at least one successful submission.
Vasya is listed as participant number 1, Petya is listed as participant number 2, all the other participants are listed in no particular order.
Output
Output a single integer — the number of new accounts Vasya needs to beat Petya, or -1 if Vasya can't achieve his goal.
Examples
Input
2
5 15 40 70 115
50 45 40 30 15
Output
2
Input
3
55 80 10 -1 -1
15 -1 79 60 -1
42 -1 13 -1 -1
Output
3
Input
5
119 119 119 119 119
0 0 0 0 -1
20 65 12 73 77
78 112 22 23 11
1 78 60 111 62
Output
27
Input
4
-1 20 40 77 119
30 10 73 50 107
21 29 -1 64 98
117 65 -1 -1 -1
Output
-1
Note
In the first example, Vasya's optimal strategy is to submit the solutions to the last three problems from two new accounts. In this case the first two problems will have the maximum point value of 1000, while the last three problems will have the maximum point value of 500. Vasya's score will be equal to 980 + 940 + 420 + 360 + 270 = 2970 points, while Petya will score just 800 + 820 + 420 + 440 + 470 = 2950 points.
In the second example, Vasya has to make a single unsuccessful submission to any problem from two new accounts, and a single successful submission to the first problem from the third new account. In this case, the maximum point values of the problems will be equal to 500, 1500, 1000, 1500, 3000. Vasya will score 2370 points, while Petya will score just 2294 points.
In the third example, Vasya can achieve his goal by submitting the solutions to the first four problems from 27 new accounts. The maximum point values of the problems will be equal to 500, 500, 500, 500, 2000. Thanks to the high cost of the fifth problem, Vasya will manage to beat Petya who solved the first four problems very quickly, but couldn't solve the fifth one.
### Input:
2
5 15 40 70 115
50 45 40 30 15
### Output:
2
### Input:
5
119 119 119 119 119
0 0 0 0 -1
20 65 12 73 77
78 112 22 23 11
1 78 60 111 62
### Output:
27
### Code:
import sys
inf = 10**9 + 7
def solve():
n = int(sys.stdin.readline())
v = [int(vi) for vi in sys.stdin.readline().split()] # Vesya
p = [int(pi) for pi in sys.stdin.readline().split()] # Petya
cnt = [0]*5
for i in range(5):
if v[i] != -1:
cnt[i] += 1
if p[i] != -1:
cnt[i] += 1
for i in range(n - 2):
a = [int(ai) for ai in sys.stdin.readline().split()]
for j in range(5):
if a[j] != -1:
cnt[j] += 1
for i in range(10**5):
if check(n, v, p, cnt, i):
print(i)
return
print(-1)
def check(n, v, p, cnt, m):
tot = n + m
solved = cnt[:]
dif = 0
for i in range(5):
if p[i] != -1 and v[i] > p[i]:
solved[i] += m
for i in range(5):
if solved[i]*2 > tot:
max_score = 500
elif solved[i]*4 > tot:
max_score = 1000
elif solved[i]*8 > tot:
max_score = 1500
elif solved[i]*16 > tot:
max_score = 2000
elif solved[i]*32 > tot:
max_score = 2500
else:
max_score = 3000
if v[i] == p[i] == -1:
pass
elif v[i] == -1:
dif -= max_score * (250 - p[i]) // 250
elif p[i] == -1:
dif += max_score * (250 - v[i]) // 250
else:
dif += max_score * (p[i] - v[i]) // 250
return dif > 0
if __name__ == '__main__':
solve()
|
831_E. Cards Sorting_28693
|
Vasily has a deck of cards consisting of n cards. There is an integer on each of the cards, this integer is between 1 and 100 000, inclusive. It is possible that some cards have the same integers on them.
Vasily decided to sort the cards. To do this, he repeatedly takes the top card from the deck, and if the number on it equals the minimum number written on the cards in the deck, then he places the card away. Otherwise, he puts it under the deck and takes the next card from the top, and so on. The process ends as soon as there are no cards in the deck. You can assume that Vasily always knows the minimum number written on some card in the remaining deck, but doesn't know where this card (or these cards) is.
You are to determine the total number of times Vasily takes the top card from the deck.
Input
The first line contains single integer n (1 ≤ n ≤ 100 000) — the number of cards in the deck.
The second line contains a sequence of n integers a1, a2, ..., an (1 ≤ ai ≤ 100 000), where ai is the number written on the i-th from top card in the deck.
Output
Print the total number of times Vasily takes the top card from the deck.
Examples
Input
4
6 3 1 2
Output
7
Input
1
1000
Output
1
Input
7
3 3 3 3 3 3 3
Output
7
Note
In the first example Vasily at first looks at the card with number 6 on it, puts it under the deck, then on the card with number 3, puts it under the deck, and then on the card with number 1. He places away the card with 1, because the number written on it is the minimum among the remaining cards. After that the cards from top to bottom are [2, 6, 3]. Then Vasily looks at the top card with number 2 and puts it away. After that the cards from top to bottom are [6, 3]. Then Vasily looks at card 6, puts it under the deck, then at card 3 and puts it away. Then there is only one card with number 6 on it, and Vasily looks at it and puts it away. Thus, in total Vasily looks at 7 cards.
|
# -*- coding: utf-8 -*-
import sys
# fout = open("output.txt", "w")
fin = sys.stdin
# fin = open("input.txt", "r")
fout = sys.stdout
n = int(fin.readline())
a = list(map(int, fin.readline().split()))
def solution(n, a):
sorted_arr = [(i, elem) for i, elem in enumerate(a)]
sorted_arr.sort(key=lambda x: (x[1], x[0]))
sorted_indexes = [x[0] for x in sorted_arr]
cnt = 0
current_n = n
prev_index = sorted_indexes[0]
prev_elem = sorted_arr[0][1]
cur_len = 1
i = 1
while i < n:
cur_index = sorted_indexes[i]
cur_elem = sorted_arr[i][1]
if prev_index < cur_index:
cur_len += 1
prev_index = sorted_indexes[i]
prev_elem = sorted_arr[i][1]
elif i+1<n and cur_elem == sorted_arr[i+1][1]: # здесь косяк
penalty = 1
last_penalty_ind = sorted_indexes[i]
while i+1 < n and sorted_arr[i+1][1] == cur_elem:
if sorted_arr[i+1][0] >= prev_index:
cur_len += 1
else:
penalty += 1
last_penalty_ind = sorted_indexes[i+1]
i += 1
cnt += current_n
current_n -= cur_len
cur_len = penalty
prev_elem = cur_elem
prev_index = last_penalty_ind
else:
cnt += current_n
current_n -= cur_len
cur_len = 1
prev_index = sorted_indexes[i]
prev_elem = sorted_arr[i][1]
i += 1
cnt += current_n
return cnt
cnt = solution(n, a)
fout.write(str(cnt))
fout.close()
|
{
"input": [
"4\n6 3 1 2\n",
"1\n1000\n",
"7\n3 3 3 3 3 3 3\n",
"87\n12 2 2 10 12 1 5 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 8 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 10 15 14 10 7 7 7 2 7 6 10\n",
"20\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"30\n6283 14661 69188 39640 41261 48019 86266 70517 4592 69008 20602 33339 29980 96844 76008 96294 27120 22671 5243 742 33692 18068 29056 48033 1223 82728 99765 38350 36425 10671\n",
"100\n9 9 72 55 14 8 55 58 35 67 3 18 73 92 41 49 15 60 18 66 9 26 97 47 43 88 71 97 19 34 48 96 79 53 8 24 69 49 12 23 77 12 21 88 66 9 29 13 61 69 54 77 41 13 4 68 37 74 7 6 29 76 55 72 89 4 78 27 29 82 18 83 12 4 32 69 89 85 66 13 92 54 38 5 26 56 17 55 29 4 17 39 29 94 3 67 85 98 21 14\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 193 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 373 322 716 202 689 857 936 806 556 153 137 863 1047 678 564 474 282 135 610 176 855 360 814 144 77 112 354 154\n",
"10\n4 3 4 3 3 3 4 4 4 3\n",
"87\n12 2 2 10 12 1 5 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 10 15 14 10 7 7 7 2 7 6 10\n",
"30\n6283 14661 69188 39640 41261 48019 86266 70517 1276 69008 20602 33339 29980 96844 76008 96294 27120 22671 5243 742 33692 18068 29056 48033 1223 82728 99765 38350 36425 10671\n",
"100\n9 9 72 55 14 8 55 58 35 67 3 18 73 92 41 49 15 60 18 66 9 26 97 47 43 88 71 97 19 34 48 96 79 53 8 24 69 49 12 23 77 12 21 88 66 9 29 13 61 69 54 77 41 13 4 68 37 74 7 6 29 76 55 72 89 4 78 27 29 82 18 83 12 4 32 69 89 85 66 13 92 54 38 5 26 6 17 55 29 4 17 39 29 94 3 67 85 98 21 14\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 193 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 373 322 716 202 689 857 936 806 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 814 144 77 112 354 154\n",
"10\n4 3 4 3 3 2 4 4 4 3\n",
"4\n6 2 1 2\n",
"1\n1001\n",
"7\n3 5 3 3 3 3 3\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 10 15 14 10 7 7 7 2 7 6 10\n",
"30\n6283 14661 69188 39640 41261 48019 86266 66388 1276 69008 20602 33339 29980 96844 76008 96294 27120 22671 5243 742 33692 18068 29056 48033 1223 82728 99765 38350 36425 10671\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 19 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 373 322 716 202 689 857 936 806 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 814 144 77 112 354 154\n",
"10\n4 6 4 3 3 2 4 4 4 3\n",
"4\n6 2 2 2\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 10 15 14 10 7 7 7 2 1 6 10\n",
"30\n6283 14661 69188 39640 41261 48019 86266 66388 1276 69008 20602 33339 29980 96844 76008 96294 27120 22671 5243 742 33692 24056 29056 48033 1223 82728 99765 38350 36425 10671\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 19 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 857 936 806 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 814 144 77 112 354 154\n",
"10\n4 6 4 3 3 2 6 4 4 3\n",
"7\n3 5 3 3 3 3 7\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 10 15 14 10 7 7 7 2 1 4 10\n",
"30\n6283 14661 69188 39640 41261 48019 86266 66388 1276 69008 20602 33339 38772 96844 76008 96294 27120 22671 5243 742 33692 24056 29056 48033 1223 82728 99765 38350 36425 10671\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 19 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 857 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 814 144 77 112 354 154\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 13 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 17 15 14 10 7 7 7 2 1 4 10\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 19 289 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 857 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 4 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 17 15 14 10 7 7 7 2 1 4 10\n",
"64\n826 142 89 337 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 857 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"87\n12 2 2 10 12 1 6 9 15 2 4 7 7 14 8 10 1 6 7 6 4 15 10 6 2 11 13 1 15 14 8 14 4 7 11 12 3 15 9 2 13 1 7 11 2 1 13 11 8 14 2 2 12 7 13 4 13 3 13 3 11 1 7 13 15 8 12 4 12 4 1 4 9 3 13 12 17 15 14 10 7 7 7 2 2 4 10\n",
"10\n2 6 8 3 3 2 8 4 1 3\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"10\n2 6 8 3 3 2 8 4 1 5\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 164 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 191 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"10\n2 6 8 3 3 1 8 4 1 5\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 191 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 200 354 154\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 191 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 364 474 282 135 610 176 855 360 128 144 77 200 354 154\n",
"64\n826 142 89 550 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 191 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 364 474 282 135 610 176 855 360 128 144 77 200 354 154\n",
"64\n826 142 89 550 897 891 1004 704 281 644 1493 852 147 19 318 384 625 695 416 944 162 939 191 1047 359 114 403 99 713 300 268 316 256 404 852 496 72 322 716 202 689 842 936 58 556 204 137 863 1047 678 364 474 282 135 610 176 855 360 128 144 77 200 354 154\n",
"100\n9 9 72 55 14 8 55 58 35 67 3 18 73 92 41 49 15 60 18 66 9 26 97 47 43 88 71 97 19 34 48 96 79 52 8 24 69 49 12 23 77 12 21 88 66 9 29 13 61 69 54 77 41 13 4 68 37 74 7 6 29 76 55 72 89 4 78 27 29 82 18 83 12 4 32 69 89 85 66 13 92 54 38 5 26 6 17 55 29 4 17 39 29 94 3 67 85 98 21 14\n",
"1\n0001\n",
"7\n3 5 3 3 3 3 4\n",
"4\n6 4 2 2\n",
"10\n4 6 8 3 3 2 6 4 4 3\n",
"4\n6 4 4 2\n",
"30\n6283 14661 69188 39640 41261 48019 86266 66388 1276 69008 20602 33339 38772 96844 76008 96294 27120 22671 2006 742 33692 24056 29056 48033 1223 82728 99765 38350 36425 10671\n",
"10\n4 6 8 3 3 2 8 4 4 3\n",
"4\n6 2 4 2\n",
"10\n2 6 8 3 3 2 8 4 4 3\n",
"4\n6 2 4 4\n",
"64\n826 142 89 349 897 891 1004 704 281 644 910 852 147 19 318 384 625 695 416 944 162 939 164 1047 359 114 499 99 713 300 268 316 256 404 852 496 72 322 716 202 689 857 936 58 556 204 137 863 1047 678 564 474 282 135 610 176 855 360 128 144 77 112 354 154\n",
"4\n10 2 4 4\n",
"4\n10 1 4 4\n",
"10\n2 6 8 3 3 3 8 4 1 5\n",
"10\n2 5 8 3 3 1 8 4 1 5\n",
"10\n2 2 8 3 3 1 8 4 1 5\n",
"10\n2 2 8 3 3 1 8 4 1 4\n"
],
"output": [
"7\n",
"1\n",
"7\n",
"580\n",
"20\n",
"235\n",
"1805\n",
"1042\n",
"15\n",
"585",
"235",
"1786",
"1044",
"20",
"7",
"1",
"8",
"570",
"234",
"1037",
"22",
"5",
"574",
"212",
"989",
"23",
"9",
"573",
"210",
"1029",
"578",
"1064",
"571",
"1102",
"563",
"28",
"1114",
"29",
"1085",
"1086",
"21",
"1139",
"1168",
"1163",
"1167",
"1786",
"1",
"8",
"7",
"23",
"8",
"210",
"22",
"7",
"20",
"5",
"1102",
"5",
"5",
"22",
"21",
"20",
"20"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vasily has a deck of cards consisting of n cards. There is an integer on each of the cards, this integer is between 1 and 100 000, inclusive. It is possible that some cards have the same integers on them.
Vasily decided to sort the cards. To do this, he repeatedly takes the top card from the deck, and if the number on it equals the minimum number written on the cards in the deck, then he places the card away. Otherwise, he puts it under the deck and takes the next card from the top, and so on. The process ends as soon as there are no cards in the deck. You can assume that Vasily always knows the minimum number written on some card in the remaining deck, but doesn't know where this card (or these cards) is.
You are to determine the total number of times Vasily takes the top card from the deck.
Input
The first line contains single integer n (1 ≤ n ≤ 100 000) — the number of cards in the deck.
The second line contains a sequence of n integers a1, a2, ..., an (1 ≤ ai ≤ 100 000), where ai is the number written on the i-th from top card in the deck.
Output
Print the total number of times Vasily takes the top card from the deck.
Examples
Input
4
6 3 1 2
Output
7
Input
1
1000
Output
1
Input
7
3 3 3 3 3 3 3
Output
7
Note
In the first example Vasily at first looks at the card with number 6 on it, puts it under the deck, then on the card with number 3, puts it under the deck, and then on the card with number 1. He places away the card with 1, because the number written on it is the minimum among the remaining cards. After that the cards from top to bottom are [2, 6, 3]. Then Vasily looks at the top card with number 2 and puts it away. After that the cards from top to bottom are [6, 3]. Then Vasily looks at card 6, puts it under the deck, then at card 3 and puts it away. Then there is only one card with number 6 on it, and Vasily looks at it and puts it away. Thus, in total Vasily looks at 7 cards.
### Input:
4
6 3 1 2
### Output:
7
### Input:
1
1000
### Output:
1
### Code:
# -*- coding: utf-8 -*-
import sys
# fout = open("output.txt", "w")
fin = sys.stdin
# fin = open("input.txt", "r")
fout = sys.stdout
n = int(fin.readline())
a = list(map(int, fin.readline().split()))
def solution(n, a):
sorted_arr = [(i, elem) for i, elem in enumerate(a)]
sorted_arr.sort(key=lambda x: (x[1], x[0]))
sorted_indexes = [x[0] for x in sorted_arr]
cnt = 0
current_n = n
prev_index = sorted_indexes[0]
prev_elem = sorted_arr[0][1]
cur_len = 1
i = 1
while i < n:
cur_index = sorted_indexes[i]
cur_elem = sorted_arr[i][1]
if prev_index < cur_index:
cur_len += 1
prev_index = sorted_indexes[i]
prev_elem = sorted_arr[i][1]
elif i+1<n and cur_elem == sorted_arr[i+1][1]: # здесь косяк
penalty = 1
last_penalty_ind = sorted_indexes[i]
while i+1 < n and sorted_arr[i+1][1] == cur_elem:
if sorted_arr[i+1][0] >= prev_index:
cur_len += 1
else:
penalty += 1
last_penalty_ind = sorted_indexes[i+1]
i += 1
cnt += current_n
current_n -= cur_len
cur_len = penalty
prev_elem = cur_elem
prev_index = last_penalty_ind
else:
cnt += current_n
current_n -= cur_len
cur_len = 1
prev_index = sorted_indexes[i]
prev_elem = sorted_arr[i][1]
i += 1
cnt += current_n
return cnt
cnt = solution(n, a)
fout.write(str(cnt))
fout.close()
|
877_A. Alex and broken contest_28699
|
One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems.
But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest by its name.
It is known, that problem is from this contest if and only if its name contains one of Alex's friends' name exactly once. His friends' names are "Danil", "Olya", "Slava", "Ann" and "Nikita".
Names are case sensitive.
Input
The only line contains string from lowercase and uppercase letters and "_" symbols of length, not more than 100 — the name of the problem.
Output
Print "YES", if problem is from this contest, and "NO" otherwise.
Examples
Input
Alex_and_broken_contest
Output
NO
Input
NikitaAndString
Output
YES
Input
Danil_and_Olya
Output
NO
|
judul = input()
nama = ["Danil", "Olya", "Slava", "Ann", "Nikita"]
cek = 0
ada = []
for i in range(0, 5):
ada.append(judul.count(nama[i]))
cek = cek + ada[i]
if cek == 1:
print("YES")
else:
print("NO")
|
{
"input": [
"Alex_and_broken_contest\n",
"NikitaAndString\n",
"Danil_and_Olya\n",
"Hardest_problem_ever\n",
"Wake_up_Neo\n",
"AnAnn\n",
"DanilOlyaOlya\n",
"And_Danil\n",
"Olya_and_energy_drinks\n",
"ann\n",
"Nikita_Nikita\n",
"Vanya\n",
"AnnAnn\n",
"Danil_Danil_Olya\n",
"AAnnnnn\n",
"Ann_Ann_Danil\n",
"Danil_Danil_Nikita\n",
"ababaca\n",
"aa\n",
"Annn\n",
"OlyOlya\n",
"Ann\n",
"AlexaaaaaaBBBBBOlyaDDDDD\n",
"oLya_adn_smth\n",
"DanilDanilSlava\n",
"DanilDanil\n",
"DDanil\n",
"danil_and_work\n",
"AndAnn\n",
"Slava____and_the_game\n",
"Batman_Nananananananan_Batman\n",
"I_dont_know_what_to_write_here\n",
"IloveDaniland\n",
"aaabbba\n",
"Olya_Nikita_Ann_Slava_Danil\n",
"DanilDanilOlya\n",
"____________________________________________________________________________________________________\n",
"Danilaaa\n",
"Unn\n",
"Danil_and_part_time_job\n",
"NikitaNikitb\n",
"Ann_and_books\n",
"abcddddDanil\n",
"AnnAnnDanil\n",
"Dilzhan\n",
"FloorISLava\n",
"A\n",
"Olya\n",
"Nikitaaa\n",
"Nikita\n",
"OlyaAnnAnn\n",
"its_me_Mario\n",
"Nikitb\n",
"AnnNikitaNikitaNikitaNikita__good_luck\n",
"Slava\n",
"Hardest_problem_evdr\n",
"AnnnA\n",
"oeN_pu_ekaW\n",
"aylOaylOlinaD\n",
"And_Dainl\n",
"Olya`and_energy_drinks\n",
"amn\n",
"Nikita^Nikita\n",
"aynaV\n",
"Ann@nn\n",
"Danil_Damil_Olya\n",
"@Annnnn\n",
"linaD_nnA_nnA\n",
"Danit_Danil_Nikila\n",
"ab`baca\n",
"ab\n",
"Anno\n",
"OayOlyl\n",
"Bnn\n",
"BlexaaaaaaBBBBBOlyaDDDDD\n",
"oLya_`dn_smth\n",
"avalSlinaDlinaD\n",
"DanikDanil\n",
"DlaniD\n",
"danil`and_work\n",
"AncAnn\n",
"Slava`___and_the_game\n",
"matBan_Nananananananan_Batman\n",
"I_dont_know_what_to^write_here\n",
"IloveDanjland\n",
"`aabbba\n",
"linaD_avalS_nnA_atikiN_aylO\n",
"DanilCanilOlya\n",
"__________________________________________________________________________________________________`_\n",
"aaalinaD\n",
"nnU\n",
"Danil_and_p`rt_time_job\n",
"NijitaNikitb\n",
"Anndan__books\n",
"abcddddDaoil\n",
"AnDAnnnanil\n",
"nahzliD\n",
"FkoorISLava\n",
"@\n",
"aylO\n",
"aaatikiN\n",
"atikiN\n",
"OlyaBnnAnn\n",
"its_me_Lario\n",
"Nilitb\n",
"AnnNikitatikitaNikitaNikiNa__good_luck\n",
"Slbva\n",
"Alex_bnd_aroken_contest\n",
"NikitaAndStsing\n",
"Danil_and_Olyb\n",
"Hardest_pmobler_evdr\n",
"oeM_pu_ekaW\n",
"BnnnA\n",
"aylPaylOlinaD\n",
"linaD_dnA\n",
"sknird_ygrene_dna`aylO\n",
"nma\n",
"Nikita^Njkita\n",
"Vbnya\n",
"nn@nnA\n",
"Danil_D`mil_Olya\n",
"@Annnno\n",
"Bnn_Ann_Danil\n",
"Danti_Danil_Nikila\n",
"acab`ba\n",
"ac\n",
"Aonn\n",
"OayOlzl\n",
"Cnn\n",
"BlexaaaaaaBBBBBOlyaEDDDD\n",
"oLxa_`dn_smth\n",
"avalSiinaDllnaD\n",
"DanikDbnil\n",
"DinalD\n",
"danhl_and_work\n",
"AncAmn\n",
"emag_eht_dna___`avalS\n",
"matBan_Nanananananaman_Batman\n",
"I_tont_know_whad_to^write_here\n",
"IloveDbnjland\n",
"`aacbba\n",
"Olya_Nikita`Ann_Slava_Danil\n",
"DaailCnnilOlya\n",
"_`__________________________________________________________________________________________________\n",
"Danila`a\n",
"nmU\n",
"Danil__nd_p`rtatime_job\n",
"NijitbNikitb\n",
"Anndan__bonks\n",
"bbcddddDaoil\n",
"linannnADnA\n"
],
"output": [
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems.
But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest by its name.
It is known, that problem is from this contest if and only if its name contains one of Alex's friends' name exactly once. His friends' names are "Danil", "Olya", "Slava", "Ann" and "Nikita".
Names are case sensitive.
Input
The only line contains string from lowercase and uppercase letters and "_" symbols of length, not more than 100 — the name of the problem.
Output
Print "YES", if problem is from this contest, and "NO" otherwise.
Examples
Input
Alex_and_broken_contest
Output
NO
Input
NikitaAndString
Output
YES
Input
Danil_and_Olya
Output
NO
### Input:
Alex_and_broken_contest
### Output:
NO
### Input:
NikitaAndString
### Output:
YES
### Code:
judul = input()
nama = ["Danil", "Olya", "Slava", "Ann", "Nikita"]
cek = 0
ada = []
for i in range(0, 5):
ada.append(judul.count(nama[i]))
cek = cek + ada[i]
if cek == 1:
print("YES")
else:
print("NO")
|
900_B. Position in Fraction_28703
|
You have a fraction <image>. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.
Input
The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).
Output
Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.
Examples
Input
1 2 0
Output
2
Input
2 3 7
Output
-1
Note
The fraction in the first example has the following decimal notation: <image>. The first zero stands on second position.
The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction.
|
a,b,c = map(int, input().split())
t = a
q, r = divmod(t, b)
for i in range(1, 10**5+1):
q, r = divmod(r*10, b)
#print(q)
if q == c:
print(i)
exit()
else:
print(-1)
|
{
"input": [
"2 3 7\n",
"1 2 0\n",
"1 10 1\n",
"53 101 6\n",
"567 1580 0\n",
"69168 84860 4\n",
"35 111 4\n",
"99971 99989 0\n",
"25102 31579 2\n",
"13805 15538 3\n",
"38790 39359 0\n",
"2 3 0\n",
"7 31 3\n",
"1 9 0\n",
"45 97 0\n",
"1636 3269 6\n",
"8 51 0\n",
"1 3 0\n",
"8880 81608 9\n",
"1 7 7\n",
"1 100 0\n",
"1 100000 1\n",
"1 57 0\n",
"1 7 0\n",
"1 2 5\n",
"1 10001 9\n",
"6873 7769 3\n",
"4942 62768 5\n",
"47117 78718 0\n",
"99999 100000 8\n",
"971 1883 3\n",
"10958 21926 3\n",
"44102 73848 2\n",
"1 4 1\n",
"69168 84860 8\n",
"25102 57486 2\n",
"13805 16262 3\n",
"38790 64660 0\n",
"7 30 3\n",
"45 151 0\n",
"1636 3269 9\n",
"16 51 0\n",
"13512 21926 3\n",
"1 4 0\n",
"1636 4367 9\n",
"17650 21926 3\n",
"558 1580 2\n",
"8880 76242 0\n",
"558 2062 3\n",
"53 101 12\n",
"567 1580 1\n",
"35 111 8\n",
"1 12 0\n",
"8880 81608 0\n",
"1 8 7\n",
"1 57 1\n",
"2 7 0\n",
"1 11001 9\n",
"433 7769 3\n",
"47117 69358 0\n",
"99999 100000 13\n",
"971 1434 3\n",
"1 3 7\n",
"1 2 1\n",
"558 1580 1\n",
"69168 84860 1\n",
"10757 57486 2\n",
"10 30 3\n",
"45 215 0\n",
"13 51 0\n",
"1 3 1\n",
"8880 52919 0\n",
"2 8 7\n",
"1 22 1\n",
"4 7 0\n",
"367 7769 3\n",
"47117 137344 0\n",
"1649 100000 13\n",
"627 1434 3\n",
"1 3 5\n",
"1 2 2\n",
"2 4 0\n",
"69168 84860 0\n",
"10757 57486 4\n",
"8 30 3\n",
"68 215 0\n",
"1636 4367 4\n",
"13 65 0\n",
"1 6 1\n",
"2 14 7\n",
"367 1552 3\n",
"1649 100000 11\n",
"778 1434 3\n",
"1 2 3\n",
"558 2062 2\n",
"69168 103222 0\n",
"8 23 3\n",
"47 215 0\n",
"1636 7762 4\n",
"1 9 1\n",
"14075 76242 0\n",
"2 14 2\n",
"367 1552 6\n",
"778 1180 3\n",
"50383 103222 0\n",
"8 23 2\n",
"47 215 1\n",
"1 9 2\n",
"14075 127808 0\n",
"2 14 4\n",
"367 3003 6\n",
"778 1180 0\n"
],
"output": [
"-1\n",
"2\n",
"1\n",
"-1\n",
"6\n",
"107\n",
"-1\n",
"9\n",
"174\n",
"164\n",
"212\n",
"-1\n",
"15\n",
"-1\n",
"39\n",
"150\n",
"10\n",
"-1\n",
"161\n",
"6\n",
"1\n",
"5\n",
"1\n",
"-1\n",
"1\n",
"5\n",
"163\n",
"122\n",
"213\n",
"-1\n",
"130\n",
"117\n",
"132\n",
"-1\n",
"1\n",
"6\n",
"20\n",
"5\n",
"2\n",
"4\n",
"10\n",
"9\n",
"41\n",
"3\n",
"8\n",
"7\n",
"12\n",
"29\n",
"22\n",
"-1\n",
"-1\n",
"-1\n",
"1\n",
"2\n",
"-1\n",
"2\n",
"-1\n",
"5\n",
"5\n",
"6\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"4\n",
"2\n",
"5\n",
"1\n",
"2\n",
"5\n",
"-1\n",
"5\n",
"-1\n",
"-1\n",
"-1\n",
"5\n",
"4\n",
"-1\n",
"2\n",
"-1\n",
"-1\n",
"2\n",
"4\n",
"10\n",
"-1\n",
"7\n",
"3\n",
"2\n",
"1\n",
"6\n",
"2\n",
"-1\n",
"5\n",
"-1\n",
"1\n",
"3\n",
"1\n",
"5\n",
"7\n",
"1\n",
"5\n",
"3\n",
"3\n",
"4\n",
"5\n",
"5\n",
"2\n",
"-1\n",
"3\n",
"2\n",
"-1\n",
"7\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have a fraction <image>. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.
Input
The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).
Output
Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.
Examples
Input
1 2 0
Output
2
Input
2 3 7
Output
-1
Note
The fraction in the first example has the following decimal notation: <image>. The first zero stands on second position.
The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction.
### Input:
2 3 7
### Output:
-1
### Input:
1 2 0
### Output:
2
### Code:
a,b,c = map(int, input().split())
t = a
q, r = divmod(t, b)
for i in range(1, 10**5+1):
q, r = divmod(r*10, b)
#print(q)
if q == c:
print(i)
exit()
else:
print(-1)
|
950_B. Intercepted Message_28710
|
Hacker Zhorik wants to decipher two secret messages he intercepted yesterday. Yeah message is a sequence of encrypted blocks, each of them consists of several bytes of information.
Zhorik knows that each of the messages is an archive containing one or more files. Zhorik knows how each of these archives was transferred through the network: if an archive consists of k files of sizes l1, l2, ..., lk bytes, then the i-th file is split to one or more blocks bi, 1, bi, 2, ..., bi, mi (here the total length of the blocks bi, 1 + bi, 2 + ... + bi, mi is equal to the length of the file li), and after that all blocks are transferred through the network, maintaining the order of files in the archive.
Zhorik thinks that the two messages contain the same archive, because their total lengths are equal. However, each file can be split in blocks in different ways in the two messages.
You are given the lengths of blocks in each of the two messages. Help Zhorik to determine what is the maximum number of files could be in the archive, if the Zhorik's assumption is correct.
Input
The first line contains two integers n, m (1 ≤ n, m ≤ 105) — the number of blocks in the first and in the second messages.
The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 106) — the length of the blocks that form the first message.
The third line contains m integers y1, y2, ..., ym (1 ≤ yi ≤ 106) — the length of the blocks that form the second message.
It is guaranteed that x1 + ... + xn = y1 + ... + ym. Also, it is guaranteed that x1 + ... + xn ≤ 106.
Output
Print the maximum number of files the intercepted array could consist of.
Examples
Input
7 6
2 5 3 1 11 4 4
7 8 2 4 1 8
Output
3
Input
3 3
1 10 100
1 100 10
Output
2
Input
1 4
4
1 1 1 1
Output
1
Note
In the first example the maximum number of files in the archive is 3. For example, it is possible that in the archive are three files of sizes 2 + 5 = 7, 15 = 3 + 1 + 11 = 8 + 2 + 4 + 1 and 4 + 4 = 8.
In the second example it is possible that the archive contains two files of sizes 1 and 110 = 10 + 100 = 100 + 10. Note that the order of files is kept while transferring archives through the network, so we can't say that there are three files of sizes 1, 10 and 100.
In the third example the only possibility is that the archive contains a single file of size 4.
|
n,m=map(int,input().split())
x=list(map(int,input().split()))
y=list(map(int,input().split()))
i=0
j=0
s1=0
s2=0
count=1
while i<n and j<m:
if s1==s2 and s1>0:
count+=1
s1=0
s2=0
elif s1>s2 or s2==0:
s2+=y[j]
j+=1
elif s1<s2 or s1==0:
s1+=x[i]
i+=1
print(count)
|
{
"input": [
"1 4\n4\n1 1 1 1\n",
"7 6\n2 5 3 1 11 4 4\n7 8 2 4 1 8\n",
"3 3\n1 10 100\n1 100 10\n",
"1 1\n1000000\n1000000\n",
"2 2\n1 1\n1 1\n",
"2 2\n2 3\n3 2\n",
"2 3\n2 2\n1 1 2\n",
"2 3\n3 2\n2 1 2\n",
"2 2\n2 3\n4 1\n",
"1 1\n1\n1\n",
"30 50\n3 3 1 3 1 2 4 3 4 1 3 2 3 3 2 3 2 1 3 4 2 1 1 3 2 2 1 3 1 60\n4 4 1 2 2 2 3 1 3 2 1 2 4 4 2 1 2 3 1 3 4 4 3 3 4 4 4 1 2 1 3 3 1 1 3 3 4 3 2 3 2 4 1 4 2 3 2 2 3 1\n",
"2 2\n500000 500000\n1 999999\n",
"2 2\n2 3\n2 3\n",
"1 2\n1000000\n999999 1\n",
"5 3\n1 1 4 1 2\n1 4 4\n",
"3 5\n2 2 9\n2 1 4 2 4\n",
"1 2\n2\n1 1\n",
"31 31\n5745 258 5486 13779 20931 407 1478 49032 30787 4957 36603 1034 5011 22319 50560 34419 22036 18235 62551 89259 36093 126169 106027 1673 52983 50127 640 30714 54574 20129 45984\n5745 258 5486 13779 20931 407 1478 49032 30787 4957 36603 1034 5011 22319 50560 34419 22036 18235 62551 89259 36093 126169 106027 1673 52983 50127 640 30714 54574 20129 45984\n",
"3 6\n8 4 1\n1 8 1 1 1 1\n",
"50 30\n2 3 1 2 2 4 3 4 3 2 1 4 2 3 1 3 1 2 2 3 1 1 1 2 3 1 4 3 1 2 1 2 2 1 2 4 4 3 3 2 2 1 1 1 2 2 2 4 3 3\n3 3 3 4 1 4 1 4 4 1 3 4 3 1 2 4 2 1 4 2 3 1 1 2 2 1 2 4 1 41\n",
"50 50\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"2 3\n2 3\n2 1 2\n",
"50 50\n5733 740 547 3647 5382 5109 6842 7102 5879 1502 3574 1628 7905 4357 8569 9564 8268 3542 2487 8532 425 7713 2585 925 6458 2697 2844 69 324 9030 495 4428 6724 3524 3304 4874 1303 2098 1136 1048 2464 7316 274 9586 534 2450 2368 8060 7795 70692\n1918 4122 6806 4914 6517 6278 9842 9480 6609 4221 9373 1728 9508 9778 8578 5589 2673 6618 6031 9016 4017 6671 6008 2268 5154 9614 6834 9512 9618 6424 1736 1464 6520 9812 1722 9197 2412 2699 73 968 2906 2715 6573 8675 548 7061 5455 88 5565 2544\n",
"2 3\n2 2\n2 1 1\n",
"2 3\n1 3\n2 1 1\n",
"5 3\n1 1 4 1 3\n2 4 4\n",
"2 2\n3 3\n3 3\n",
"3 5\n2 3 9\n2 1 4 2 5\n",
"3 5\n3 1 9\n2 1 4 2 4\n",
"2 2\n2 1\n2 1\n",
"2 2\n2 5\n2 5\n",
"3 5\n2 3 9\n2 2 4 2 4\n",
"2 2\n3 2\n2 3\n",
"2 3\n4 2\n1 1 4\n",
"2 2\n2 4\n3 3\n",
"3 3\n2 10 100\n2 100 10\n",
"2 2\n2 2\n2 2\n",
"2 3\n3 1\n1 1 2\n",
"1 1\n2\n2\n"
],
"output": [
"1\n",
"3\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"12\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"31\n",
"2\n",
"12\n",
"50\n",
"2\n",
"1\n",
"2\n",
"1\n",
"3\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Hacker Zhorik wants to decipher two secret messages he intercepted yesterday. Yeah message is a sequence of encrypted blocks, each of them consists of several bytes of information.
Zhorik knows that each of the messages is an archive containing one or more files. Zhorik knows how each of these archives was transferred through the network: if an archive consists of k files of sizes l1, l2, ..., lk bytes, then the i-th file is split to one or more blocks bi, 1, bi, 2, ..., bi, mi (here the total length of the blocks bi, 1 + bi, 2 + ... + bi, mi is equal to the length of the file li), and after that all blocks are transferred through the network, maintaining the order of files in the archive.
Zhorik thinks that the two messages contain the same archive, because their total lengths are equal. However, each file can be split in blocks in different ways in the two messages.
You are given the lengths of blocks in each of the two messages. Help Zhorik to determine what is the maximum number of files could be in the archive, if the Zhorik's assumption is correct.
Input
The first line contains two integers n, m (1 ≤ n, m ≤ 105) — the number of blocks in the first and in the second messages.
The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 106) — the length of the blocks that form the first message.
The third line contains m integers y1, y2, ..., ym (1 ≤ yi ≤ 106) — the length of the blocks that form the second message.
It is guaranteed that x1 + ... + xn = y1 + ... + ym. Also, it is guaranteed that x1 + ... + xn ≤ 106.
Output
Print the maximum number of files the intercepted array could consist of.
Examples
Input
7 6
2 5 3 1 11 4 4
7 8 2 4 1 8
Output
3
Input
3 3
1 10 100
1 100 10
Output
2
Input
1 4
4
1 1 1 1
Output
1
Note
In the first example the maximum number of files in the archive is 3. For example, it is possible that in the archive are three files of sizes 2 + 5 = 7, 15 = 3 + 1 + 11 = 8 + 2 + 4 + 1 and 4 + 4 = 8.
In the second example it is possible that the archive contains two files of sizes 1 and 110 = 10 + 100 = 100 + 10. Note that the order of files is kept while transferring archives through the network, so we can't say that there are three files of sizes 1, 10 and 100.
In the third example the only possibility is that the archive contains a single file of size 4.
### Input:
1 4
4
1 1 1 1
### Output:
1
### Input:
7 6
2 5 3 1 11 4 4
7 8 2 4 1 8
### Output:
3
### Code:
n,m=map(int,input().split())
x=list(map(int,input().split()))
y=list(map(int,input().split()))
i=0
j=0
s1=0
s2=0
count=1
while i<n and j<m:
if s1==s2 and s1>0:
count+=1
s1=0
s2=0
elif s1>s2 or s2==0:
s2+=y[j]
j+=1
elif s1<s2 or s1==0:
s1+=x[i]
i+=1
print(count)
|
978_E. Bus Video System_28714
|
The busses in Berland are equipped with a video surveillance system. The system records information about changes in the number of passengers in a bus after stops.
If x is the number of passengers in a bus just before the current bus stop and y is the number of passengers in the bus just after current bus stop, the system records the number y-x. So the system records show how number of passengers changed.
The test run was made for single bus and n bus stops. Thus, the system recorded the sequence of integers a_1, a_2, ..., a_n (exactly one number for each bus stop), where a_i is the record for the bus stop i. The bus stops are numbered from 1 to n in chronological order.
Determine the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w (that is, at any time in the bus there should be from 0 to w passengers inclusive).
Input
The first line contains two integers n and w (1 ≤ n ≤ 1 000, 1 ≤ w ≤ 10^{9}) — the number of bus stops and the capacity of the bus.
The second line contains a sequence a_1, a_2, ..., a_n (-10^{6} ≤ a_i ≤ 10^{6}), where a_i equals to the number, which has been recorded by the video system after the i-th bus stop.
Output
Print the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w. If the situation is contradictory (i.e. for any initial number of passengers there will be a contradiction), print 0.
Examples
Input
3 5
2 1 -3
Output
3
Input
2 4
-1 1
Output
4
Input
4 10
2 4 1 2
Output
2
Note
In the first example initially in the bus could be 0, 1 or 2 passengers.
In the second example initially in the bus could be 1, 2, 3 or 4 passengers.
In the third example initially in the bus could be 0 or 1 passenger.
|
l=input().split()
n=int(l[0])
w=int(l[1])
l=input().split()
li=[int(i) for i in l]
left=0
right=w
sumi=0
for i in range(n):
sumi+=li[i]
left=max(left,-1*sumi)
right=min(right,w-sumi)
print(max(right-left+1,0))
|
{
"input": [
"4 10\n2 4 1 2\n",
"3 5\n2 1 -3\n",
"2 4\n-1 1\n",
"5 21\n-3 2 -4 -1 -5\n",
"2 1000000000\n-1000000 1000000\n",
"2 1000000000\n-1000000 -1000000\n",
"1 1000000000\n0\n",
"5 9\n-2 -1 2 -1 -2\n",
"10 1\n-1 -1 3 -4 2 3 0 -3 3 2\n",
"3 4\n1 2 3\n",
"2 1000000000\n1000000 1000000\n",
"3 4\n-3 -4 4\n",
"1 1234564\n1\n",
"8 7\n-5 0 -3 1 -1 5 0 -6\n",
"2 10\n-1 2\n",
"3 4\n-2 -1 0\n",
"2 1000000000\n1000000 -1000000\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"5 36\n-3 2 -4 -1 -5\n",
"2 1000010000\n-1000000 1000000\n",
"5 9\n-3 -1 2 -1 -2\n",
"10 1\n-1 -1 3 -8 2 3 0 -3 3 2\n",
"3 4\n-3 -1 4\n",
"1 730859\n1\n",
"4 18\n2 4 1 2\n",
"3 5\n3 1 -3\n",
"2 4\n0 1\n",
"5 36\n-3 2 0 -1 -5\n",
"3 6\n-2 -2 0\n",
"5 21\n-3 0 -4 -1 -5\n",
"2 1000000000\n-1000000 1000010\n",
"2 1000000100\n-1000000 -1000000\n",
"1 1000000000\n1\n",
"5 16\n-2 -1 2 -1 -2\n",
"2 1000000000\n1000000 1100000\n",
"1 1234564\n0\n",
"2 10\n-1 3\n",
"2 1000000100\n1000000 -1000000\n",
"5 36\n-3 2 -4 -1 -8\n",
"2 1000010100\n-1000000 1000000\n",
"1 730859\n0\n",
"3 4\n1 1 3\n",
"8 7\n-5 1 -3 1 -1 5 0 -6\n",
"3 4\n-2 -2 0\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"5 3\n-3 -1 2 -1 -2\n",
"10 1\n-1 -1 3 -8 2 3 0 -3 0 2\n",
"3 4\n2 1 3\n",
"3 4\n0 -1 4\n",
"8 7\n-5 1 -3 1 -1 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1\n",
"3 5\n3 0 -3\n",
"2 2\n0 1\n",
"5 2\n-3 -1 2 -1 -2\n",
"10 1\n0 -1 3 -8 2 3 0 -3 0 2\n",
"3 4\n4 1 3\n",
"8 7\n-5 1 -3 1 -2 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1\n",
"3 5\n4 0 -3\n",
"2 4\n0 0\n",
"5 2\n-2 -1 2 -1 -2\n",
"10 1\n0 -1 3 -8 2 6 0 -3 0 2\n",
"8 7\n-5 2 -3 1 -2 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1\n",
"3 5\n6 0 -3\n",
"10 1\n0 -1 3 -8 2 6 -1 -3 0 2\n",
"8 7\n-5 2 -2 1 -2 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1\n",
"10 1\n0 -1 3 -8 0 6 -1 -3 0 2\n",
"8 7\n-5 2 -1 1 -2 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1\n",
"8 7\n-5 2 0 1 -2 9 0 -6\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n2 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"102 1\n2 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1\n",
"10 1\n-1 -1 4 -4 2 3 0 -3 3 2\n",
"3 2\n-3 -4 4\n",
"8 7\n-5 0 -3 1 -1 5 1 -6\n",
"3 0\n-2 -1 0\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"4 10\n2 6 1 2\n",
"3 5\n2 0 -3\n",
"2 4\n-1 0\n",
"5 9\n-3 -1 2 -1 -4\n",
"10 1\n-1 -1 3 -8 2 3 0 -3 3 1\n",
"3 8\n1 1 3\n",
"3 4\n-5 -1 4\n",
"8 7\n-1 1 -3 1 -1 5 0 -6\n",
"3 5\n-2 -2 0\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"4 18\n2 4 2 2\n",
"3 5\n4 1 -3\n",
"2 1\n0 0\n",
"5 8\n-3 2 0 -1 -5\n",
"10 1\n-1 -1 3 -8 2 1 0 -3 0 2\n",
"3 4\n2 1 2\n",
"8 7\n-5 1 -3 1 -1 9 1 -6\n",
"3 6\n-2 -4 0\n",
"102 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1\n",
"3 5\n3 0 0\n",
"2 2\n0 0\n",
"5 2\n-3 -1 0 -1 -2\n",
"10 1\n-1 0 3 -8 2 3 0 -3 0 2\n",
"3 4\n8 1 3\n",
"102 1\n1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1\n",
"3 5\n4 0 -1\n",
"2 4\n1 0\n",
"5 0\n-2 -1 2 -1 -2\n"
],
"output": [
"2\n",
"3\n",
"4\n",
"11\n",
"999000001\n",
"998000001\n",
"1000000001\n",
"6\n",
"0\n",
"0\n",
"998000001\n",
"0\n",
"1234564\n",
"0\n",
"9\n",
"2\n",
"999000001\n",
"0\n",
"26\n",
"999010001\n",
"5\n",
"0\n",
"1\n",
"730859\n",
"10\n",
"2\n",
"4\n",
"30\n",
"3\n",
"9\n",
"998999991\n",
"998000101\n",
"1000000000\n",
"13\n",
"997900001\n",
"1234565\n",
"8\n",
"999000101\n",
"23\n",
"999010101\n",
"730860\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"3\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"5\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"3\n",
"4\n",
"3\n",
"0\n",
"4\n",
"0\n",
"2\n",
"2\n",
"0\n",
"9\n",
"1\n",
"2\n",
"2\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"3\n",
"3\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"4\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The busses in Berland are equipped with a video surveillance system. The system records information about changes in the number of passengers in a bus after stops.
If x is the number of passengers in a bus just before the current bus stop and y is the number of passengers in the bus just after current bus stop, the system records the number y-x. So the system records show how number of passengers changed.
The test run was made for single bus and n bus stops. Thus, the system recorded the sequence of integers a_1, a_2, ..., a_n (exactly one number for each bus stop), where a_i is the record for the bus stop i. The bus stops are numbered from 1 to n in chronological order.
Determine the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w (that is, at any time in the bus there should be from 0 to w passengers inclusive).
Input
The first line contains two integers n and w (1 ≤ n ≤ 1 000, 1 ≤ w ≤ 10^{9}) — the number of bus stops and the capacity of the bus.
The second line contains a sequence a_1, a_2, ..., a_n (-10^{6} ≤ a_i ≤ 10^{6}), where a_i equals to the number, which has been recorded by the video system after the i-th bus stop.
Output
Print the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w. If the situation is contradictory (i.e. for any initial number of passengers there will be a contradiction), print 0.
Examples
Input
3 5
2 1 -3
Output
3
Input
2 4
-1 1
Output
4
Input
4 10
2 4 1 2
Output
2
Note
In the first example initially in the bus could be 0, 1 or 2 passengers.
In the second example initially in the bus could be 1, 2, 3 or 4 passengers.
In the third example initially in the bus could be 0 or 1 passenger.
### Input:
4 10
2 4 1 2
### Output:
2
### Input:
3 5
2 1 -3
### Output:
3
### Code:
l=input().split()
n=int(l[0])
w=int(l[1])
l=input().split()
li=[int(i) for i in l]
left=0
right=w
sumi=0
for i in range(n):
sumi+=li[i]
left=max(left,-1*sumi)
right=min(right,w-sumi)
print(max(right-left+1,0))
|
998_D. Roman Digits_28718
|
Let's introduce a number system which is based on a roman digits. There are digits I, V, X, L which correspond to the numbers 1, 5, 10 and 50 respectively. The use of other roman digits is not allowed.
Numbers in this system are written as a sequence of one or more digits. We define the value of the sequence simply as the sum of digits in it.
For example, the number XXXV evaluates to 35 and the number IXI — to 12.
Pay attention to the difference to the traditional roman system — in our system any sequence of digits is valid, moreover the order of digits doesn't matter, for example IX means 11, not 9.
One can notice that this system is ambiguous, and some numbers can be written in many different ways. Your goal is to determine how many distinct integers can be represented by exactly n roman digits I, V, X, L.
Input
The only line of the input file contains a single integer n (1 ≤ n ≤ 10^9) — the number of roman digits to use.
Output
Output a single integer — the number of distinct integers which can be represented using n roman digits exactly.
Examples
Input
1
Output
4
Input
2
Output
10
Input
10
Output
244
Note
In the first sample there are exactly 4 integers which can be represented — I, V, X and L.
In the second sample it is possible to represent integers 2 (II), 6 (VI), 10 (VV), 11 (XI), 15 (XV), 20 (XX), 51 (IL), 55 (VL), 60 (XL) and 100 (LL).
|
a = [0, 4, 10, 20, 35, 56, 83, 116, 155, 198, 244, 292]
n = int(input())
if n < len(a):
print (a[n])
else:
print (a[11] + 49*(n-11))
|
{
"input": [
"1\n",
"2\n",
"10\n",
"111199\n",
"1000\n",
"10000\n",
"11\n",
"244\n",
"1000000000\n",
"14\n",
"55\n",
"2000\n",
"116\n",
"20\n",
"6\n",
"600000000\n",
"198\n",
"12\n",
"999999999\n",
"100\n",
"83\n",
"13\n",
"8\n",
"150\n",
"4\n",
"35\n",
"709000900\n",
"1200\n",
"292\n",
"9\n",
"100000000\n",
"3\n",
"101232812\n",
"5\n",
"5000\n",
"7\n",
"500000000\n",
"56\n",
"9999999\n",
"155\n",
"134707\n",
"1100\n",
"17\n",
"255\n",
"1000000100\n",
"89\n",
"3891\n",
"201\n",
"22\n",
"15\n",
"753689004\n",
"157\n",
"33\n",
"1517731607\n",
"101\n",
"52\n",
"23\n",
"36\n",
"219\n",
"54\n",
"357895503\n",
"41\n",
"21\n",
"16\n",
"100001000\n",
"89307055\n",
"24\n",
"3435\n",
"733753181\n",
"59\n",
"4312251\n",
"106\n",
"28\n",
"257068\n",
"1110\n",
"25\n",
"203\n",
"1000001100\n",
"88\n",
"5915\n",
"268\n",
"38\n",
"344581682\n",
"238\n",
"29\n",
"507921316\n",
"001\n",
"97\n",
"47\n",
"263\n",
"80\n",
"591333944\n",
"19\n",
"42\n",
"110001000\n",
"90283358\n",
"4519\n",
"762592880\n",
"102\n",
"2996787\n",
"209\n",
"119397\n",
"0110\n",
"18\n",
"246\n",
"1000001000\n",
"72\n",
"11188\n",
"249\n",
"65\n",
"684857025\n",
"362\n",
"50\n"
],
"output": [
"4\n",
"10\n",
"244\n",
"5448504\n",
"48753\n",
"489753\n",
"292\n",
"11709\n",
"48999999753\n",
"439\n",
"2448\n",
"97753\n",
"5437\n",
"733\n",
"83\n",
"29399999753\n",
"9455\n",
"341\n",
"48999999704\n",
"4653\n",
"3820\n",
"390\n",
"155\n",
"7103\n",
"35\n",
"1468\n",
"34741043853\n",
"58553\n",
"14061\n",
"198\n",
"4899999753\n",
"20\n",
"4960407541\n",
"56\n",
"244753\n",
"116\n",
"24499999753\n",
"2497\n",
"489999704\n",
"7348\n",
"6600396\n",
"53653\n",
"586\n",
"12248\n",
"49000004653\n",
"4114\n",
"190412\n",
"9602\n",
"831\n",
"488\n",
"36930760949\n",
"7446\n",
"1370\n",
"74368848496\n",
"4702\n",
"2301\n",
"880\n",
"1517\n",
"10484\n",
"2399\n",
"17536879400\n",
"1762\n",
"782\n",
"537\n",
"4900048753\n",
"4376045448\n",
"929\n",
"168068\n",
"35953905622\n",
"2644\n",
"211300052\n",
"4947\n",
"1125\n",
"12596085\n",
"54143\n",
"978\n",
"9700\n",
"49000053653\n",
"4065\n",
"289588\n",
"12885\n",
"1615\n",
"16884502171\n",
"11415\n",
"1174\n",
"24888144237\n",
"4\n",
"4506\n",
"2056\n",
"12640\n",
"3673\n",
"28975363009\n",
"684\n",
"1811\n",
"5390048753\n",
"4423884295\n",
"221184\n",
"37367050873\n",
"4751\n",
"146842316\n",
"9994\n",
"5850206\n",
"5143\n",
"635\n",
"11807\n",
"49000048753\n",
"3281\n",
"547965\n",
"11954\n",
"2938\n",
"33557993978\n",
"17491\n",
"2203\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Let's introduce a number system which is based on a roman digits. There are digits I, V, X, L which correspond to the numbers 1, 5, 10 and 50 respectively. The use of other roman digits is not allowed.
Numbers in this system are written as a sequence of one or more digits. We define the value of the sequence simply as the sum of digits in it.
For example, the number XXXV evaluates to 35 and the number IXI — to 12.
Pay attention to the difference to the traditional roman system — in our system any sequence of digits is valid, moreover the order of digits doesn't matter, for example IX means 11, not 9.
One can notice that this system is ambiguous, and some numbers can be written in many different ways. Your goal is to determine how many distinct integers can be represented by exactly n roman digits I, V, X, L.
Input
The only line of the input file contains a single integer n (1 ≤ n ≤ 10^9) — the number of roman digits to use.
Output
Output a single integer — the number of distinct integers which can be represented using n roman digits exactly.
Examples
Input
1
Output
4
Input
2
Output
10
Input
10
Output
244
Note
In the first sample there are exactly 4 integers which can be represented — I, V, X and L.
In the second sample it is possible to represent integers 2 (II), 6 (VI), 10 (VV), 11 (XI), 15 (XV), 20 (XX), 51 (IL), 55 (VL), 60 (XL) and 100 (LL).
### Input:
1
### Output:
4
### Input:
2
### Output:
10
### Code:
a = [0, 4, 10, 20, 35, 56, 83, 116, 155, 198, 244, 292]
n = int(input())
if n < len(a):
print (a[n])
else:
print (a[11] + 49*(n-11))
|
p02661 AtCoder Beginner Contest 169 - Count Median_28732
|
There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i. Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.
Constraints
* 2 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
:
A_N B_N
Output
Print the answer.
Examples
Input
2
1 2
2 3
Output
3
Input
3
100 100
10 10000
1 1000000000
Output
9991
|
N = int(input())
A = [0]*N
B = [0]*N
for i in range(N):
A[i],B[i] = map(int, input().split())
A.sort()
B.sort()
if len(A)%2 != 0:
ans = B[N//2]-A[N//2]+1
else:
ans = (B[N//2]+B[N//2-1]) - (A[N//2]+A[N//2-1]) + 1
print(ans)
|
{
"input": [
"3\n100 100\n10 10000\n1 1000000000",
"2\n1 2\n2 3",
"3\n100 100\n8 10000\n1 1000000000",
"2\n1 2\n2 4",
"3\n100 100\n8 11000\n1 1000000000",
"2\n1 1\n2 4",
"2\n1 1\n1 7",
"2\n0 1\n1 7",
"2\n0 1\n0 7",
"3\n000 010\n8 11000\n1 1001000000",
"2\n0 1\n0 8",
"3\n000 010\n8 11000\n2 1001000000",
"3\n000 010\n8 01000\n2 1001000000",
"2\n0 0\n0 14",
"3\n010 010\n8 01000\n2 1001000000",
"2\n0 0\n-1 14",
"3\n010 010\n8 01010\n2 1001000000",
"2\n0 0\n-1 23",
"3\n010 010\n2 01010\n2 1001000000",
"2\n0 1\n-1 23",
"2\n0 2\n-1 23",
"2\n-1 2\n-1 23",
"3\n010 000\n4 00111\n1 1001000000",
"2\n0 1\n-2 1",
"2\n0 2\n-2 1",
"3\n001 001\n4 00111\n0 1001000000",
"2\n1 2\n0 0",
"2\n1 2\n0 -1",
"2\n2 2\n0 -1",
"3\n000 001\n2 00111\n0 1001000000",
"2\n2 2\n1 -1",
"2\n1 2\n2 -2",
"3\n100 001\n0 00101\n0 1001000000",
"3\n111 100\n0 00011\n0 1001000000",
"2\n0 2\n6 0",
"3\n111 100\n1 00011\n-1 1001010000",
"3\n110 000\n1 00011\n-1 1001011000",
"2\n0 6\n10 -1",
"2\n0 0\n10 -1",
"2\n0 0\n10 0",
"2\n0 0\n6 0",
"2\n1 0\n6 0",
"2\n1 0\n16 1",
"2\n1 0\n19 1",
"2\n2 0\n19 1",
"2\n2 0\n9 2",
"3\n001 000\n1 00110\n-1 1001100000",
"2\n3 0\n9 0",
"2\n5 0\n9 0",
"2\n5 -1\n9 0",
"2\n1 -1\n11 0",
"3\n011 100\n2 00001\n-2 1001100010",
"3\n001 100\n2 10011\n-2 1001000010",
"3\n011 100\n2 10011\n-2 1001000010",
"3\n000 100\n2 10011\n-3 1000010010",
"3\n000 100\n2 11011\n-3 1000010010",
"3\n100 100\n2 11011\n-3 0000010010",
"3\n100 000\n3 10011\n-3 0000010010",
"3\n101 000\n4 10011\n-3 0000010010",
"3\n101 000\n4 10001\n-3 0000010010",
"3\n111 000\n6 10001\n-5 0100110010",
"3\n101 000\n4 10000\n-7 0100110000",
"3\n110 010\n2 10000\n-12 0100111000",
"3\n000 011\n2 10000\n-12 0100111000",
"3\n001 110\n4 11010\n-7 0100111000",
"3\n001 010\n4 01010\n-7 0100111000",
"3\n101 010\n3 01010\n-8 0100111000",
"3\n001 010\n3 01000\n-8 0100111000",
"3\n100 000\n8 10010\n0 1110101000",
"2\n-9 0\n-1 1",
"2\n-17 0\n0 1",
"2\n-14 -1\n-1 2",
"2\n-19 -2\n-2 2",
"2\n-19 -3\n-2 2",
"3\n000 110\n7 10001\n2 1011000010",
"3\n000 100\n7 11000\n3 1011000010",
"3\n000 100\n7 01000\n3 1011000010",
"3\n000 101\n7 01001\n1 0011000010",
"2\n-23 -1\n4 1",
"2\n-23 -1\n0 1",
"3\n000 101\n7 01001\n0 0011000010",
"2\n-31 -1\n0 1",
"3\n100 101\n7 01001\n0 0011000010",
"2\n-31 -1\n1 1",
"3\n100 101\n7 00001\n0 0011000010",
"2\n-31 -1\n2 1",
"2\n-46 -1\n2 1",
"3\n100 101\n9 00001\n0 0011001010",
"2\n-46 -1\n2 0",
"2\n-46 -2\n2 0",
"3\n100 101\n10 01001\n0 0011001010",
"3\n100 101\n18 01001\n-1 0011001010",
"3\n100 101\n19 01001\n-1 0011001010",
"3\n100 101\n36 01001\n-1 0011001000",
"3\n110 101\n36 01101\n-1 1111001010",
"3\n110 101\n66 01101\n-2 1111001010",
"3\n110 101\n66 11101\n-2 1111001010",
"3\n110 111\n66 11100\n-2 1111001010",
"3\n111 110\n111 11100\n-2 1111011010",
"3\n011 110\n111 11100\n-2 1111011010",
"3\n010 110\n111 11100\n-2 1111011010",
"3\n000 010\n010 11100\n-2 0111011011"
],
"output": [
"9991",
"3",
"9993\n",
"4\n",
"10993\n",
"3\n",
"7\n",
"8\n",
"9\n",
"11000\n",
"10\n",
"10999\n",
"999\n",
"15\n",
"993\n",
"16\n",
"1003\n",
"25\n",
"1009\n",
"26\n",
"27\n",
"28\n",
"108\n",
"5\n",
"6\n",
"111\n",
"2\n",
"1\n",
"0\n",
"112\n",
"-1\n",
"-2\n",
"102\n",
"101\n",
"-3\n",
"100\n",
"11\n",
"-4\n",
"-10\n",
"-9\n",
"-5\n",
"-6\n",
"-15\n",
"-18\n",
"-19\n",
"-8\n",
"110\n",
"-11\n",
"-13\n",
"-14\n",
"-12\n",
"99\n",
"10011\n",
"10010\n",
"10012\n",
"11012\n",
"10009\n",
"10008\n",
"10007\n",
"9998\n",
"9996\n",
"9997\n",
"9999\n",
"10001\n",
"11010\n",
"1010\n",
"1008\n",
"1000\n",
"10003\n",
"12\n",
"19\n",
"17\n",
"22\n",
"21\n",
"10000\n",
"10998\n",
"998\n",
"1001\n",
"20\n",
"24\n",
"1002\n",
"32\n",
"995\n",
"31\n",
"95\n",
"30\n",
"45\n",
"93\n",
"44\n",
"43\n",
"992\n",
"984\n",
"983\n",
"966\n",
"1066\n",
"1036\n",
"11036\n",
"11035\n",
"10990\n",
"11090\n",
"11091\n",
"11101\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i. Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.
Constraints
* 2 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
:
A_N B_N
Output
Print the answer.
Examples
Input
2
1 2
2 3
Output
3
Input
3
100 100
10 10000
1 1000000000
Output
9991
### Input:
3
100 100
10 10000
1 1000000000
### Output:
9991
### Input:
2
1 2
2 3
### Output:
3
### Code:
N = int(input())
A = [0]*N
B = [0]*N
for i in range(N):
A[i],B[i] = map(int, input().split())
A.sort()
B.sort()
if len(A)%2 != 0:
ans = B[N//2]-A[N//2]+1
else:
ans = (B[N//2]+B[N//2-1]) - (A[N//2]+A[N//2-1]) + 1
print(ans)
|
p02790 AtCoder Beginner Contest 152 - Comparing Strings_28736
|
Given are 1-digit positive integers a and b. Consider these two strings: the concatenation of b copies of the digit a, and the concatenation of a copies of the digit b. Which of these is lexicographically smaller?
Constraints
* 1 \leq a \leq 9
* 1 \leq b \leq 9
* a and b are integers.
Input
Input is given from Standard Input in the following format:
a b
Output
Print the lexicographically smaller of the two strings. (If the two strings are equal, print one of them.)
Examples
Input
4 3
Output
3333
Input
7 7
Output
7777777
|
N = list(map(int, input().split()))
a = N.sort()
print(str(N[0])*N[1])
|
{
"input": [
"7 7",
"4 3",
"7 2",
"4 6",
"7 4",
"7 8",
"5 7",
"1 3",
"5 2",
"6 6",
"6 7",
"4 5",
"4 4",
"2 8",
"3 7",
"1 5",
"9 2",
"2 4",
"1 4",
"1 7",
"1 6",
"6 5",
"6 9",
"9 3",
"9 7",
"2 1",
"1 8",
"8 4",
"9 4",
"3 4",
"2 2",
"3 2",
"1 1",
"8 3",
"5 9",
"2 6",
"9 9",
"3 5",
"9 1",
"3 6",
"5 8",
"1 18",
"17 1",
"6 8",
"3 3",
"1 13",
"12 11",
"12 1",
"16 1",
"10 11",
"15 1",
"10 14",
"25 2",
"22 1",
"1 21",
"28 1",
"10 13",
"19 11",
"10 12",
"1 19",
"39 1",
"1 41",
"20 12",
"63 1",
"1 76",
"34 1",
"67 1",
"1 64",
"8 8",
"1 20",
"5 5",
"14 1",
"10 10",
"19 14",
"32 2",
"2 34",
"10 20",
"10 18",
"39 2",
"25 12",
"96 1",
"2 24",
"36 1",
"37 1",
"10 19",
"36 2",
"3 34",
"10 22",
"19 18",
"37 12",
"80 1",
"44 1",
"14 14",
"1 55",
"37 2",
"10 25",
"36 3",
"10 33",
"32 18",
"37 14",
"20 14",
"10 40"
],
"output": [
"7777777",
"3333",
"2222222\n",
"444444\n",
"4444444\n",
"77777777\n",
"5555555\n",
"111\n",
"22222\n",
"666666\n",
"6666666\n",
"44444\n",
"4444\n",
"22222222\n",
"3333333\n",
"11111\n",
"222222222\n",
"2222\n",
"1111\n",
"1111111\n",
"111111\n",
"555555\n",
"666666666\n",
"333333333\n",
"777777777\n",
"11\n",
"11111111\n",
"44444444\n",
"444444444\n",
"3333\n",
"22\n",
"222\n",
"1\n",
"33333333\n",
"555555555\n",
"222222\n",
"999999999\n",
"33333\n",
"111111111\n",
"333333\n",
"55555555\n",
"111111111111111111\n",
"11111111111111111\n",
"66666666\n",
"333\n",
"1111111111111\n",
"111111111111111111111111\n",
"111111111111\n",
"1111111111111111\n",
"1010101010101010101010\n",
"111111111111111\n",
"1010101010101010101010101010\n",
"2222222222222222222222222\n",
"1111111111111111111111\n",
"111111111111111111111\n",
"1111111111111111111111111111\n",
"10101010101010101010101010\n",
"11111111111111111111111111111111111111\n",
"101010101010101010101010\n",
"1111111111111111111\n",
"111111111111111111111111111111111111111\n",
"11111111111111111111111111111111111111111\n",
"1212121212121212121212121212121212121212\n",
"111111111111111111111111111111111111111111111111111111111111111\n",
"1111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1111111111111111111111111111111111\n",
"1111111111111111111111111111111111111111111111111111111111111111111\n",
"1111111111111111111111111111111111111111111111111111111111111111\n",
"88888888\n",
"11111111111111111111\n",
"55555\n",
"11111111111111\n",
"10101010101010101010\n",
"14141414141414141414141414141414141414\n",
"22222222222222222222222222222222\n",
"2222222222222222222222222222222222\n",
"1010101010101010101010101010101010101010\n",
"101010101010101010101010101010101010\n",
"222222222222222222222222222222222222222\n",
"12121212121212121212121212121212121212121212121212\n",
"111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"222222222222222222222222\n",
"111111111111111111111111111111111111\n",
"1111111111111111111111111111111111111\n",
"10101010101010101010101010101010101010\n",
"222222222222222222222222222222222222\n",
"3333333333333333333333333333333333\n",
"10101010101010101010101010101010101010101010\n",
"18181818181818181818181818181818181818\n",
"12121212121212121212121212121212121212121212121212121212121212121212121212\n",
"11111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"11111111111111111111111111111111111111111111\n",
"1414141414141414141414141414\n",
"1111111111111111111111111111111111111111111111111111111\n",
"2222222222222222222222222222222222222\n",
"10101010101010101010101010101010101010101010101010\n",
"333333333333333333333333333333333333\n",
"101010101010101010101010101010101010101010101010101010101010101010\n",
"1818181818181818181818181818181818181818181818181818181818181818\n",
"14141414141414141414141414141414141414141414141414141414141414141414141414\n",
"1414141414141414141414141414141414141414\n",
"10101010101010101010101010101010101010101010101010101010101010101010101010101010\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Given are 1-digit positive integers a and b. Consider these two strings: the concatenation of b copies of the digit a, and the concatenation of a copies of the digit b. Which of these is lexicographically smaller?
Constraints
* 1 \leq a \leq 9
* 1 \leq b \leq 9
* a and b are integers.
Input
Input is given from Standard Input in the following format:
a b
Output
Print the lexicographically smaller of the two strings. (If the two strings are equal, print one of them.)
Examples
Input
4 3
Output
3333
Input
7 7
Output
7777777
### Input:
7 7
### Output:
7777777
### Input:
4 3
### Output:
3333
### Code:
N = list(map(int, input().split()))
a = N.sort()
print(str(N[0])*N[1])
|
p02926 AtCoder Beginner Contest 139 - Engines_28740
|
E869120 is initially standing at the origin (0, 0) in a two-dimensional plane.
He has N engines, which can be used as follows:
* When E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).
* E869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines.
He wants to go as far as possible from the origin. Let (X, Y) be his final coordinates. Find the maximum possible value of \sqrt{X^2 + Y^2}, the distance from the origin.
Constraints
* 1 \leq N \leq 100
* -1 \ 000 \ 000 \leq x_i \leq 1 \ 000 \ 000
* -1 \ 000 \ 000 \leq y_i \leq 1 \ 000 \ 000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
: :
x_N y_N
Output
Print the maximum possible final distance from the origin, as a real value. Your output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.
Examples
Input
3
0 10
5 -5
-5 -5
Output
10.000000000000000000000000000000000000000000000000
Input
5
1 1
1 0
0 1
-1 0
0 -1
Output
2.828427124746190097603377448419396157139343750753
Input
5
1 1
2 2
3 3
4 4
5 5
Output
21.213203435596425732025330863145471178545078130654
Input
3
0 0
0 1
1 0
Output
1.414213562373095048801688724209698078569671875376
Input
1
90447 91000
Output
128303.000000000000000000000000000000000000000000000000
Input
2
96000 -72000
-72000 54000
Output
120000.000000000000000000000000000000000000000000000000
Input
10
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
Output
148.660687473185055226120082139313966514489855137208
|
n = int(input())
pi = 3.141592653589793238462643383279
xy = [list(map(int, input().split())) for _ in range(n)]
import math
atan = [math.atan2(x[0], x[1]) for x in xy]
d = []
def hoge(a):
ret = 0
if a % (2*pi) < pi:
ret = (a % pi)
elif a % (2*pi) > pi:
ret = (a % pi)-pi
else:
ret = (a)
#assert pi <= ret <= pi, 'range over'
return ret # -pi <= a <= pi
def seikika(A):
ret = []
for a in A:
ret.append(hoge(a))
return ret
gyoukaku = atan.copy()
gyoukaku.extend(seikika([a + pi for a in atan]))
M=60
for m in range(M):
gyoukaku.extend(seikika([a + pi*(2*pi/M*m) for a in atan]))
def dist(xy):
xx = sum([x[0] for x in xy])
yy = sum([y[1] for y in xy])
return (xx ** 2 + yy ** 2) ** 0.5
for g in gyoukaku:
anglist = seikika([hoge(a - g) for a in atan])
anglist = seikika(anglist)
finalxy = []
for i in range(n):
if -pi / 2 -0.000001 <= anglist[i] <= pi / 2+0.000001:
finalxy.append(xy[i])
d.append(dist(finalxy))
print(max(d))
|
{
"input": [
"1\n90447 91000",
"2\n96000 -72000\n-72000 54000",
"3\n0 10\n5 -5\n-5 -5",
"10\n1 2\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20",
"5\n1 1\n1 0\n0 1\n-1 0\n0 -1",
"3\n0 0\n0 1\n1 0",
"5\n1 1\n2 2\n3 3\n4 4\n5 5",
"1\n52551 91000",
"2\n96000 -130259\n-72000 54000",
"3\n0 10\n5 -3\n-5 -5",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20",
"5\n1 1\n1 0\n0 2\n-1 0\n0 -1",
"3\n0 0\n0 1\n2 0",
"5\n1 1\n2 2\n3 3\n4 2\n5 5",
"1\n76279 91000",
"2\n49801 -130259\n-72000 54000",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n4 18\n19 20",
"5\n1 1\n0 0\n0 2\n-1 0\n0 -1",
"5\n1 1\n2 2\n3 3\n4 2\n3 5",
"1\n93262 91000",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n4 18\n19 21",
"5\n1 1\n0 1\n0 2\n-1 0\n0 -1",
"1\n148324 91000",
"2\n33334 -130259\n-72000 89448",
"3\n0 10\n1 -6\n-5 -5",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n3 18\n19 21",
"5\n1 1\n2 0\n5 3\n4 2\n3 5",
"1\n232944 91000",
"2\n33334 -247097\n-72000 89448",
"10\n1 0\n3 4\n5 6\n7 8\n8 10\n11 12\n13 14\n15 16\n3 18\n19 21",
"5\n1 1\n2 0\n5 3\n4 1\n3 5",
"1\n323092 91000",
"2\n33334 -460653\n-72000 89448",
"3\n0 16\n1 -6\n-5 -3",
"3\n1 1\n0 0\n3 -1",
"5\n1 1\n2 -1\n5 3\n4 1\n3 5",
"1\n323092 178351",
"3\n0 18\n1 -6\n-5 -3",
"10\n1 0\n3 4\n5 6\n8 8\n8 10\n11 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n0 1\n1 0\n-2 0\n0 -1",
"5\n1 1\n4 -1\n5 3\n4 1\n3 5",
"1\n568221 178351",
"10\n1 0\n3 4\n5 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 3\n4 1\n3 5",
"1\n568221 83257",
"3\n0 20\n1 -6\n-10 -3",
"10\n1 0\n3 7\n5 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 0\n4 1\n3 5",
"1\n568221 48623",
"2\n13872 -460653\n-72000 104892",
"10\n1 0\n3 7\n2 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 0\n4 1\n3 9",
"1\n568221 60327",
"5\n1 3\n0 1\n1 0\n-2 -2\n0 -1",
"1\n568221 71355",
"10\n1 0\n3 7\n2 6\n11 8\n8 10\n20 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 3\n0 1\n1 0\n-4 -2\n0 -1",
"5\n1 1\n7 -2\n5 -1\n4 1\n3 9",
"1\n311727 71355",
"10\n1 0\n3 7\n2 10\n11 8\n8 10\n20 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 1\n7 -2\n5 -1\n4 0\n3 9",
"1\n311727 72656",
"2\n13872 -232879\n-39358 153670",
"10\n1 0\n3 7\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 6\n0 1\n2 0\n-4 -2\n0 -1",
"1\n311727 85902",
"2\n13872 -200911\n-39358 153670",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 1\n7 -2\n5 -2\n4 0\n3 7",
"1\n311727 113970",
"2\n13872 -201534\n-39358 153670",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n29 21",
"1\n21552 113970",
"2\n5694 -201534\n-39358 153670",
"3\n1 13\n1 -2\n-11 -5",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 6\n0 1\n2 0\n-4 -3\n1 0",
"1\n21552 24120",
"10\n0 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 6\n0 1\n2 1\n-4 -3\n1 0",
"3\n2 5\n0 -1\n-1 -1",
"5\n1 1\n7 -2\n10 -2\n4 0\n3 10",
"1\n21552 17969",
"2\n6614 -201534\n-39358 141694",
"3\n1 13\n0 -2\n-11 -4",
"10\n0 0\n1 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 1\n7 -2\n10 -2\n2 0\n3 10",
"1\n4519 17969",
"10\n0 0\n1 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 6\n-1 1\n4 1\n-4 -3\n1 0",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 10",
"1\n4519 21907",
"2\n6614 -289203\n-47857 141694",
"10\n0 0\n1 13\n2 10\n11 8\n8 4\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 6\n-1 1\n4 2\n-4 -3\n1 0",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 9",
"1\n3382 21907",
"2\n6614 -350970\n-47857 141694",
"3\n1 0\n-1 0\n-11 -4",
"10\n0 0\n1 13\n2 10\n11 15\n8 4\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 3",
"1\n464 21907",
"10\n0 0\n1 13\n2 10\n11 15\n8 4\n17 12\n13 7\n15 16\n3 27\n29 24",
"3\n2 6\n0 0\n-2 0",
"5\n1 1\n7 -2\n15 -2\n3 0\n3 3",
"1\n464 28468",
"3\n1 0\n0 -1\n-11 -4"
],
"output": [
"128303.000000000000000000000000000000000000000000000000",
"120000.000000000000000000000000000000000000000000000000",
"10.000000000000000000000000000000000000000000000000",
"148.660687473185055226120082139313966514489855137208",
"2.828427124746190097603377448419396157139343750753",
"1.414213562373095048801688724209698078569671875376",
"21.213203435596425732025330863145471178545078130654",
"105083.812269\n",
"161812.876747\n",
"10.0\n",
"147.186955944\n",
"3.60555127546\n",
"2.2360679775\n",
"19.8494332413\n",
"118741.255851\n",
"139454.460961\n",
"138.683091976\n",
"3.16227766017\n",
"18.3847763109\n",
"130302.726925\n",
"139.46325681\n",
"4.12310562562\n",
"174014.393014\n",
"134456.545534\n",
"11.7046999107\n",
"138.841636406\n",
"18.6010752377\n",
"250087.798855\n",
"249335.282231\n",
"138.224455145\n",
"18.0277563773\n",
"335662.688519\n",
"461857.49097\n",
"16.0\n",
"4.0\n",
"17.4928556845\n",
"369049.481323\n",
"18.0\n",
"131.137332594\n",
"2.82842712475\n",
"19.2353840617\n",
"595553.678556\n",
"137.207871494\n",
"21.9317121995\n",
"574288.109654\n",
"20.0\n",
"139.387947829\n",
"20.8806130178\n",
"570297.554764\n",
"460861.8218\n",
"137.36083867\n",
"22.360679775\n",
"571414.430838\n",
"4.472135955\n",
"572683.718003\n",
"141.598022585\n",
"5.0\n",
"21.5406592285\n",
"319789.397188\n",
"144.589072893\n",
"21.1896201004\n",
"320082.203293\n",
"233291.793737\n",
"142.635900109\n",
"7.61577310586\n",
"323346.371764\n",
"201389.330167\n",
"147.271857461\n",
"20.3960780544\n",
"331907.944209\n",
"202010.855005\n",
"153.71727294\n",
"115989.86854\n",
"201614.421091\n",
"13.0384048104\n",
"160.561514691\n",
"8.0622577483\n",
"32345.9905398\n",
"159.928108849\n",
"8.94427191\n",
"5.38516480713\n",
"25.9615099715\n",
"28060.1793473\n",
"201642.500857\n",
"13.4536240471\n",
"158.672618936\n",
"24.0416305603\n",
"18528.5272485\n",
"169.838158257\n",
"9.43398113206\n",
"28.8617393793\n",
"22368.2366314\n",
"289278.620373\n",
"165.0\n",
"10.295630141\n",
"28.6356421266\n",
"22166.51919\n",
"351032.314604\n",
"12.6491106407\n",
"170.651692051\n",
"28.0\n",
"21911.9133122\n",
"161.817798774\n",
"6.32455532034\n",
"29.0\n",
"28471.7811175\n",
"12.0830459736\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
E869120 is initially standing at the origin (0, 0) in a two-dimensional plane.
He has N engines, which can be used as follows:
* When E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).
* E869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines.
He wants to go as far as possible from the origin. Let (X, Y) be his final coordinates. Find the maximum possible value of \sqrt{X^2 + Y^2}, the distance from the origin.
Constraints
* 1 \leq N \leq 100
* -1 \ 000 \ 000 \leq x_i \leq 1 \ 000 \ 000
* -1 \ 000 \ 000 \leq y_i \leq 1 \ 000 \ 000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
: :
x_N y_N
Output
Print the maximum possible final distance from the origin, as a real value. Your output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.
Examples
Input
3
0 10
5 -5
-5 -5
Output
10.000000000000000000000000000000000000000000000000
Input
5
1 1
1 0
0 1
-1 0
0 -1
Output
2.828427124746190097603377448419396157139343750753
Input
5
1 1
2 2
3 3
4 4
5 5
Output
21.213203435596425732025330863145471178545078130654
Input
3
0 0
0 1
1 0
Output
1.414213562373095048801688724209698078569671875376
Input
1
90447 91000
Output
128303.000000000000000000000000000000000000000000000000
Input
2
96000 -72000
-72000 54000
Output
120000.000000000000000000000000000000000000000000000000
Input
10
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
Output
148.660687473185055226120082139313966514489855137208
### Input:
1
90447 91000
### Output:
128303.000000000000000000000000000000000000000000000000
### Input:
2
96000 -72000
-72000 54000
### Output:
120000.000000000000000000000000000000000000000000000000
### Code:
n = int(input())
pi = 3.141592653589793238462643383279
xy = [list(map(int, input().split())) for _ in range(n)]
import math
atan = [math.atan2(x[0], x[1]) for x in xy]
d = []
def hoge(a):
ret = 0
if a % (2*pi) < pi:
ret = (a % pi)
elif a % (2*pi) > pi:
ret = (a % pi)-pi
else:
ret = (a)
#assert pi <= ret <= pi, 'range over'
return ret # -pi <= a <= pi
def seikika(A):
ret = []
for a in A:
ret.append(hoge(a))
return ret
gyoukaku = atan.copy()
gyoukaku.extend(seikika([a + pi for a in atan]))
M=60
for m in range(M):
gyoukaku.extend(seikika([a + pi*(2*pi/M*m) for a in atan]))
def dist(xy):
xx = sum([x[0] for x in xy])
yy = sum([y[1] for y in xy])
return (xx ** 2 + yy ** 2) ** 0.5
for g in gyoukaku:
anglist = seikika([hoge(a - g) for a in atan])
anglist = seikika(anglist)
finalxy = []
for i in range(n):
if -pi / 2 -0.000001 <= anglist[i] <= pi / 2+0.000001:
finalxy.append(xy[i])
d.append(dist(finalxy))
print(max(d))
|
p03061 AtCoder Beginner Contest 125 - GCD on Blackboard_28744
|
There are N integers, A_1, A_2, ..., A_N, written on the blackboard.
You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.
Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.
Constraints
* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
Output
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.
Examples
Input
3
7 6 8
Output
2
Input
3
12 15 18
Output
6
Input
2
1000000000 1000000000
Output
1000000000
|
from fractions import gcd
n=int(input())
a=list(map(int,input().split()))
l=[0]*(n+1)
r=[0]*(n+1)
for i in range(n):
l[i+1]=gcd(l[i],a[i])
for i in range(n-1,-1,-1):
r[i]=gcd(r[i+1],a[i])
ans=l[-1]
for i in range(n):
ans=max(ans,gcd(l[i],r[i+1]))
print(ans)
|
{
"input": [
"3\n7 6 8",
"2\n1000000000 1000000000",
"3\n12 15 18",
"3\n7 6 7",
"2\n1000010000 1000000000",
"3\n12 29 18",
"2\n1000000000 1000001000",
"3\n4 8 7",
"2\n1001000000 1000001000",
"3\n9 28 18",
"3\n9 28 30",
"2\n1001100000 1000001100",
"2\n1101000000 1000001100",
"3\n4 2 5",
"2\n1101100000 1000000100",
"2\n1111100000 1000000100",
"2\n1111101000 1100000100",
"3\n36 36 10",
"3\n53 36 11",
"2\n1111101100 1100101000",
"2\n1111101101 1100101000",
"2\n0111101101 1100101000",
"3\n114 36 12",
"2\n0111101101 1100101010",
"2\n0011101011 1000101000",
"2\n0011101011 1000101001",
"3\n144 24 2",
"2\n0011101011 1100101001",
"2\n1011101011 1100101101",
"2\n1011101011 1101101101",
"3\n32 24 1",
"2\n1011101111 1101111101",
"2\n1011101111 1101111111",
"2\n1011101100 1100111101",
"2\n0001011001 1101101111",
"2\n0001011001 1001101111",
"2\n0011010001 1001101110",
"2\n0011011001 1001101010",
"2\n0011011001 0001101010",
"2\n0011011101 0001101010",
"2\n0011001101 0001101010",
"2\n0111001101 0001101010",
"2\n0111001001 1001100010",
"2\n1111001101 1001100010",
"2\n1110001101 1001100000",
"2\n1110000101 1001100000",
"2\n1110100101 1101101101",
"2\n1110100001 1101101101",
"2\n1110101001 1101101111",
"2\n1001101001 0101101111",
"2\n1001101000 0110101101",
"2\n1101101000 0110101101",
"2\n1101101100 0110101101",
"2\n0101101100 0110101101",
"2\n0110101100 0110101001",
"2\n0110101110 0110001001",
"2\n0010101110 0110001001",
"2\n0010101110 0110001011",
"2\n0010101100 0110101001",
"2\n0010101100 0110100001",
"2\n0010101100 0010100001",
"2\n0000101100 0010100001",
"2\n0000101100 0010100000",
"2\n0000101100 0010100010",
"2\n0000101100 0011100010",
"2\n0010100100 0010100010",
"2\n0010110100 0010100010",
"2\n0010110100 1010100010",
"2\n0010110100 1110100010",
"2\n0010110100 1110100011",
"2\n0010110100 1111100011",
"2\n1010110100 1110100111",
"2\n1010110100 1110101111",
"2\n1010111000 1111101111",
"2\n0000000100 1111100101",
"2\n0001000100 1111000101",
"2\n1011000100 0111000101",
"2\n1111000100 0111000101",
"2\n1111000110 0011000101",
"2\n1111001110 0011000101",
"2\n1110001110 1011000101",
"2\n1110001111 1011000101",
"2\n1111001111 0011000101",
"2\n0111001111 0011000101",
"2\n0001011001 0011000101",
"2\n0001011001 0011000111",
"2\n0001111001 1011000101",
"2\n0001111011 1011100101",
"2\n1010010111 0110000101",
"2\n1010000111 0110001101",
"2\n1000000111 0111001101",
"2\n1001000111 0111001101",
"2\n1001000011 0101001100",
"2\n1000000111 1101001110",
"2\n1000000111 1101011110",
"2\n1000100111 0101011110",
"2\n1000110111 0101011110",
"2\n1000010111 0101001100",
"2\n0000010111 0101001100",
"2\n0001010111 0100001100",
"2\n1001010111 0100001100",
"2\n1001000110 0000011100",
"2\n0001000110 0001001100"
],
"output": [
"2",
"1000000000",
"6",
"7\n",
"1000010000\n",
"6\n",
"1000001000\n",
"4\n",
"1001000000\n",
"9\n",
"3\n",
"1001100000\n",
"1101000000\n",
"2\n",
"1101100000\n",
"1111100000\n",
"1111101000\n",
"36\n",
"1\n",
"1111101100\n",
"1111101101\n",
"1100101000\n",
"12\n",
"1100101010\n",
"1000101000\n",
"1000101001\n",
"24\n",
"1100101001\n",
"1100101101\n",
"1101101101\n",
"8\n",
"1101111101\n",
"1101111111\n",
"1100111101\n",
"1101101111\n",
"1001101111\n",
"1001101110\n",
"1001101010\n",
"11011001\n",
"11011101\n",
"11001101\n",
"111001101\n",
"1001100010\n",
"1111001101\n",
"1110001101\n",
"1110000101\n",
"1110100101\n",
"1110100001\n",
"1110101001\n",
"1001101001\n",
"1001101000\n",
"1101101000\n",
"1101101100\n",
"110101101\n",
"110101100\n",
"110101110\n",
"110001001\n",
"110001011\n",
"110101001\n",
"110100001\n",
"10101100\n",
"10100001\n",
"10100000\n",
"10100010\n",
"11100010\n",
"10100100\n",
"10110100\n",
"1010100010\n",
"1110100010\n",
"1110100011\n",
"1111100011\n",
"1110100111\n",
"1110101111\n",
"1111101111\n",
"1111100101\n",
"1111000101\n",
"1011000100\n",
"1111000100\n",
"1111000110\n",
"1111001110\n",
"1110001110\n",
"1110001111\n",
"1111001111\n",
"111001111\n",
"11000101\n",
"11000111\n",
"1011000101\n",
"1011100101\n",
"1010010111\n",
"1010000111\n",
"1000000111\n",
"1001000111\n",
"1001000011\n",
"1101001110\n",
"1101011110\n",
"1000100111\n",
"1000110111\n",
"1000010111\n",
"101001100\n",
"100001100\n",
"1001010111\n",
"1001000110\n",
"1001100\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N integers, A_1, A_2, ..., A_N, written on the blackboard.
You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.
Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.
Constraints
* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
Output
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.
Examples
Input
3
7 6 8
Output
2
Input
3
12 15 18
Output
6
Input
2
1000000000 1000000000
Output
1000000000
### Input:
3
7 6 8
### Output:
2
### Input:
2
1000000000 1000000000
### Output:
1000000000
### Code:
from fractions import gcd
n=int(input())
a=list(map(int,input().split()))
l=[0]*(n+1)
r=[0]*(n+1)
for i in range(n):
l[i+1]=gcd(l[i],a[i])
for i in range(n-1,-1,-1):
r[i]=gcd(r[i+1],a[i])
ans=l[-1]
for i in range(n):
ans=max(ans,gcd(l[i],r[i+1]))
print(ans)
|
p03352 AtCoder Beginner Contest 097 - Exponential_28750
|
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
|
x=int(input())
l=[]
for b in range (1,32):
for i in range (2,10):
if b**i <=x:
l.append (b**i)
print(max(l))
|
{
"input": [
"10",
"1",
"999",
"20",
"610",
"38",
"159",
"107",
"72",
"136",
"217",
"261",
"011",
"001",
"7",
"689",
"747",
"52",
"83",
"8",
"124",
"34",
"235",
"27",
"197",
"25",
"1074",
"324",
"186",
"309",
"390",
"126",
"485",
"354",
"250",
"524",
"826",
"639",
"424",
"452",
"870",
"552",
"1023",
"905",
"989",
"1298",
"1357",
"1746",
"44",
"158",
"167",
"65",
"161",
"110",
"111",
"19",
"101",
"15",
"13",
"16",
"2",
"3",
"6",
"4",
"21",
"5",
"36",
"100",
"17",
"114",
"95",
"102",
"39",
"14",
"11",
"9",
"12",
"18",
"59",
"586",
"75",
"86",
"22",
"146",
"30",
"91",
"116",
"24",
"63",
"154",
"35",
"28",
"60",
"66",
"157",
"67",
"279",
"32",
"62",
"33",
"90",
"26",
"31"
],
"output": [
"9",
"1",
"961",
"16\n",
"576\n",
"36\n",
"144\n",
"100\n",
"64\n",
"128\n",
"216\n",
"256\n",
"9\n",
"1\n",
"4\n",
"676\n",
"729\n",
"49\n",
"81\n",
"8\n",
"121\n",
"32\n",
"225\n",
"27\n",
"196\n",
"25\n",
"1024\n",
"324\n",
"169\n",
"289\n",
"361\n",
"125\n",
"484\n",
"343\n",
"243\n",
"512\n",
"784\n",
"625\n",
"400\n",
"441\n",
"841\n",
"529\n",
"1000\n",
"900\n",
"961\n",
"1296\n",
"1331\n",
"1728\n",
"36\n",
"144\n",
"144\n",
"64\n",
"144\n",
"100\n",
"100\n",
"16\n",
"100\n",
"9\n",
"9\n",
"16\n",
"1\n",
"1\n",
"4\n",
"4\n",
"16\n",
"4\n",
"36\n",
"100\n",
"16\n",
"100\n",
"81\n",
"100\n",
"36\n",
"9\n",
"9\n",
"9\n",
"9\n",
"16\n",
"49\n",
"576\n",
"64\n",
"81\n",
"16\n",
"144\n",
"27\n",
"81\n",
"100\n",
"16\n",
"49\n",
"144\n",
"32\n",
"27\n",
"49\n",
"64\n",
"144\n",
"64\n",
"256\n",
"32\n",
"49\n",
"32\n",
"81\n",
"25\n",
"27\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
### Input:
10
### Output:
9
### Input:
1
### Output:
1
### Code:
x=int(input())
l=[]
for b in range (1,32):
for i in range (2,10):
if b**i <=x:
l.append (b**i)
print(max(l))
|
p03512 Code Festival Team Relay (Parallel) - Akashic Records_28753
|
Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 ≤ i ≤ Q) is as follows:
* For every positive integer j, add x_i to the value of a_{j × m_i}.
Find the value of the largest term after these Q operations.
Constraints
* 1 ≤ Q ≤ 299
* 2 ≤ m_i ≤ 300
* -10^6 ≤ x_i ≤ 10^6
* All m_i are distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
Q
m_1 x_1
:
m_Q x_Q
Output
Print the value of the largest term after the Q operations.
Examples
Input
3
2 10
3 -20
6 15
Output
10
Input
3
10 -3
50 4
100 -5
Output
1
Input
5
56 114834
72 -149861
100 190757
192 -132693
240 133108
Output
438699
|
from itertools import product
Q = int(input())
mxs = [tuple(map(int, input().split())) for _ in range(Q)]
p1s = [2,3,5,7,11,13,17]
nums = [9,6,4,3,3,3,3]
rangeNums = [range(num) for num in nums]
p2s = [19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293]
mx1s = []
mx2ss = [[] for _ in range(len(p2s))]
for m, x in mxs:
for i, p2 in enumerate(p2s):
if m % p2 == 0:
mx2ss[i].append((m, x))
break
else:
mx1s.append((m, x))
ans = 0
for es in product(*rangeNums):
f = 1
for p1, e in zip(p1s, es):
f *= p1**e
A = 0
for m1, x1 in mx1s:
if f % m1 == 0:
A += x1
for p2, mx2s in zip(p2s, mx2ss):
A2 = 0
for m2, x2 in mx2s:
if f*p2 % m2 == 0:
A2 += x2
if A2 > 0:
A += A2
ans = max(ans, A)
print(ans)
|
{
"input": [
"3\n10 -3\n50 4\n100 -5",
"3\n2 10\n3 -20\n6 15",
"5\n56 114834\n72 -149861\n100 190757\n192 -132693\n240 133108",
"3\n10 -3\n50 4\n101 -5",
"3\n2 18\n3 -20\n6 15",
"5\n56 114834\n72 -134386\n100 190757\n192 -132693\n240 133108",
"3\n10 -3\n91 4\n101 -5",
"3\n18 -3\n91 4\n101 1",
"5\n92 114834\n125 -176641\n100 13125\n192 -68478\n240 133108",
"5\n42 114834\n125 -176641\n100 13125\n140 -68478\n240 133108",
"3\n44 -3\n15 1\n111 1",
"3\n7 -3\n15 0\n110 0",
"3\n2 18\n4 -20\n6 15",
"5\n56 114834\n72 -134386\n100 190757\n192 -132693\n240 261716",
"5\n56 114834\n72 -134386\n100 119537\n192 -68478\n240 133108",
"3\n10 -3\n91 7\n101 0",
"5\n56 114834\n72 -176641\n100 242597\n192 -68478\n240 133108",
"5\n92 114834\n125 -176641\n100 13125\n192 -68478\n240 62192",
"3\n36 -3\n6 4\n111 2",
"5\n42 114834\n125 -176641\n100 13125\n140 -39699\n240 133108",
"3\n44 -3\n15 2\n111 1",
"3\n4 18\n3 -20\n2 18",
"3\n44 -3\n4 8\n111 1",
"3\n4 24\n3 -20\n2 18",
"5\n25 114834\n8 -149861\n100 190757\n104 -132693\n240 133108",
"5\n56 150056\n72 -134386\n100 190757\n176 -65223\n240 261716",
"3\n4 47\n3 -20\n2 18",
"5\n56 114834\n78 -176641\n101 372457\n192 -68478\n16 133108",
"5\n92 114834\n125 -176641\n101 3465\n192 -68478\n189 62192",
"5\n92 114834\n125 -80332\n110 13125\n270 -102981\n240 99516",
"5\n92 217221\n125 -17608\n100 13125\n31 -68478\n240 133108",
"3\n4 89\n3 -20\n2 18",
"5\n92 384326\n125 -17608\n100 13125\n31 -68478\n240 133108",
"5\n56 150056\n72 -134386\n100 190757\n274 -65223\n240 233516",
"3\n4 9\n3 -20\n2 18",
"3\n5 0\n91 14\n111 0",
"3\n51 -4\n176 4\n111 4",
"5\n56 150056\n72 -134386\n100 71353\n274 -65223\n240 233516",
"3\n5 1\n91 14\n111 0",
"5\n92 164718\n125 -17608\n100 13125\n31 -5858\n240 133108",
"5\n33 114834\n8 -110171\n100 190757\n104 -82350\n240 133108",
"5\n20 114834\n37 -176641\n101 557168\n192 -68478\n10 133108",
"5\n92 114834\n125 -71017\n101 125951\n124 -9260\n46 133108",
"5\n92 57423\n125 -17608\n100 13125\n31 -5858\n240 133108",
"5\n33 114834\n8 -110171\n100 61496\n104 -82350\n240 133108",
"5\n56 150056\n72 -134034\n100 50425\n274 -65223\n240 233516",
"5\n107 114834\n142 -28092\n100 242597\n171 -68478\n41 180385",
"5\n56 137351\n72 -134034\n100 50425\n274 -65223\n240 233516",
"5\n51 114834\n8 -110171\n100 27913\n104 -82350\n240 133108",
"5\n13 114834\n72 -134386\n110 119537\n473 -25250\n278 253378",
"5\n107 114834\n142 -28092\n100 86682\n122 -68478\n41 180385",
"5\n51 114834\n7 -110171\n100 27913\n104 -82350\n240 133108",
"5\n56 137351\n72 -52672\n100 50425\n274 -65223\n240 130574",
"5\n107 158676\n240 -28092\n100 86682\n207 -68478\n41 180385",
"5\n75 114834\n14 -110171\n100 50568\n104 -82350\n240 133108",
"3\n29 -6\n4 11\n110 0",
"5\n282 57423\n125 -17608\n110 13125\n66 -636\n240 133108",
"5\n75 114834\n14 -110171\n100 50568\n50 -67233\n240 133108",
"5\n88 158676\n240 -28092\n100 86682\n207 -82155\n21 1454",
"5\n282 57423\n125 -17608\n110 22314\n66 -636\n240 133108",
"5\n282 57423\n125 -17608\n100 22314\n66 -636\n240 133108",
"5\n75 114834\n14 -110171\n110 50568\n50 -11199\n240 133108",
"5\n88 195113\n240 -43027\n100 86682\n207 -82155\n21 1454",
"5\n282 44220\n125 -17608\n100 22314\n66 -636\n240 133108",
"5\n282 7930\n125 -17608\n100 22314\n66 -636\n240 133108",
"5\n148 138365\n14 -110171\n110 50568\n50 -11199\n240 133108",
"5\n282 7930\n62 -17608\n100 15638\n66 -636\n240 133108",
"5\n148 15741\n14 -63165\n110 50568\n50 -11199\n240 133108",
"5\n88 195113\n287 -43027\n100 154868\n276 -82155\n24 1454",
"5\n148 13198\n14 -63165\n110 50568\n51 -11199\n240 133108",
"5\n88 195113\n287 -26746\n100 267245\n276 -82155\n24 1454",
"5\n282 7930\n104 -17608\n100 29775\n125 -413\n240 133108",
"5\n99 195113\n287 -26746\n100 267245\n276 -82155\n24 1065",
"5\n282 7930\n104 -17608\n100 22712\n125 -308\n240 133108",
"5\n282 7733\n104 -17608\n100 22712\n125 -308\n240 133108",
"5\n148 13198\n33 -16307\n110 50568\n157 -11199\n240 133108",
"5\n147 195113\n287 -1106\n100 267245\n276 -82155\n24 667",
"5\n148 13198\n33 -16307\n110 76434\n157 -11199\n240 133108",
"5\n148 13198\n33 -16307\n110 76434\n157 -11199\n240 60136",
"5\n148 13198\n33 -16307\n110 22750\n157 -11199\n240 60136",
"5\n148 23263\n33 -16307\n110 22750\n157 -11199\n240 60136",
"5\n148 18310\n33 -16307\n110 22750\n157 -11199\n240 60136",
"5\n228 195113\n558 -71\n100 267245\n276 -18356\n24 663",
"5\n148 18310\n33 -6616\n110 22750\n157 -11199\n240 60136",
"5\n148 18310\n33 -2192\n110 22750\n157 -11199\n240 60136",
"5\n228 195113\n225 -71\n100 267245\n276 -10163\n11 802",
"5\n228 195113\n225 -71\n100 267245\n276 -10163\n11 911",
"5\n261 195113\n225 -71\n100 267245\n276 -10163\n2 911",
"5\n261 195113\n225 -71\n100 169878\n276 -10163\n2 911",
"5\n261 195113\n225 -103\n100 169878\n276 -18616\n2 911",
"5\n261 195113\n225 -103\n101 169878\n411 -30216\n3 911",
"3\n7 9\n62 0\n111 1",
"3\n2 10\n3 -4\n6 15",
"5\n56 114834\n72 -149861\n100 190757\n25 -132693\n240 133108",
"5\n56 114834\n72 -134386\n100 42660\n192 -132693\n240 133108",
"5\n56 64042\n72 -134386\n100 190757\n192 -68478\n240 133108",
"5\n56 114834\n72 -176641\n100 190757\n192 -68478\n240 195018",
"5\n92 114834\n125 -176641\n100 7291\n140 -68478\n240 133108",
"5\n25 114834\n2 -149861\n100 190757\n192 -132693\n240 133108",
"3\n2 1\n4 -20\n6 15",
"5\n56 171149\n72 -176641\n100 242597\n192 -68478\n240 133108",
"5\n92 114834\n125 -176641\n100 93986\n192 -68478\n46 133108",
"5\n42 96508\n125 -176641\n100 13125\n140 -39699\n240 133108"
],
"output": [
"1",
"10",
"438699",
"1\n",
"18\n",
"438699\n",
"4\n",
"5\n",
"261067\n",
"192589\n",
"2\n",
"0\n",
"33\n",
"567307\n",
"367479\n",
"7\n",
"490539\n",
"190151\n",
"6\n",
"221368\n",
"3\n",
"36\n",
"9\n",
"42\n",
"305591\n",
"602529\n",
"65\n",
"620399\n",
"180491\n",
"227475\n",
"363454\n",
"107\n",
"530559\n",
"574329\n",
"27\n",
"14\n",
"8\n",
"454925\n",
"15\n",
"310951\n",
"328528\n",
"805110\n",
"373893\n",
"203656\n",
"199267\n",
"433997\n",
"537816\n",
"421292\n",
"165684\n",
"487749\n",
"381901\n",
"275855\n",
"318350\n",
"425743\n",
"298510\n",
"11\n",
"203020\n",
"231277\n",
"246812\n",
"212209\n",
"212845\n",
"287311\n",
"283249\n",
"199642\n",
"163352\n",
"322041\n",
"156676\n",
"199417\n",
"351435\n",
"196874\n",
"463812\n",
"170813\n",
"463423\n",
"163750\n",
"163553\n",
"180567\n",
"463025\n",
"206433\n",
"133461\n",
"79777\n",
"89842\n",
"84889\n",
"463021\n",
"94580\n",
"99004\n",
"463160\n",
"463269\n",
"463198\n",
"365831\n",
"365799\n",
"365902\n",
"10\n",
"21\n",
"306006\n",
"290602\n",
"387907\n",
"500609\n",
"255233\n",
"288838\n",
"16\n",
"546854\n",
"341928\n",
"203042\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 ≤ i ≤ Q) is as follows:
* For every positive integer j, add x_i to the value of a_{j × m_i}.
Find the value of the largest term after these Q operations.
Constraints
* 1 ≤ Q ≤ 299
* 2 ≤ m_i ≤ 300
* -10^6 ≤ x_i ≤ 10^6
* All m_i are distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
Q
m_1 x_1
:
m_Q x_Q
Output
Print the value of the largest term after the Q operations.
Examples
Input
3
2 10
3 -20
6 15
Output
10
Input
3
10 -3
50 4
100 -5
Output
1
Input
5
56 114834
72 -149861
100 190757
192 -132693
240 133108
Output
438699
### Input:
3
10 -3
50 4
100 -5
### Output:
1
### Input:
3
2 10
3 -20
6 15
### Output:
10
### Code:
from itertools import product
Q = int(input())
mxs = [tuple(map(int, input().split())) for _ in range(Q)]
p1s = [2,3,5,7,11,13,17]
nums = [9,6,4,3,3,3,3]
rangeNums = [range(num) for num in nums]
p2s = [19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293]
mx1s = []
mx2ss = [[] for _ in range(len(p2s))]
for m, x in mxs:
for i, p2 in enumerate(p2s):
if m % p2 == 0:
mx2ss[i].append((m, x))
break
else:
mx1s.append((m, x))
ans = 0
for es in product(*rangeNums):
f = 1
for p1, e in zip(p1s, es):
f *= p1**e
A = 0
for m1, x1 in mx1s:
if f % m1 == 0:
A += x1
for p2, mx2s in zip(p2s, mx2ss):
A2 = 0
for m2, x2 in mx2s:
if f*p2 % m2 == 0:
A2 += x2
if A2 > 0:
A += A2
ans = max(ans, A)
print(ans)
|
p03674 AtCoder Beginner Contest 066 - 11_28757
|
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
|
# ------ combination -------
N, MOD = 10**5 + 1, 10**9 + 7
fc, ifc = [0] * (N+1), [0] * (N+1)
def power(n, a):
res, exp = 1, n
while(a):
if a & 1:
res = res * exp % MOD
exp = exp * exp % MOD
a = a >> 1
return res
fc[0] = 1
for i in range(1, N+1):
fc[i] = fc[i-1] * i % MOD
ifc[N] = power(fc[N], MOD-2)
for i in range(N-1, -1, -1):
ifc[i] = ifc[i+1] * (i+1) % MOD
def Comb(n, r):
if n < 0 or r < 0 or n < r:
return 0
return fc[n] * ifc[r] % MOD * ifc[n-r] % MOD
# --------------------------
n = int(input())
a = list(map(int, input().split()))
num = [-1] * (n+1)
l = r = -1
for i in range(len(a)):
if num[a[i]] != -1:
l, r = num[a[i]], i
break
num[a[i]] = i
for k in range(1, len(a)+1):
ans = Comb(len(a), k) - Comb(l+len(a)-r-1, k-1)
while ans < 0:
ans += MOD
print(ans)
|
{
"input": [
"1\n1 1",
"32\n29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9",
"3\n1 2 1 3",
"3\n1 3 1 3",
"3\n1 0 0 2",
"3\n1 3 2 1",
"3\n1 3 1 2",
"3\n1 0 1 2",
"3\n1 0 1 0",
"3\n1 0 2 0",
"3\n2 0 2 0",
"3\n1 3 2 3",
"3\n2 3 2 3",
"3\n2 3 2 1",
"3\n2 3 2 0",
"3\n1 2 2 3",
"3\n1 3 1 0",
"3\n1 0 2 2",
"3\n-1 0 2 0",
"3\n1 3 0 0",
"3\n1 -1 2 2",
"3\n2 3 0 0",
"3\n0 0 1 2",
"3\n1 0 2 1",
"3\n2 0 2 1",
"3\n2 3 3 1",
"3\n2 1 2 1",
"3\n1 -1 1 0",
"3\n1 1 2 0",
"3\n1 2 2 0",
"3\n0 0 1 3",
"3\n0 0 2 1",
"3\n2 1 2 0",
"3\n0 0 1 1",
"3\n0 1 2 0",
"3\n2 2 1 3",
"3\n1 3 2 2",
"3\n2 0 1 0",
"3\n1 -1 0 0",
"3\n1 1 2 3",
"3\n2 0 1 2",
"3\n2 2 3 3",
"3\n0 3 2 2",
"3\n1 1 2 2",
"3\n-1 0 1 0",
"3\n1 -2 2 2",
"3\n2 1 0 0",
"3\n1 0 1 3",
"3\n2 -1 0 0",
"3\n-1 0 1 -1",
"3\n-1 3 1 3",
"3\n1 0 -1 0",
"3\n0 0 2 2",
"3\n2 0 0 1",
"3\n2 1 3 2",
"3\n1 1 0 0",
"3\n0 1 2 1",
"3\n-1 0 1 1",
"3\n2 2 0 3",
"3\n1 1 0 3",
"3\n2 1 3 3",
"3\n0 1 2 2",
"3\n2 1 0 1",
"3\n1 0 0 3",
"3\n3 1 3 2",
"3\n0 1 1 2",
"3\n2 2 1 1",
"3\n2 0 3 3",
"3\n3 1 3 1",
"3\n0 3 1 1",
"3\n2 3 1 1",
"3\n0 2 2 3",
"3\n3 3 1 0",
"3\n1 3 3 2",
"3\n2 0 1 1",
"3\n1 1 3 0",
"3\n-1 0 0 1",
"3\n-1 2 2 0",
"3\n1 1 3 3",
"3\n2 2 3 0",
"3\n2 1 1 3",
"3\n1 2 0 0",
"3\n1 0 -1 1",
"3\n2 1 1 0",
"3\n-1 1 2 1",
"3\n2 0 0 3",
"3\n0 0 2 3",
"3\n2 1 0 2",
"3\n3 2 3 2",
"3\n1 2 3 1",
"3\n3 3 1 1",
"3\n2 -1 1 1",
"3\n-1 0 -1 1",
"3\n-1 2 2 1",
"3\n2 2 3 1",
"3\n2 0 -1 0",
"3\n2 2 1 0",
"3\n0 1 0 3",
"3\n1 2 0 1",
"3\n2 -2 1 1",
"3\n-1 -1 0 1",
"3\n3 2 3 1",
"3\n0 1 1 3"
],
"output": [
"1\n1",
"32\n525\n5453\n40919\n237336\n1107568\n4272048\n13884156\n38567100\n92561040\n193536720\n354817320\n573166440\n818809200\n37158313\n166803103\n166803103\n37158313\n818809200\n573166440\n354817320\n193536720\n92561040\n38567100\n13884156\n4272048\n1107568\n237336\n40920\n5456\n528\n33\n1",
"3\n5\n4\n1",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n5\n4\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n6\n4\n1\n",
"3\n5\n4\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n6\n4\n1\n",
"3\n4\n3\n1\n",
"3\n4\n3\n1\n",
"3\n5\n4\n1\n",
"3\n4\n3\n1\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
### Input:
1
1 1
### Output:
1
1
### Input:
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
### Output:
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
### Code:
# ------ combination -------
N, MOD = 10**5 + 1, 10**9 + 7
fc, ifc = [0] * (N+1), [0] * (N+1)
def power(n, a):
res, exp = 1, n
while(a):
if a & 1:
res = res * exp % MOD
exp = exp * exp % MOD
a = a >> 1
return res
fc[0] = 1
for i in range(1, N+1):
fc[i] = fc[i-1] * i % MOD
ifc[N] = power(fc[N], MOD-2)
for i in range(N-1, -1, -1):
ifc[i] = ifc[i+1] * (i+1) % MOD
def Comb(n, r):
if n < 0 or r < 0 or n < r:
return 0
return fc[n] * ifc[r] % MOD * ifc[n-r] % MOD
# --------------------------
n = int(input())
a = list(map(int, input().split()))
num = [-1] * (n+1)
l = r = -1
for i in range(len(a)):
if num[a[i]] != -1:
l, r = num[a[i]], i
break
num[a[i]] = i
for k in range(1, len(a)+1):
ans = Comb(len(a), k) - Comb(l+len(a)-r-1, k-1)
while ans < 0:
ans += MOD
print(ans)
|
p03828 AtCoder Beginner Contest 052 - Factors of Factorial_28761
|
You are given an integer N. Find the number of the positive divisors of N!, modulo 10^9+7.
Constraints
* 1≤N≤10^3
Input
The input is given from Standard Input in the following format:
N
Output
Print the number of the positive divisors of N!, modulo 10^9+7.
Examples
Input
3
Output
4
Input
6
Output
30
Input
1000
Output
972926972
|
n = int(input())
multiplier = [0 for _ in range(n)]
for m in range(2, n+1):
a = m
i = 2
while i ** 2 <= m:
while a % i == 0:
a = int(a / i)
multiplier[i-1] += 1
i += 1
if a != 1:
multiplier[a-1] += 1
ans = 1
for x in multiplier:
ans *= x + 1
print(ans % (10**9 + 7))
|
{
"input": [
"6",
"3",
"1000",
"8",
"0",
"15",
"18",
"2",
"4",
"9",
"5",
"10",
"7",
"11",
"13",
"17",
"23",
"21",
"42",
"35",
"38",
"54",
"34",
"65",
"30",
"12",
"22",
"20",
"26",
"37",
"19",
"16",
"14",
"25",
"36",
"29",
"27",
"28",
"66",
"43",
"55",
"68",
"31",
"90",
"83",
"44",
"50",
"39",
"24",
"33",
"32",
"41",
"49",
"52",
"56",
"67",
"108",
"111",
"101",
"100",
"110",
"48",
"1001",
"46",
"45",
"53",
"64",
"59",
"70",
"76",
"40",
"115",
"47",
"102",
"87",
"51",
"116",
"57",
"82",
"63",
"80",
"104",
"107",
"185",
"72",
"75",
"74",
"61",
"60",
"69",
"81",
"62",
"78",
"136",
"97",
"58",
"93",
"71",
"112",
"132",
"109",
"144",
"149"
],
"output": [
"30",
"4",
"972926972",
"96\n",
"1\n",
"4032\n",
"14688\n",
"2\n",
"8\n",
"160\n",
"16\n",
"270\n",
"60\n",
"540\n",
"1584\n",
"10752\n",
"192000\n",
"60800\n",
"258048000\n",
"16422912\n",
"60466176\n",
"559756674\n",
"12165120\n",
"105219839\n",
"2332800\n",
"792\n",
"96000\n",
"41040\n",
"532224\n",
"39191040\n",
"29376\n",
"5376\n",
"2592\n",
"340032\n",
"19595520\n",
"1834560\n",
"677376\n",
"917280\n",
"195900610\n",
"516096000\n",
"984916319\n",
"889436190\n",
"4665600\n",
"729407917\n",
"999147209\n",
"677376000\n",
"464046052\n",
"85100544\n",
"242880\n",
"7864320\n",
"5529600\n",
"204871680\n",
"698576619\n",
"87039944\n",
"217548604\n",
"391801220\n",
"875619122\n",
"130571620\n",
"167902493\n",
"583951250\n",
"277966376\n",
"876670706\n",
"513172208\n",
"258709753\n",
"819624960\n",
"174079888\n",
"50952999\n",
"218175167\n",
"845412639\n",
"665186745\n",
"102435840\n",
"813661707\n",
"517419506\n",
"687346296\n",
"775916997\n",
"210846678\n",
"582700142\n",
"16857327\n",
"999573608\n",
"139926156\n",
"790600338\n",
"229757313\n",
"781592107\n",
"591770736\n",
"891132264\n",
"31280490\n",
"316684054\n",
"212862082\n",
"106431041\n",
"472974756\n",
"524719291\n",
"535421074\n",
"764748573\n",
"626955546\n",
"976972733\n",
"609087587\n",
"520705814\n",
"690825271\n",
"574892396\n",
"489345615\n",
"751238237\n",
"464103226\n",
"978268519\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an integer N. Find the number of the positive divisors of N!, modulo 10^9+7.
Constraints
* 1≤N≤10^3
Input
The input is given from Standard Input in the following format:
N
Output
Print the number of the positive divisors of N!, modulo 10^9+7.
Examples
Input
3
Output
4
Input
6
Output
30
Input
1000
Output
972926972
### Input:
6
### Output:
30
### Input:
3
### Output:
4
### Code:
n = int(input())
multiplier = [0 for _ in range(n)]
for m in range(2, n+1):
a = m
i = 2
while i ** 2 <= m:
while a % i == 0:
a = int(a / i)
multiplier[i-1] += 1
i += 1
if a != 1:
multiplier[a-1] += 1
ans = 1
for x in multiplier:
ans *= x + 1
print(ans % (10**9 + 7))
|
p03995 CODE FESTIVAL 2016 qual A - Grid and Integers_28765
|
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
|
import sys
readline = sys.stdin.readline
class UFP():
def __init__(self, num):
self.par = [-1]*num
self.dist = [0]*num
def find(self, x):
if self.par[x] < 0:
return x
else:
res = 0
xo = x
while self.par[x] >= 0:
res += self.dist[x]
x = self.par[x]
self.dist[xo] = res
self.par[xo] = x
return x
def union(self, x, y, d):
rx = self.find(x)
ry = self.find(y)
if rx != ry:
if self.par[rx] > self.par[ry]:
rx, ry = ry, rx
x, y = y, x
d = -d
self.par[rx] += self.par[ry]
self.par[ry] = rx
self.dist[ry] = d + self.dist[x] - self.dist[y]
return True
else:
if d + self.dist[x] - self.dist[y]:
return False
return True
INF = 3*10**9
def check():
H, W = map(int, readline().split())
N = int(readline())
Hm = [INF]*H
Wm = [INF]*W
HP = [[] for _ in range(H)]
WP = [[] for _ in range(W)]
for _ in range(N):
h, w, a = map(int, readline().split())
h -= 1
w -= 1
Hm[h] = min(Hm[h], a)
Wm[w] = min(Wm[w], a)
HP[h].append((w, a))
WP[w].append((h, a))
Th = UFP(H)
Tw = UFP(W)
for h in range(H):
L = len(HP[h])
if L > 1:
HP[h].sort()
for i in range(L-1):
wp, ap = HP[h][i]
wn, an = HP[h][i+1]
if not Tw.union(wp, wn, an-ap):
return False
for w in range(W):
L = len(WP[w])
if L > 1:
WP[w].sort()
for i in range(L-1):
hp, ap = WP[w][i]
hn, an = WP[w][i+1]
if not Th.union(hp, hn, an-ap):
return False
cmh = [INF]*H
for h in range(H):
rh = Th.find(h)
cmh[rh] = min(cmh[rh], Th.dist[h])
cmw = [INF]*W
for w in range(W):
rw = Tw.find(w)
cmw[rw] = min(cmw[rw], Tw.dist[w])
for h in range(H):
if Hm[h] - Th.dist[h] + cmh[Th.find(h)] < 0:
return False
for w in range(W):
if Wm[w] - Tw.dist[w] + cmw[Tw.find(w)] < 0:
return False
return True
print('Yes' if check() else 'No')
|
{
"input": [
"2 2\n4\n1 1 0\n1 2 10\n2 1 30\n2 2 20",
"2 2\n3\n1 1 0\n1 2 10\n2 1 20",
"3 3\n4\n1 1 0\n1 3 10\n3 1 10\n3 3 20",
"2 2\n3\n1 1 20\n1 2 10\n2 1 0",
"2 3\n5\n1 1 0\n1 2 10\n1 3 20\n2 1 30\n2 3 40",
"2 4\n4\n1 1 0\n1 2 10\n2 1 30\n2 2 20",
"2 2\n3\n1 1 0\n1 2 10\n2 1 22",
"3 3\n4\n1 2 0\n1 3 10\n3 1 10\n3 3 20",
"2 2\n3\n2 1 20\n1 2 10\n2 1 0",
"2 4\n4\n1 1 0\n2 2 10\n2 1 30\n2 2 20",
"3 3\n4\n1 2 1\n1 3 10\n3 1 10\n3 3 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 10\n3 3 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 17\n3 3 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 17\n1 3 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 17\n2 3 20",
"3 3\n4\n1 1 1\n1 3 10\n3 2 17\n2 3 20",
"3 3\n4\n1 1 1\n1 1 10\n3 2 17\n2 3 20",
"3 3\n4\n2 1 1\n1 1 10\n3 2 17\n2 3 20",
"2 2\n4\n1 1 0\n1 2 8\n2 1 30\n2 2 20",
"2 2\n3\n1 1 0\n1 2 10\n2 1 14",
"3 3\n4\n1 1 0\n1 3 19\n3 1 10\n3 3 20",
"2 3\n5\n2 1 0\n1 2 10\n1 3 20\n2 1 30\n2 3 40",
"2 4\n4\n1 1 -1\n1 2 10\n2 1 30\n2 2 20",
"2 4\n3\n1 1 0\n1 2 10\n2 1 22",
"2 4\n4\n1 0 0\n2 2 10\n2 1 30\n2 2 20",
"3 3\n4\n1 2 1\n1 3 15\n3 1 10\n3 3 20",
"3 3\n4\n2 1 1\n1 3 10\n3 2 17\n2 3 20",
"3 3\n4\n1 1 1\n1 1 10\n2 2 17\n2 3 20",
"3 3\n4\n2 2 1\n1 1 10\n3 2 17\n2 3 20",
"2 2\n3\n1 1 0\n1 2 10\n1 1 14",
"2 3\n5\n2 1 0\n1 2 10\n1 3 37\n2 1 30\n2 3 40",
"2 4\n4\n1 1 -1\n1 3 10\n2 1 30\n2 2 20",
"2 4\n3\n1 1 1\n1 2 10\n2 1 22",
"2 4\n4\n1 1 0\n1 3 10\n2 1 30\n2 2 20",
"2 4\n4\n1 2 0\n1 3 10\n2 1 30\n2 2 20",
"2 4\n4\n1 0 0\n1 3 10\n2 1 30\n2 2 20",
"2 2\n4\n1 1 0\n1 2 10\n2 1 30\n1 2 20",
"4 3\n5\n2 1 0\n1 2 10\n1 3 20\n2 1 30\n2 3 40",
"2 4\n4\n1 1 0\n1 2 10\n2 2 30\n2 2 20",
"2 2\n3\n1 1 0\n2 2 10\n2 1 22",
"2 2\n3\n1 2 20\n1 2 10\n2 1 0",
"2 4\n4\n1 1 0\n2 4 10\n2 1 30\n2 2 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 14\n3 3 20",
"3 3\n4\n1 2 1\n1 2 10\n3 2 17\n3 3 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 29\n1 3 20",
"6 3\n4\n1 1 1\n1 1 10\n3 2 17\n2 3 20",
"3 3\n4\n2 1 1\n1 1 10\n3 1 17\n2 3 20",
"2 2\n4\n1 1 0\n1 2 1\n2 1 30\n2 2 20",
"2 2\n3\n1 1 1\n1 2 10\n2 1 14",
"2 4\n4\n1 1 -1\n1 2 10\n2 1 22\n2 2 20",
"2 4\n3\n1 1 0\n1 2 10\n2 1 41",
"2 4\n4\n1 0 0\n2 2 10\n2 1 30\n2 1 20",
"3 3\n4\n1 2 1\n1 3 15\n3 1 10\n3 3 27",
"3 3\n4\n3 1 1\n1 3 10\n3 2 17\n2 3 20",
"3 3\n4\n1 1 1\n1 2 10\n2 2 17\n2 3 20",
"2 2\n3\n1 2 0\n1 2 10\n1 1 14",
"2 4\n4\n1 1 -1\n1 3 10\n2 1 30\n1 2 20",
"2 4\n3\n1 1 1\n2 2 10\n2 1 22",
"2 5\n4\n1 1 0\n1 3 10\n2 1 30\n2 2 20",
"2 3\n3\n1 1 0\n2 2 10\n2 1 22",
"4 4\n4\n1 1 0\n2 4 10\n2 1 30\n2 2 20",
"3 3\n4\n1 2 1\n1 3 10\n3 2 14\n3 2 20",
"3 3\n4\n1 2 1\n1 3 16\n3 2 29\n1 3 20",
"2 4\n4\n1 1 -1\n2 2 10\n2 1 22\n2 2 20",
"2 4\n3\n1 1 0\n1 2 10\n2 1 13",
"3 3\n4\n1 2 1\n1 1 15\n3 1 10\n3 3 27",
"4 2\n3\n1 2 0\n1 2 10\n1 1 14",
"2 8\n4\n1 1 -1\n1 3 10\n2 1 30\n1 2 20",
"2 5\n4\n1 1 0\n1 3 10\n2 1 4\n2 2 20",
"2 3\n3\n1 1 0\n2 2 20\n2 1 22",
"2 4\n4\n1 1 -1\n2 2 10\n2 1 29\n2 2 20",
"2 4\n3\n1 1 0\n1 2 10\n2 1 11",
"2 8\n4\n1 2 -1\n1 3 10\n2 1 30\n1 2 20",
"2 5\n4\n1 1 -1\n1 3 10\n2 1 4\n2 2 20",
"2 4\n4\n1 1 -1\n2 2 10\n2 1 46\n2 2 20",
"2 4\n3\n1 1 0\n1 3 10\n2 1 11",
"4 8\n4\n1 2 -1\n1 3 10\n2 1 30\n1 2 20",
"2 5\n4\n2 1 -1\n1 3 10\n2 1 4\n2 2 20",
"2 4\n4\n1 1 -1\n1 2 10\n2 1 46\n2 2 20",
"4 8\n4\n1 2 -1\n1 3 10\n2 1 57\n1 2 20",
"2 5\n4\n2 1 -1\n1 0 10\n2 1 4\n2 2 20",
"2 4\n4\n1 1 -1\n1 2 10\n2 1 46\n2 2 2",
"4 8\n4\n1 2 -1\n1 5 10\n2 1 57\n1 2 20",
"2 6\n4\n2 1 -1\n1 0 10\n2 1 4\n2 2 20",
"4 16\n4\n1 2 -1\n1 5 10\n2 1 57\n1 2 20",
"2 6\n4\n2 1 -1\n1 1 10\n2 1 4\n2 2 20",
"2 4\n3\n1 1 20\n1 2 10\n2 1 0",
"2 3\n5\n1 1 0\n1 2 10\n1 3 20\n2 1 33\n2 3 40",
"2 4\n4\n1 1 0\n1 1 10\n2 1 30\n2 2 20",
"2 4\n4\n1 1 0\n2 2 10\n2 1 30\n2 2 7",
"3 3\n4\n1 2 1\n1 3 10\n3 2 16\n2 3 20",
"3 3\n4\n1 1 0\n1 1 10\n3 2 17\n2 3 20",
"3 3\n4\n2 1 1\n1 1 10\n3 2 27\n2 3 20",
"2 2\n4\n1 1 0\n1 2 8\n2 1 30\n2 2 32",
"2 2\n3\n1 1 0\n1 2 10\n2 1 17",
"3 3\n4\n1 1 0\n1 3 19\n3 1 10\n3 3 35",
"2 4\n4\n1 1 -1\n2 2 10\n2 1 30\n2 2 20",
"2 4\n3\n1 1 0\n2 2 10\n2 1 22",
"3 3\n4\n3 2 1\n1 1 10\n3 2 17\n2 3 20",
"2 2\n3\n1 1 0\n2 2 10\n1 1 14",
"2 4\n4\n1 1 -1\n1 3 20\n2 1 30\n2 2 20",
"2 4\n3\n1 1 1\n1 2 10\n1 1 22",
"4 3\n5\n2 1 0\n2 2 10\n1 3 20\n2 1 30\n2 3 40",
"2 6\n4\n1 1 0\n1 2 10\n2 2 30\n2 2 20",
"2 2\n3\n1 1 -1\n2 2 10\n2 1 22"
],
"output": [
"No",
"Yes",
"Yes",
"No",
"No",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
### Input:
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
### Output:
No
### Input:
2 2
3
1 1 0
1 2 10
2 1 20
### Output:
Yes
### Code:
import sys
readline = sys.stdin.readline
class UFP():
def __init__(self, num):
self.par = [-1]*num
self.dist = [0]*num
def find(self, x):
if self.par[x] < 0:
return x
else:
res = 0
xo = x
while self.par[x] >= 0:
res += self.dist[x]
x = self.par[x]
self.dist[xo] = res
self.par[xo] = x
return x
def union(self, x, y, d):
rx = self.find(x)
ry = self.find(y)
if rx != ry:
if self.par[rx] > self.par[ry]:
rx, ry = ry, rx
x, y = y, x
d = -d
self.par[rx] += self.par[ry]
self.par[ry] = rx
self.dist[ry] = d + self.dist[x] - self.dist[y]
return True
else:
if d + self.dist[x] - self.dist[y]:
return False
return True
INF = 3*10**9
def check():
H, W = map(int, readline().split())
N = int(readline())
Hm = [INF]*H
Wm = [INF]*W
HP = [[] for _ in range(H)]
WP = [[] for _ in range(W)]
for _ in range(N):
h, w, a = map(int, readline().split())
h -= 1
w -= 1
Hm[h] = min(Hm[h], a)
Wm[w] = min(Wm[w], a)
HP[h].append((w, a))
WP[w].append((h, a))
Th = UFP(H)
Tw = UFP(W)
for h in range(H):
L = len(HP[h])
if L > 1:
HP[h].sort()
for i in range(L-1):
wp, ap = HP[h][i]
wn, an = HP[h][i+1]
if not Tw.union(wp, wn, an-ap):
return False
for w in range(W):
L = len(WP[w])
if L > 1:
WP[w].sort()
for i in range(L-1):
hp, ap = WP[w][i]
hn, an = WP[w][i+1]
if not Th.union(hp, hn, an-ap):
return False
cmh = [INF]*H
for h in range(H):
rh = Th.find(h)
cmh[rh] = min(cmh[rh], Th.dist[h])
cmw = [INF]*W
for w in range(W):
rw = Tw.find(w)
cmw[rw] = min(cmw[rw], Tw.dist[w])
for h in range(H):
if Hm[h] - Th.dist[h] + cmh[Th.find(h)] < 0:
return False
for w in range(W):
if Wm[w] - Tw.dist[w] + cmw[Tw.find(w)] < 0:
return False
return True
print('Yes' if check() else 'No')
|
p00083 Era Name Transformation_28769
|
Create a program that converts the date expressed in the Christian era to the Japanese calendar using the era name and outputs the date. The input is three integers, as shown in the example, in the order year, month, and day. Convert this as shown in the sample output. If the date before the Meiji era is entered, please display "pre-meiji".
The first year of each year will be output as "1 year" instead of "first year".
Era | Period
--- | ---
meiji | 1868. 9. 8 ~ 1912. 7.29
taisho | 1912. 7.30 ~ 1926.12.24
showa | 1926.12.25 ~ 1989. 1. 7
heisei | 1989. 1. 8 ~
input
Multiple data are given. As each data, three integers representing year, month and day are given on one line separated by blanks.
Please process until the end of the input. The number of data does not exceed 50.
output
Output the blank-separated era, year, month, day, or "pre-meiji" on one line.
Example
Input
2005 9 3
1868 12 2
1868 9 7
Output
heisei 17 9 3
meiji 1 12 2
pre-meiji
|
from bisect import bisect_left
import sys
name = ["pre-meiji", "meiji", "taisho", "showa", "heisei"]
period = [(1868,9,7), (1912,7,29), (1926,12,24), (1989,1,7)]
for t in (tuple(map(int, l.split())) for l in sys.stdin):
index = bisect_left(period, t)
if index:
date = "{} {} {}".format(t[0]-period[index-1][0]+1, t[1], t[2])
print(name[index], date)
else:
print(name[index])
|
{
"input": [
"2005 9 3\n1868 12 2\n1868 9 7",
"2005 5 3\n1868 12 2\n1868 9 7",
"2005 5 3\n1868 12 2\n1868 9 9",
"2005 7 3\n1868 12 2\n1868 9 9",
"2005 9 3\n1868 12 3\n1868 9 7",
"2005 5 3\n1703 12 2\n1868 9 7",
"2005 5 3\n411 12 2\n1868 9 9",
"2005 5 6\n1703 12 2\n1868 9 7",
"2005 9 3\n1868 9 3\n359 9 7",
"2005 5 6\n1703 12 2\n1868 9 11",
"2005 9 3\n1868 10 3\n359 9 7",
"2005 9 6\n1703 10 1\n1184 9 11",
"2005 5 3\n1868 12 2\n3210 9 7",
"2005 7 3\n1868 12 2\n1868 9 7",
"2005 5 2\n1703 12 2\n1868 9 7",
"2005 5 3\n411 12 2\n1868 9 10",
"1659 5 6\n1703 12 2\n1868 9 7",
"2965 9 3\n1868 9 3\n359 9 7",
"2005 9 4\n1868 10 3\n359 9 7",
"2534 5 6\n1703 12 1\n1868 9 11",
"2005 5 9\n1703 12 1\n1184 9 11",
"2005 9 5\n1743 12 2\n1868 9 7",
"2005 6 3\n1868 12 2\n3210 9 7",
"2005 7 3\n1868 1 2\n1868 9 7",
"4983 9 3\n1868 9 3\n359 9 7",
"2534 1 6\n1703 12 1\n1868 9 11",
"2005 10 9\n1703 12 1\n1184 9 11",
"2005 1 6\n1703 10 1\n1184 9 15",
"3559 9 5\n1743 12 2\n1868 9 7",
"2005 6 3\n2027 12 2\n3210 9 7",
"1810 5 2\n1703 12 2\n1868 9 9",
"2005 9 7\n1868 10 3\n359 9 14",
"2534 1 6\n1703 12 1\n309 9 11",
"3559 9 5\n2425 12 2\n1868 9 7",
"2005 6 3\n2027 12 2\n3210 9 1",
"1668 9 7\n1868 10 3\n359 9 14",
"2005 1 6\n2268 10 2\n1184 9 15",
"2005 6 3\n2027 12 3\n3210 9 1",
"1668 9 7\n2354 10 3\n359 9 14",
"2534 1 6\n2096 12 1\n309 9 14",
"3559 9 5\n2425 12 2\n2980 9 7",
"3080 6 3\n2027 12 3\n3210 9 1",
"2005 1 6\n1920 10 2\n1184 9 15",
"3559 9 5\n2425 12 2\n2980 9 14",
"3080 8 3\n2027 12 3\n3210 9 1",
"2005 6 3\n53 5 1\n581 9 2",
"2447 6 3\n53 5 1\n581 9 2",
"1668 9 2\n2354 10 2\n359 9 7",
"1214 1 6\n2096 12 1\n309 2 6",
"2005 1 6\n1920 10 3\n1184 6 15",
"2223 1 6\n2096 12 1\n309 2 6",
"2005 1 3\n1920 10 3\n1184 6 15",
"1668 8 2\n2354 10 1\n359 9 7",
"2005 1 1\n1920 10 3\n1184 6 19",
"2005 1 1\n1627 10 3\n1184 6 19",
"2005 1 2\n1627 10 3\n1184 6 19",
"2005 1 3\n1627 10 3\n1184 6 19",
"2005 9 3\n1868 12 2\n1868 4 7",
"2005 5 5\n1868 12 2\n1868 9 7",
"2005 7 3\n1868 12 3\n1868 9 9",
"2005 9 3\n1868 12 3\n3530 9 7",
"2005 5 1\n1703 12 2\n1868 9 7",
"2005 5 4\n411 12 2\n1868 9 9",
"2005 5 4\n1703 12 2\n1868 9 7",
"2005 4 3\n1868 9 3\n359 9 7",
"2005 9 3\n3729 10 3\n359 9 7",
"2005 11 3\n1868 10 3\n329 9 7",
"3378 9 3\n373 10 3\n329 9 7",
"2005 9 11\n1703 10 1\n1184 9 11",
"2005 5 3\n1050 12 2\n3210 9 7",
"2005 7 3\n1868 12 2\n1868 9 12",
"2005 9 2\n1868 12 3\n1868 6 7",
"2005 5 2\n1703 12 2\n3125 9 7",
"1659 5 6\n1703 12 2\n1868 9 10",
"2005 9 4\n2465 10 3\n359 9 7",
"2534 3 6\n1703 12 1\n1868 9 11",
"2005 9 3\n1868 10 1\n329 2 7",
"2005 9 6\n2772 10 1\n282 9 11",
"2005 7 3\n1868 1 2\n1868 9 11",
"3185 9 4\n1868 10 3\n359 9 14",
"2005 5 18\n1703 12 1\n1184 9 11",
"3559 9 5\n2899 12 2\n1868 9 7",
"2005 6 3\n2027 12 1\n3210 9 7",
"2005 7 6\n900 1 2\n1868 9 7",
"2005 5 3\n411 5 1\n2430 9 10",
"4983 9 4\n1868 9 3\n356 9 7",
"2005 9 7\n1868 12 3\n359 9 14",
"2005 2 6\n1703 10 2\n1184 9 15",
"3559 9 5\n2425 12 1\n1868 9 7",
"2005 6 3\n2823 12 2\n3210 9 1",
"2532 7 3\n900 1 1\n1868 9 7",
"4983 8 3\n1868 9 3\n356 9 12",
"2005 6 3\n2027 12 3\n2093 9 1",
"2297 5 3\n411 5 1\n581 9 2",
"529 9 6\n1963 5 2\n282 3 11",
"3559 9 7\n2425 12 2\n2980 9 7",
"3080 6 5\n2027 12 3\n3210 9 1",
"4983 10 3\n601 9 3\n356 9 12",
"2029 1 6\n1920 10 2\n1184 9 15",
"1668 9 2\n3637 10 3\n359 9 7",
"2350 1 6\n1920 10 3\n1184 6 15"
],
"output": [
"heisei 17 9 3\nmeiji 1 12 2\npre-meiji",
"heisei 17 5 3\nmeiji 1 12 2\npre-meiji\n",
"heisei 17 5 3\nmeiji 1 12 2\nmeiji 1 9 9\n",
"heisei 17 7 3\nmeiji 1 12 2\nmeiji 1 9 9\n",
"heisei 17 9 3\nmeiji 1 12 3\npre-meiji\n",
"heisei 17 5 3\npre-meiji\npre-meiji\n",
"heisei 17 5 3\npre-meiji\nmeiji 1 9 9\n",
"heisei 17 5 6\npre-meiji\npre-meiji\n",
"heisei 17 9 3\npre-meiji\npre-meiji\n",
"heisei 17 5 6\npre-meiji\nmeiji 1 9 11\n",
"heisei 17 9 3\nmeiji 1 10 3\npre-meiji\n",
"heisei 17 9 6\npre-meiji\npre-meiji\n",
"heisei 17 5 3\nmeiji 1 12 2\nheisei 1222 9 7\n",
"heisei 17 7 3\nmeiji 1 12 2\npre-meiji\n",
"heisei 17 5 2\npre-meiji\npre-meiji\n",
"heisei 17 5 3\npre-meiji\nmeiji 1 9 10\n",
"pre-meiji\npre-meiji\npre-meiji\n",
"heisei 977 9 3\npre-meiji\npre-meiji\n",
"heisei 17 9 4\nmeiji 1 10 3\npre-meiji\n",
"heisei 546 5 6\npre-meiji\nmeiji 1 9 11\n",
"heisei 17 5 9\npre-meiji\npre-meiji\n",
"heisei 17 9 5\npre-meiji\npre-meiji\n",
"heisei 17 6 3\nmeiji 1 12 2\nheisei 1222 9 7\n",
"heisei 17 7 3\npre-meiji\npre-meiji\n",
"heisei 2995 9 3\npre-meiji\npre-meiji\n",
"heisei 546 1 6\npre-meiji\nmeiji 1 9 11\n",
"heisei 17 10 9\npre-meiji\npre-meiji\n",
"heisei 17 1 6\npre-meiji\npre-meiji\n",
"heisei 1571 9 5\npre-meiji\npre-meiji\n",
"heisei 17 6 3\nheisei 39 12 2\nheisei 1222 9 7\n",
"pre-meiji\npre-meiji\nmeiji 1 9 9\n",
"heisei 17 9 7\nmeiji 1 10 3\npre-meiji\n",
"heisei 546 1 6\npre-meiji\npre-meiji\n",
"heisei 1571 9 5\nheisei 437 12 2\npre-meiji\n",
"heisei 17 6 3\nheisei 39 12 2\nheisei 1222 9 1\n",
"pre-meiji\nmeiji 1 10 3\npre-meiji\n",
"heisei 17 1 6\nheisei 280 10 2\npre-meiji\n",
"heisei 17 6 3\nheisei 39 12 3\nheisei 1222 9 1\n",
"pre-meiji\nheisei 366 10 3\npre-meiji\n",
"heisei 546 1 6\nheisei 108 12 1\npre-meiji\n",
"heisei 1571 9 5\nheisei 437 12 2\nheisei 992 9 7\n",
"heisei 1092 6 3\nheisei 39 12 3\nheisei 1222 9 1\n",
"heisei 17 1 6\ntaisho 9 10 2\npre-meiji\n",
"heisei 1571 9 5\nheisei 437 12 2\nheisei 992 9 14\n",
"heisei 1092 8 3\nheisei 39 12 3\nheisei 1222 9 1\n",
"heisei 17 6 3\npre-meiji\npre-meiji\n",
"heisei 459 6 3\npre-meiji\npre-meiji\n",
"pre-meiji\nheisei 366 10 2\npre-meiji\n",
"pre-meiji\nheisei 108 12 1\npre-meiji\n",
"heisei 17 1 6\ntaisho 9 10 3\npre-meiji\n",
"heisei 235 1 6\nheisei 108 12 1\npre-meiji\n",
"heisei 17 1 3\ntaisho 9 10 3\npre-meiji\n",
"pre-meiji\nheisei 366 10 1\npre-meiji\n",
"heisei 17 1 1\ntaisho 9 10 3\npre-meiji\n",
"heisei 17 1 1\npre-meiji\npre-meiji\n",
"heisei 17 1 2\npre-meiji\npre-meiji\n",
"heisei 17 1 3\npre-meiji\npre-meiji\n",
"heisei 17 9 3\nmeiji 1 12 2\npre-meiji\n",
"heisei 17 5 5\nmeiji 1 12 2\npre-meiji\n",
"heisei 17 7 3\nmeiji 1 12 3\nmeiji 1 9 9\n",
"heisei 17 9 3\nmeiji 1 12 3\nheisei 1542 9 7\n",
"heisei 17 5 1\npre-meiji\npre-meiji\n",
"heisei 17 5 4\npre-meiji\nmeiji 1 9 9\n",
"heisei 17 5 4\npre-meiji\npre-meiji\n",
"heisei 17 4 3\npre-meiji\npre-meiji\n",
"heisei 17 9 3\nheisei 1741 10 3\npre-meiji\n",
"heisei 17 11 3\nmeiji 1 10 3\npre-meiji\n",
"heisei 1390 9 3\npre-meiji\npre-meiji\n",
"heisei 17 9 11\npre-meiji\npre-meiji\n",
"heisei 17 5 3\npre-meiji\nheisei 1222 9 7\n",
"heisei 17 7 3\nmeiji 1 12 2\nmeiji 1 9 12\n",
"heisei 17 9 2\nmeiji 1 12 3\npre-meiji\n",
"heisei 17 5 2\npre-meiji\nheisei 1137 9 7\n",
"pre-meiji\npre-meiji\nmeiji 1 9 10\n",
"heisei 17 9 4\nheisei 477 10 3\npre-meiji\n",
"heisei 546 3 6\npre-meiji\nmeiji 1 9 11\n",
"heisei 17 9 3\nmeiji 1 10 1\npre-meiji\n",
"heisei 17 9 6\nheisei 784 10 1\npre-meiji\n",
"heisei 17 7 3\npre-meiji\nmeiji 1 9 11\n",
"heisei 1197 9 4\nmeiji 1 10 3\npre-meiji\n",
"heisei 17 5 18\npre-meiji\npre-meiji\n",
"heisei 1571 9 5\nheisei 911 12 2\npre-meiji\n",
"heisei 17 6 3\nheisei 39 12 1\nheisei 1222 9 7\n",
"heisei 17 7 6\npre-meiji\npre-meiji\n",
"heisei 17 5 3\npre-meiji\nheisei 442 9 10\n",
"heisei 2995 9 4\npre-meiji\npre-meiji\n",
"heisei 17 9 7\nmeiji 1 12 3\npre-meiji\n",
"heisei 17 2 6\npre-meiji\npre-meiji\n",
"heisei 1571 9 5\nheisei 437 12 1\npre-meiji\n",
"heisei 17 6 3\nheisei 835 12 2\nheisei 1222 9 1\n",
"heisei 544 7 3\npre-meiji\npre-meiji\n",
"heisei 2995 8 3\npre-meiji\npre-meiji\n",
"heisei 17 6 3\nheisei 39 12 3\nheisei 105 9 1\n",
"heisei 309 5 3\npre-meiji\npre-meiji\n",
"pre-meiji\nshowa 38 5 2\npre-meiji\n",
"heisei 1571 9 7\nheisei 437 12 2\nheisei 992 9 7\n",
"heisei 1092 6 5\nheisei 39 12 3\nheisei 1222 9 1\n",
"heisei 2995 10 3\npre-meiji\npre-meiji\n",
"heisei 41 1 6\ntaisho 9 10 2\npre-meiji\n",
"pre-meiji\nheisei 1649 10 3\npre-meiji\n",
"heisei 362 1 6\ntaisho 9 10 3\npre-meiji\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Create a program that converts the date expressed in the Christian era to the Japanese calendar using the era name and outputs the date. The input is three integers, as shown in the example, in the order year, month, and day. Convert this as shown in the sample output. If the date before the Meiji era is entered, please display "pre-meiji".
The first year of each year will be output as "1 year" instead of "first year".
Era | Period
--- | ---
meiji | 1868. 9. 8 ~ 1912. 7.29
taisho | 1912. 7.30 ~ 1926.12.24
showa | 1926.12.25 ~ 1989. 1. 7
heisei | 1989. 1. 8 ~
input
Multiple data are given. As each data, three integers representing year, month and day are given on one line separated by blanks.
Please process until the end of the input. The number of data does not exceed 50.
output
Output the blank-separated era, year, month, day, or "pre-meiji" on one line.
Example
Input
2005 9 3
1868 12 2
1868 9 7
Output
heisei 17 9 3
meiji 1 12 2
pre-meiji
### Input:
2005 9 3
1868 12 2
1868 9 7
### Output:
heisei 17 9 3
meiji 1 12 2
pre-meiji
### Input:
2005 5 3
1868 12 2
1868 9 7
### Output:
heisei 17 5 3
meiji 1 12 2
pre-meiji
### Code:
from bisect import bisect_left
import sys
name = ["pre-meiji", "meiji", "taisho", "showa", "heisei"]
period = [(1868,9,7), (1912,7,29), (1926,12,24), (1989,1,7)]
for t in (tuple(map(int, l.split())) for l in sys.stdin):
index = bisect_left(period, t)
if index:
date = "{} {} {}".format(t[0]-period[index-1][0]+1, t[1], t[2])
print(name[index], date)
else:
print(name[index])
|
p00215 Pachimon Creature_28772
|
A popular game in a certain country, Pachimon Creature, has been remade and released in Japan. If you love games, after playing this game many times, you've come to think about how you can clear it the fastest. However, no matter how much you think about it, you didn't know the fastest way to capture it, so you decided to create a program that asks how quickly you can clear the game.
The details of the game are as follows.
The game is set in a world where many creatures called Pachimon creatures (hereinafter referred to as Pachikuri) exist. Each pachikuri has one of five attributes: fire, ice, wood, soil, and water. At the beginning of the game, the main character of the game chooses one pachikuri with his favorite attributes as an adventure partner. The purpose of the game is to aim for the goal with the pachikuri, defeat the rivals in the goal and become the pachikuri master.
However, in order to defeat a rival, you cannot win without the pachikuri of all attributes, so you have to catch the pachikuri of all attributes on the way. Attributes are the key to catching pachikuri. A fire-type crackle can catch an ice-type crackle, and similarly, an ice-type crackle can catch a wood-type, a wood-type can catch a soil-type, a soil-type can catch a water-type, and a water-type can catch a fire-type. The relationship between the attributes is shown in the figure below.
<image>
The figure below shows an example of a map where the game is played.
<image>
The main character starts from the starting point "S" with a pachikuri and aims at the goal point "G" while moving one square at a time. On the way, if you catch the pachikuri of four attributes other than the first pachikuri you have and move to the square that is the goal point, the game will end.
The main character can move from the current square to the next square that shares the side, and counts it as one move. When the main character moves to a square with a pachikuri, if he has a pachikuri with an attribute that can catch that pachikuri, he has caught that pachikuri. You can move to all the squares as many times as you like, regardless of whether you can catch the pachikuri in that square.
Enter the size of the map (number of columns in the horizontal direction, number of rows in the vertical direction) and the initial state of the map, and start to catch the pachikuri attribute selected at the beginning and the pachikuri of the other four attributes. Create a program that outputs the minimum number of movements from the point to the goal point.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:
W H
c11c12 ... c1W
c21c22 ... c2W
::
cH1cH2 ... cHW
The first row gives the number of horizontal columns W and the number of vertical rows H (2 ≤ W, H ≤ 1000) of the map. The following line H is given the information on line i of the map. The state of each cell is given to the input map. "S" is the starting point of the main character, "G" is the goal point, "1" "2" "3" "4" "5" is the attribute of the pachikuri there (1: fire attribute, 2: ice) Attribute, 3: Tree attribute, 4: Earth attribute, 5: Water attribute), ". (Period)" represents an empty cell, respectively. The number of pachikuri for each attribute should be 0 or more and 1000 or less.
The number of datasets does not exceed 140. Also, for 80% of the dataset, W and H do not exceed 100.
Output
For each input data set, the attribute of the first selected Pachikuri and the minimum number of movements are output on one line. No matter how you select the first pachikuri, if you cannot catch the pachikuri of those four attributes no matter what route you move, output NA. Also, if there are multiple ways to select the first pachikuri so that the minimum number of movements is the same, output the one with the smaller attribute number.
Example
Input
6 6
S.1..4
3..5..
..4.1.
4....5
.2.32.
5.1..G
3 2
...
S.G
0 0
Output
2 10
NA
|
from heapq import heappop,heappush
# from line_profiler import LineProfiler
def main():
while(True):
W, H = map(int,input().split())
if not W: break
B = float('inf')
Bi = -1
consequNodes = []
monsterNodes = [[] for _ in range(5)]
idx = 0
for i in range(H):
for j,a in enumerate(input()):
if a == ".":
continue
elif a == "S":
consequNodes.append([i,j,idx,5])
startNode = [i,j,idx,5]
idx+=1
elif a == "G":
consequNodes.append([i,j,idx,6])
goalNode = [i,j,idx,6]
idx+=1
elif a != ".":
consequNodes.append([i,j,idx,int(a)-1])
monsterNodes[int(a)-1].append([i,j,idx])
idx+=1
for z in range(5):
consequNodes[startNode[2]][3] = z
dist = [[float('inf')]*idx for _ in range(6)]
dist[1][startNode[2]] = 0
que = [(0,1,startNode[2],0)]
reached = False
while que:
cst,numrep,nid,huristicCost = heappop(que)
cst = int(cst)-int(huristicCost)
if numrep == 5:
reached = True
cst += abs(consequNodes[nid][0]-goalNode[0]) + abs(consequNodes[nid][1]-goalNode[1])
break
nxtmonster = (consequNodes[nid][3]+1)%5
for nxty,nxtx,nxtid in monsterNodes[nxtmonster]:
tmpCost = dist[numrep][nid] + abs(nxty-consequNodes[nid][0]) + abs(nxtx-consequNodes[nid][1])
if tmpCost < dist[numrep+1][nxtid]:
dist[numrep+1][nxtid] = tmpCost
h = abs(nxty-goalNode[0]) + abs(nxtx-goalNode[1])
h *= 0.99
heappush(que,(tmpCost+h,numrep+1,nxtid,h))
if reached and cst < B:
B = cst
Bi = z+1
if Bi == -1:
print("NA")
else:
print(Bi,B)
if __name__ == "__main__":
# prf = LineProfiler()
# prf.add_function(main)
# prf.runcall(main)
# prf.print_stats()
main()
|
{
"input": [
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n5..3..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n4..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nS.G\n0 0",
"6 6\n4.1..S\n..53..\n..14..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n5..3..\n..41..\n4....5\n.2.32.\nG..1.5\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4...5.\n.2.32.\n..15.G\n3 2\n...\nS.G\n0 0",
"6 6\n4..1.S\n4..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1G..\n3 2\n...\nS.G\n0 0",
"6 6\n..1S.4\n35....\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n5..3..\n..4.1.\n5....4\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n4....5\n.2.32.\nG..1.5\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n5..3..\n..41..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n4....4\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n1.4...\n4....5\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4...5.\n.3.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n..53..\n..14..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n4....4\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n4..5..\n..4.1.\n4....5\n.2.42.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..5\n3..5..\n..4.1.\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n3..5..\n.1.4..\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..54..\n..41..\n4....4\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..5\n3..5..\n..4.1.\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n.1.4..\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nG.S\n0 0",
"6 6\n..1.S4\n..54..\n..41..\n4....4\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..5\n2..5..\n..4.1.\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..3\n5..3..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n5....4\n.2.32.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS..1.4\n3..5..\n1.4...\n4....5\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n..53..\n..14..\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.GS\n0 0",
"6 6\n4.1..S\n..53..\n..14..\n4....5\n.23.2.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n..54..\n..4.1.\n4....4\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS41...\n3..5..\n.1.4..\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nG.S\n0 0",
"6 6\nS..1.4\n3..5..\n1.4...\n4....5\n.23.2.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n..53..\n.1.4..\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.GS\n0 0",
"6 6\nS.1..3\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n5..3..\n..41..\n4....5\n.23.2.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..53..\n..41..\n4....5\n.2.42.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..4\n2..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\nS41...\n3..5..\n..4.1.\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n..5..4\n..4.1.\n4....5\n.2.42.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..5\n3..5..\n..4.1.\n4...5.\n.2.23.\n5.1..G\n3 2\n...\nG.S\n0 0",
"6 6\n4.1..S\n.5.3..\n..14..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nSG.\n0 0",
"6 6\nS.1..5\n3..5..\n.1.4..\n4...5.\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3....5\n.1.4..\n4...5.\n.3.32.\nG..1.5\n3 2\n...\nG.S\n0 0",
"6 6\nS.1..4\n3..5..\n..3.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n....14\n4...5.\n.2.32.\n..15.G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..3.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.1..4\n3.5...\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n3..5..\n.1.4..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n3....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n35....\n..4.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n5....4\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n3...5.\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1.S4\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.2.32.\nG..1.5\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n5....4\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n4..1.S\n3..5..\n.1.4..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.1..4\n5..3..\n..4.1.\n5....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n4....5\n.2.3.2\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n5....4\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.1..5\n3..5..\n.1.4..\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n..4.2.\n4....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..1S.4\n3..5..\n..4.1.\n5....4\n.23.2.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..2.S4\n3..5..\n..4.1.\n3...5.\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.2..4\n3..5..\n..4.1.\n5....4\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n5..3..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..1S.4\n..5..3\n..4.1.\n4....5\n.2.3.2\n5.1..G\n3 2\n...\nS.G\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n5....4\n.2.32.\nG..1.5\n3 2\n...\n.SG\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n4....5\n.2.32.\nG..1.5\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n.24...\n4....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..2S.4\n3..5..\n..4.1.\n4....5\n.1.32.\nG..1.5\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n.24...\n5....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..2S4.\n3..5..\n..4.1.\n4....5\n.1.32.\nG..1.5\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n.24...\n5....5\n.23.2.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\nS.1..4\n3..5..\n..4.1.\n4....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..3\n3.5...\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n4.S2..\n3..5..\n..4.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\nGS.\n0 0",
"6 6\n..1S.4\n3..5..\n.1.4..\n4....5\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\n..1.S4\n3..5..\n..4.1.\n4....5\n.2.32.\nG..1.5\n3 2\n...\nS.G\n0 0",
"6 6\n4..1.S\n3..5..\n..4.1.\n4....5\n.2.32.\nG..1.5\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n5..3..\n..3.1.\n5....4\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n5..3..\n..4.1.\n5....5\n2..32.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.2..4\n3..5..\n..4.1.\n5....4\n.23.2.\n5.1..G\n3 2\n...\n.SG\n0 0",
"6 6\nS.1..4\n5..3..\n..3.1.\n4....5\n.2.32.\n5.1..G\n3 2\n...\n.SG\n0 0"
],
"output": [
"2 10\nNA",
"3 12\nNA\n",
"2 10\nNA\n",
"3 10\nNA\n",
"2 13\nNA\n",
"1 13\nNA\n",
"4 13\nNA\n",
"2 12\nNA\n",
"4 11\nNA\n",
"4 9\nNA\n",
"2 8\nNA\n",
"3 11\nNA\n",
"4 12\nNA\n",
"4 10\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"3 10\nNA\n",
"2 10\nNA\n",
"2 13\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"2 13\nNA\n",
"3 10\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"2 13\nNA\n",
"3 12\nNA\n",
"2 13\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"3 12\nNA\n",
"2 13\nNA\n",
"3 12\nNA\n",
"2 10\nNA\n",
"1 13\nNA\n",
"2 10\nNA\n",
"2 13\nNA\n",
"2 10\nNA\n",
"2 12\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"4 9\nNA\n",
"4 9\nNA\n",
"4 9\nNA\n",
"4 9\nNA\n",
"2 10\nNA\n",
"3 11\nNA\n",
"4 9\nNA\n",
"3 11\nNA\n",
"3 11\nNA\n",
"4 9\nNA\n",
"3 10\nNA\n",
"2 13\nNA\n",
"2 12\nNA\n",
"1 13\nNA\n",
"4 12\nNA\n",
"2 10\nNA\n",
"3 11\nNA\n",
"2 12\nNA\n",
"2 10\nNA\n",
"2 13\nNA\n",
"3 11\nNA\n",
"3 10\nNA\n",
"2 12\nNA\n",
"3 12\nNA\n",
"3 11\nNA\n",
"2 13\nNA\n",
"4 10\nNA\n",
"2 13\nNA\n",
"4 10\nNA\n",
"4 13\nNA\n",
"4 10\nNA\n",
"4 13\nNA\n",
"2 10\nNA\n",
"2 10\nNA\n",
"3 10\nNA\n",
"4 11\nNA\n",
"4 11\nNA\n",
"4 12\nNA\n",
"4 12\nNA\n",
"4 12\nNA\n",
"2 12\nNA\n",
"3 12\nNA\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A popular game in a certain country, Pachimon Creature, has been remade and released in Japan. If you love games, after playing this game many times, you've come to think about how you can clear it the fastest. However, no matter how much you think about it, you didn't know the fastest way to capture it, so you decided to create a program that asks how quickly you can clear the game.
The details of the game are as follows.
The game is set in a world where many creatures called Pachimon creatures (hereinafter referred to as Pachikuri) exist. Each pachikuri has one of five attributes: fire, ice, wood, soil, and water. At the beginning of the game, the main character of the game chooses one pachikuri with his favorite attributes as an adventure partner. The purpose of the game is to aim for the goal with the pachikuri, defeat the rivals in the goal and become the pachikuri master.
However, in order to defeat a rival, you cannot win without the pachikuri of all attributes, so you have to catch the pachikuri of all attributes on the way. Attributes are the key to catching pachikuri. A fire-type crackle can catch an ice-type crackle, and similarly, an ice-type crackle can catch a wood-type, a wood-type can catch a soil-type, a soil-type can catch a water-type, and a water-type can catch a fire-type. The relationship between the attributes is shown in the figure below.
<image>
The figure below shows an example of a map where the game is played.
<image>
The main character starts from the starting point "S" with a pachikuri and aims at the goal point "G" while moving one square at a time. On the way, if you catch the pachikuri of four attributes other than the first pachikuri you have and move to the square that is the goal point, the game will end.
The main character can move from the current square to the next square that shares the side, and counts it as one move. When the main character moves to a square with a pachikuri, if he has a pachikuri with an attribute that can catch that pachikuri, he has caught that pachikuri. You can move to all the squares as many times as you like, regardless of whether you can catch the pachikuri in that square.
Enter the size of the map (number of columns in the horizontal direction, number of rows in the vertical direction) and the initial state of the map, and start to catch the pachikuri attribute selected at the beginning and the pachikuri of the other four attributes. Create a program that outputs the minimum number of movements from the point to the goal point.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:
W H
c11c12 ... c1W
c21c22 ... c2W
::
cH1cH2 ... cHW
The first row gives the number of horizontal columns W and the number of vertical rows H (2 ≤ W, H ≤ 1000) of the map. The following line H is given the information on line i of the map. The state of each cell is given to the input map. "S" is the starting point of the main character, "G" is the goal point, "1" "2" "3" "4" "5" is the attribute of the pachikuri there (1: fire attribute, 2: ice) Attribute, 3: Tree attribute, 4: Earth attribute, 5: Water attribute), ". (Period)" represents an empty cell, respectively. The number of pachikuri for each attribute should be 0 or more and 1000 or less.
The number of datasets does not exceed 140. Also, for 80% of the dataset, W and H do not exceed 100.
Output
For each input data set, the attribute of the first selected Pachikuri and the minimum number of movements are output on one line. No matter how you select the first pachikuri, if you cannot catch the pachikuri of those four attributes no matter what route you move, output NA. Also, if there are multiple ways to select the first pachikuri so that the minimum number of movements is the same, output the one with the smaller attribute number.
Example
Input
6 6
S.1..4
3..5..
..4.1.
4....5
.2.32.
5.1..G
3 2
...
S.G
0 0
Output
2 10
NA
### Input:
6 6
S.1..4
3..5..
..4.1.
4....5
.2.32.
5.1..G
3 2
...
S.G
0 0
### Output:
2 10
NA
### Input:
6 6
S.1..4
5..3..
..4.1.
4....5
.2.32.
5.1..G
3 2
...
S.G
0 0
### Output:
3 12
NA
### Code:
from heapq import heappop,heappush
# from line_profiler import LineProfiler
def main():
while(True):
W, H = map(int,input().split())
if not W: break
B = float('inf')
Bi = -1
consequNodes = []
monsterNodes = [[] for _ in range(5)]
idx = 0
for i in range(H):
for j,a in enumerate(input()):
if a == ".":
continue
elif a == "S":
consequNodes.append([i,j,idx,5])
startNode = [i,j,idx,5]
idx+=1
elif a == "G":
consequNodes.append([i,j,idx,6])
goalNode = [i,j,idx,6]
idx+=1
elif a != ".":
consequNodes.append([i,j,idx,int(a)-1])
monsterNodes[int(a)-1].append([i,j,idx])
idx+=1
for z in range(5):
consequNodes[startNode[2]][3] = z
dist = [[float('inf')]*idx for _ in range(6)]
dist[1][startNode[2]] = 0
que = [(0,1,startNode[2],0)]
reached = False
while que:
cst,numrep,nid,huristicCost = heappop(que)
cst = int(cst)-int(huristicCost)
if numrep == 5:
reached = True
cst += abs(consequNodes[nid][0]-goalNode[0]) + abs(consequNodes[nid][1]-goalNode[1])
break
nxtmonster = (consequNodes[nid][3]+1)%5
for nxty,nxtx,nxtid in monsterNodes[nxtmonster]:
tmpCost = dist[numrep][nid] + abs(nxty-consequNodes[nid][0]) + abs(nxtx-consequNodes[nid][1])
if tmpCost < dist[numrep+1][nxtid]:
dist[numrep+1][nxtid] = tmpCost
h = abs(nxty-goalNode[0]) + abs(nxtx-goalNode[1])
h *= 0.99
heappush(que,(tmpCost+h,numrep+1,nxtid,h))
if reached and cst < B:
B = cst
Bi = z+1
if Bi == -1:
print("NA")
else:
print(Bi,B)
if __name__ == "__main__":
# prf = LineProfiler()
# prf.add_function(main)
# prf.runcall(main)
# prf.print_stats()
main()
|
p00375 Celsius and Fahrenheit_28776
|
In Japan, temperature is usually expressed using the Celsius (℃) scale. In America, they used the Fahrenheit (℉) scale instead. $20$ degrees Celsius is roughly equal to $68$ degrees Fahrenheit. A phrase such as "Today’s temperature is $68$ degrees" is commonly encountered while you are in America.
A value in Fahrenheit can be converted to Celsius by first subtracting $32$ and then multiplying by $\frac{5}{9}$. A simplified method may be used to produce a rough estimate: first subtract $30$ and then divide by $2$. Using the latter method, $68$ Fahrenheit is converted to $19$ Centigrade, i.e., $\frac{(68-30)}{2}$.
Make a program to convert Fahrenheit to Celsius using the simplified method: $C = \frac{F - 30}{2}$.
Input
The input is given in the following format.
$F$
The input line provides a temperature in Fahrenheit $F$ ($30 \leq F \leq 100$), which is an integer divisible by $2$.
Output
Output the converted Celsius temperature in a line.
Examples
Input
68
Output
19
Input
50
Output
10
|
x=input()
x=int(x)
y=(x-30)//2
print(y)
|
{
"input": [
"68",
"50",
"82",
"60",
"116",
"85",
"162",
"51",
"149",
"96",
"238",
"65",
"311",
"558",
"633",
"1080",
"1303",
"2092",
"3794",
"6199",
"10347",
"9393",
"10699",
"19116",
"1106",
"355",
"642",
"390",
"298",
"57",
"31",
"24",
"104",
"41",
"164",
"319",
"111",
"215",
"192",
"103",
"709",
"1263",
"1682",
"864",
"3288",
"2981",
"9202",
"11734",
"14312",
"10436",
"19258",
"90",
"269",
"350",
"542",
"326",
"10",
"6",
"265",
"607",
"101",
"321",
"291",
"135",
"1123",
"2275",
"562",
"246",
"144",
"4725",
"5878",
"4512",
"22485",
"19786",
"37535",
"256",
"159",
"498",
"647",
"39",
"46",
"37",
"114",
"397",
"66",
"000",
"304",
"371",
"71",
"1684",
"2835",
"22",
"346",
"7124",
"8199",
"6248",
"11587",
"8024",
"54760",
"54",
"62",
"308"
],
"output": [
"19",
"10",
"26\n",
"15\n",
"43\n",
"27\n",
"66\n",
"10\n",
"59\n",
"33\n",
"104\n",
"17\n",
"140\n",
"264\n",
"301\n",
"525\n",
"636\n",
"1031\n",
"1882\n",
"3084\n",
"5158\n",
"4681\n",
"5334\n",
"9543\n",
"538\n",
"162\n",
"306\n",
"180\n",
"134\n",
"13\n",
"0\n",
"-3\n",
"37\n",
"5\n",
"67\n",
"144\n",
"40\n",
"92\n",
"81\n",
"36\n",
"339\n",
"616\n",
"826\n",
"417\n",
"1629\n",
"1475\n",
"4586\n",
"5852\n",
"7141\n",
"5203\n",
"9614\n",
"30\n",
"119\n",
"160\n",
"256\n",
"148\n",
"-10\n",
"-12\n",
"117\n",
"288\n",
"35\n",
"145\n",
"130\n",
"52\n",
"546\n",
"1122\n",
"266\n",
"108\n",
"57\n",
"2347\n",
"2924\n",
"2241\n",
"11227\n",
"9878\n",
"18752\n",
"113\n",
"64\n",
"234\n",
"308\n",
"4\n",
"8\n",
"3\n",
"42\n",
"183\n",
"18\n",
"-15\n",
"137\n",
"170\n",
"20\n",
"827\n",
"1402\n",
"-4\n",
"158\n",
"3547\n",
"4084\n",
"3109\n",
"5778\n",
"3997\n",
"27365\n",
"12\n",
"16\n",
"139\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In Japan, temperature is usually expressed using the Celsius (℃) scale. In America, they used the Fahrenheit (℉) scale instead. $20$ degrees Celsius is roughly equal to $68$ degrees Fahrenheit. A phrase such as "Today’s temperature is $68$ degrees" is commonly encountered while you are in America.
A value in Fahrenheit can be converted to Celsius by first subtracting $32$ and then multiplying by $\frac{5}{9}$. A simplified method may be used to produce a rough estimate: first subtract $30$ and then divide by $2$. Using the latter method, $68$ Fahrenheit is converted to $19$ Centigrade, i.e., $\frac{(68-30)}{2}$.
Make a program to convert Fahrenheit to Celsius using the simplified method: $C = \frac{F - 30}{2}$.
Input
The input is given in the following format.
$F$
The input line provides a temperature in Fahrenheit $F$ ($30 \leq F \leq 100$), which is an integer divisible by $2$.
Output
Output the converted Celsius temperature in a line.
Examples
Input
68
Output
19
Input
50
Output
10
### Input:
68
### Output:
19
### Input:
50
### Output:
10
### Code:
x=input()
x=int(x)
y=(x-30)//2
print(y)
|
p00593 JPEG Compression_28780
|
The fundamental idea in the JPEG compression algorithm is to sort coeffi- cient of given image by zigzag path and encode it. In this problem, we don’t discuss about details of the algorithm, but you are asked to make simple pro- gram. You are given single integer N , and you must output zigzag path on a matrix where size is N by N . The zigzag scanning is start at the upper-left corner (0, 0) and end up at the bottom-right corner. See the following Figure and sample output to make sure rule of the zigzag scanning. For example, if you are given N = 8, corresponding output should be a matrix shown in right-side of the Figure. This matrix consists of visited time for each element.
<image>
Input
Several test cases are given. Each test case consists of one integer N (0 < N < 10) in a line. The input will end at a line contains single zero.
Output
For each input, you must output a matrix where each element is the visited time. All numbers in the matrix must be right justified in a field of width 3. Each matrix should be prefixed by a header “Case x:” where x equals test case number.
Example
Input
3
4
0
Output
Case 1:
1 2 6
3 5 7
4 8 9
Case 2:
1 2 6 7
3 5 8 13
4 9 12 14
10 11 15 16
|
t = 1
while 1:
N = int(input())
if N == 0:
break
print("Case %d:" % t); t += 1
M = [[0]*N for i in range(N)]
c = 1
for i in range(2*N-1):
for j in range(max(i-N+1, 0), min(N, i+1)):
if i % 2 == 0:
M[i-j][j] = "%3d" % c
else:
M[j][i-j] = "%3d" % c
c += 1
for l in M:
print(*l,sep='')
|
{
"input": [
"3\n4\n0",
"3\n7\n0",
"3\n3\n0",
"3\n0\n0",
"3\n1\n0",
"3\n2\n0",
"3\n-1\n0",
"3\n5\n0",
"3\n8\n0",
"3\n6\n0",
"3\n9\n0",
"3\n0\n-1",
"3\n0\n1",
"3\n0\n-2",
"3\n0\n2",
"3\n0\n-4",
"3\n0\n-5",
"3\n0\n3",
"3\n0\n-3",
"3\n0\n4",
"3\n0\n8",
"3\n0\n5",
"3\n0\n16",
"3\n0\n30",
"3\n0\n6",
"3\n0\n-8",
"3\n0\n-6",
"3\n0\n22",
"3\n0\n18",
"3\n0\n-11",
"3\n0\n25",
"3\n0\n-16",
"3\n0\n-30",
"3\n0\n-24",
"3\n0\n7",
"3\n0\n10",
"3\n0\n14",
"3\n0\n26",
"3\n0\n28",
"3\n0\n24",
"3\n0\n-20",
"3\n0\n-35",
"3\n0\n12",
"3\n0\n-7",
"3\n0\n50",
"3\n0\n11",
"3\n0\n20",
"3\n0\n19",
"3\n0\n9",
"3\n0\n-9",
"3\n0\n36",
"3\n0\n-10",
"3\n0\n32",
"3\n0\n23",
"3\n0\n17",
"3\n0\n43",
"3\n0\n13",
"3\n0\n-17",
"3\n0\n55",
"3\n0\n33",
"3\n0\n-21",
"3\n0\n45",
"3\n0\n44",
"3\n0\n40",
"3\n0\n-12",
"3\n0\n15",
"3\n0\n-36",
"3\n0\n29",
"3\n0\n46",
"3\n0\n31",
"3\n0\n-15",
"3\n0\n63",
"3\n0\n35",
"3\n0\n90",
"3\n0\n-13",
"3\n0\n56",
"3\n0\n54",
"3\n0\n-60",
"3\n0\n76",
"3\n0\n34",
"3\n0\n49",
"3\n0\n-14",
"3\n0\n-18",
"3\n0\n51",
"3\n0\n-19",
"3\n0\n21",
"3\n0\n85",
"3\n0\n38",
"3\n0\n62",
"3\n0\n159",
"3\n0\n88",
"3\n0\n77",
"3\n0\n-68",
"3\n0\n-22",
"3\n0\n248",
"3\n0\n-48",
"3\n0\n160",
"3\n0\n37",
"3\n0\n48",
"3\n0\n74",
"3\n0\n-26"
],
"output": [
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7\n 3 5 8 13\n 4 9 12 14\n 10 11 15 16",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7 15 16 28\n 3 5 8 14 17 27 29\n 4 9 13 18 26 30 39\n 10 12 19 25 31 38 40\n 11 20 24 32 37 41 46\n 21 23 33 36 42 45 47\n 22 34 35 43 44 48 49\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2\n 3 4\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7 15\n 3 5 8 14 16\n 4 9 13 17 22\n 10 12 18 21 23\n 11 19 20 24 25\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7 15 16 28 29\n 3 5 8 14 17 27 30 43\n 4 9 13 18 26 31 42 44\n 10 12 19 25 32 41 45 54\n 11 20 24 33 40 46 53 55\n 21 23 34 39 47 52 56 61\n 22 35 38 48 51 57 60 62\n 36 37 49 50 58 59 63 64\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7 15 16\n 3 5 8 14 17 26\n 4 9 13 18 25 27\n 10 12 19 24 28 33\n 11 20 23 29 32 34\n 21 22 30 31 35 36\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7 15 16 28 29 45\n 3 5 8 14 17 27 30 44 46\n 4 9 13 18 26 31 43 47 60\n 10 12 19 25 32 42 48 59 61\n 11 20 24 33 41 49 58 62 71\n 21 23 34 40 50 57 63 70 72\n 22 35 39 51 56 64 69 73 78\n 36 38 52 55 65 68 74 77 79\n 37 53 54 66 67 75 76 80 81\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n",
"Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The fundamental idea in the JPEG compression algorithm is to sort coeffi- cient of given image by zigzag path and encode it. In this problem, we don’t discuss about details of the algorithm, but you are asked to make simple pro- gram. You are given single integer N , and you must output zigzag path on a matrix where size is N by N . The zigzag scanning is start at the upper-left corner (0, 0) and end up at the bottom-right corner. See the following Figure and sample output to make sure rule of the zigzag scanning. For example, if you are given N = 8, corresponding output should be a matrix shown in right-side of the Figure. This matrix consists of visited time for each element.
<image>
Input
Several test cases are given. Each test case consists of one integer N (0 < N < 10) in a line. The input will end at a line contains single zero.
Output
For each input, you must output a matrix where each element is the visited time. All numbers in the matrix must be right justified in a field of width 3. Each matrix should be prefixed by a header “Case x:” where x equals test case number.
Example
Input
3
4
0
Output
Case 1:
1 2 6
3 5 7
4 8 9
Case 2:
1 2 6 7
3 5 8 13
4 9 12 14
10 11 15 16
### Input:
3
4
0
### Output:
Case 1:
1 2 6
3 5 7
4 8 9
Case 2:
1 2 6 7
3 5 8 13
4 9 12 14
10 11 15 16
### Input:
3
7
0
### Output:
Case 1:
1 2 6
3 5 7
4 8 9
Case 2:
1 2 6 7 15 16 28
3 5 8 14 17 27 29
4 9 13 18 26 30 39
10 12 19 25 31 38 40
11 20 24 32 37 41 46
21 23 33 36 42 45 47
22 34 35 43 44 48 49
### Code:
t = 1
while 1:
N = int(input())
if N == 0:
break
print("Case %d:" % t); t += 1
M = [[0]*N for i in range(N)]
c = 1
for i in range(2*N-1):
for j in range(max(i-N+1, 0), min(N, i+1)):
if i % 2 == 0:
M[i-j][j] = "%3d" % c
else:
M[j][i-j] = "%3d" % c
c += 1
for l in M:
print(*l,sep='')
|
p00729 Analyzing Login/Logout Records_28784
|
You have a computer literacy course in your university. In the computer system, the login/logout records of all PCs in a day are stored in a file. Although students may use two or more PCs at a time, no one can log in to a PC which has been logged in by someone who has not logged out of that PC yet.
You are asked to write a program that calculates the total time of a student that he/she used at least one PC in a given time period (probably in a laboratory class) based on the records in the file.
The following are example login/logout records.
* The student 1 logged in to the PC 1 at 12:55
* The student 2 logged in to the PC 4 at 13:00
* The student 1 logged in to the PC 2 at 13:10
* The student 1 logged out of the PC 2 at 13:20
* The student 1 logged in to the PC 3 at 13:30
* The student 1 logged out of the PC 1 at 13:40
* The student 1 logged out of the PC 3 at 13:45
* The student 1 logged in to the PC 1 at 14:20
* The student 2 logged out of the PC 4 at 14:30
* The student 1 logged out of the PC 1 at 14:40
For a query such as "Give usage of the student 1 between 13:00 and 14:30", your program should answer "55 minutes", that is, the sum of 45 minutes from 13:00 to 13:45 and 10 minutes from 14:20 to 14:30, as depicted in the following figure.
<image>
Input
The input is a sequence of a number of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets never exceeds 10.
Each dataset is formatted as follows.
> N M
> r
> record1
> ...
> recordr
> q
> query1
> ...
> queryq
>
The numbers N and M in the first line are the numbers of PCs and the students, respectively. r is the number of records. q is the number of queries. These four are integers satisfying the following.
> 1 ≤ N ≤ 1000, 1 ≤ M ≤ 10000, 2 ≤ r ≤ 1000, 1 ≤ q ≤ 50
Each record consists of four integers, delimited by a space, as follows.
> t n m s
s is 0 or 1. If s is 1, this line means that the student m logged in to the PC n at time t . If s is 0, it means that the student m logged out of the PC n at time t . The time is expressed as elapsed minutes from 0:00 of the day. t , n and m satisfy the following.
> 540 ≤ t ≤ 1260, 1 ≤ n ≤ N , 1 ≤ m ≤ M
You may assume the following about the records.
* Records are stored in ascending order of time t.
* No two records for the same PC has the same time t.
* No PCs are being logged in before the time of the first record nor after that of the last record in the file.
* Login and logout records for one PC appear alternatingly, and each of the login-logout record pairs is for the same student.
Each query consists of three integers delimited by a space, as follows.
> ts te m
It represents "Usage of the student m between ts and te ". ts , te and m satisfy the following.
> 540 ≤ ts < te ≤ 1260, 1 ≤ m ≤ M
Output
For each query, print a line having a decimal integer indicating the time of usage in minutes. Output lines should not have any character other than this number.
Example
Input
4 2
10
775 1 1 1
780 4 2 1
790 2 1 1
800 2 1 0
810 3 1 1
820 1 1 0
825 3 1 0
860 1 1 1
870 4 2 0
880 1 1 0
1
780 870 1
13 15
12
540 12 13 1
600 12 13 0
650 13 15 1
660 12 15 1
665 11 13 1
670 13 15 0
675 11 13 0
680 12 15 0
1000 11 14 1
1060 12 14 1
1060 11 14 0
1080 12 14 0
3
540 700 13
600 1000 15
1000 1200 11
1 1
2
600 1 1 1
700 1 1 0
5
540 600 1
550 650 1
610 620 1
650 750 1
700 800 1
0 0
Output
55
70
30
0
0
50
10
50
0
|
def main(N, M):
member = [[0] * 721 for i in range(M)]
r = int(input())
for _ in range(r):
t, _, m, s = map(int, input().split())
t -= 540
if s == 0:
member[m - 1][t] -= 1
else:
member[m - 1][t] += 1
for i in range(M):
for t in range(1,721):
member[i][t] += member[i][t - 1]
q = int(input())
for i in range(q):
ts, te, m = map(int, input().split())
ts -= 540
te -= 540
ans = 0
#print(member[m-1][ts:te])
for t in range(ts, te):
ans += (member[m-1][t] > 0)
print(ans)
while 1:
n, m = map(int, input().split())
if n == m == 0:
break
main(n,m)
|
{
"input": [
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n610 620 1\n1045 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n606 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n107 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 1192 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 1178 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n1265 1 1 1\n1239 4 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n1018 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 1\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 1050 1\n266 620 1\n650 750 1\n700 1165 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n755 12 14 0\n3\n540 578 13\n600 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 1178 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1010 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n911 650 1\n610 620 1\n650 1192 1\n806 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n951 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 1160 1\n650 937 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n883 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n609 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n1117 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n241 700 13\n983 1000 2\n1000 934 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 20\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 -1\n3\n540 700 10\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n1053 620 1\n650 750 1\n700 1092 2\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 937 1\n233 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n820 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 1\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n1119 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n1018 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 1150 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1064 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n989 700 13\n983 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n923 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 826 1\n550 171 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n61 4 2 0\n880 1 1 0\n1\n780 909 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 1\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n1018 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 1150 1\n610 620 1\n166 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n342 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n3 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 266 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n61 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n610 620 1\n88 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n209 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n951 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 152 1\n550 461 1\n48 620 1\n650 937 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n531 761 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n453 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 0\n550 650 1\n610 620 2\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n342 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 889 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n585 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n1133 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n969 11 14 0\n1080 12 14 0\n3\n937 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n192 650 1\n266 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 1110 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 1\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 1050 1\n266 620 1\n650 750 1\n700 1165 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 -1\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 1128 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n1221 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 11\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n61 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n179 620 1\n88 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n654 4 0 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1010 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n911 650 1\n610 620 1\n650 1192 1\n319 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n42 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n135 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n598 1123 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 0 0\n880 1 1 0\n1\n361 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 393 1\n606 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 -1\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 1128 1\n550 650 1\n610 620 1\n650 750 1\n513 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n537 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 2\n1001 934 11\n1 1\n2\n600 1 1 1\n906 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n42 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n135 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 1053 1\n550 650 1\n598 1123 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 -1\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 1128 1\n550 650 1\n795 620 1\n650 750 1\n513 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n537 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 2\n1001 934 11\n1 1\n2\n600 1 1 1\n906 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 828 1\n0 0",
"4 2\n10\n632 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 924 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n606 650 1\n610 620 1\n650 937 1\n506 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 1\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 420 1\n266 620 1\n650 750 1\n700 1165 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 961 1\n550 650 1\n610 1123 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 1\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n616 650 1\n266 620 1\n650 750 1\n1119 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n1018 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n861 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 1150 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n590 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 1\n1080 12 14 1\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n606 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n342 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n342 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n3 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n453 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 1192 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n61 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 712 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 2\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 1165 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n585 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 2\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 20\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n969 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1010 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 1192 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n61 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1001 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 171 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 2\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 1\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 1165 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n1239 4 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n1262 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n969 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n1294 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n635 4 2 0\n880 1 1 0\n1\n91 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n587 600 1\n550 650 1\n266 620 1\n650 750 1\n1119 800 1\n0 0",
"6 2\n10\n775 1 1 1\n453 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n556 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 2\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1000 2\n1000 934 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 3 2 0\n880 1 1 0\n1\n404 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n156 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n755 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n2 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 1178 1\n650 750 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1010 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n983 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 1192 1\n806 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n951 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 650 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n1068 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n241 700 13\n983 1000 2\n1000 934 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n951 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 238 1\n550 461 1\n610 620 1\n650 937 1\n700 800 1\n0 0",
"6 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n951 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1294 12 14 0\n3\n540 700 13\n600 1100 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 152 1\n550 461 1\n610 620 1\n650 937 1\n700 800 1\n0 0"
],
"output": [
"55\n70\n30\n0\n0\n50\n10\n50\n0",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n0\n0\n",
"55\n70\n30\n0\n0\n44\n10\n50\n0\n",
"60\n70\n0\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n90\n50\n0\n",
"50\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n368\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n100\n20\n50\n0\n",
"60\n38\n30\n0\n0\n50\n90\n50\n0\n",
"55\n70\n0\n0\n0\n0\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n90\n50\n0\n",
"0\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n91\n",
"0\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n0\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n0\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n100\n",
"55\n70\n0\n0\n0\n50\n0\n50\n0\n",
"60\n70\n0\n0\n0\n50\n20\n50\n0\n",
"60\n70\n368\n0\n0\n100\n10\n50\n0\n",
"55\n0\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n100\n0\n10\n50\n0\n",
"65\n70\n30\n0\n0\n0\n10\n50\n0\n",
"60\n70\n368\n0\n0\n100\n10\n100\n0\n",
"60\n70\n30\n0\n0\n0\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n100\n0\n",
"55\n70\n0\n0\n0\n50\n20\n50\n0\n",
"55\n70\n30\n0\n0\n0\n20\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n100\n0\n",
"55\n26\n30\n0\n0\n50\n0\n50\n0\n",
"60\n70\n30\n0\n0\n100\n10\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n0\n0\n",
"60\n0\n30\n0\n0\n50\n20\n50\n0\n",
"70\n70\n30\n0\n0\n100\n20\n50\n0\n",
"55\n70\n30\n0\n100\n50\n10\n50\n0\n",
"55\n0\n350\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n20\n100\n0\n",
"55\n70\n0\n0\n0\n0\n10\n50\n100\n",
"60\n70\n30\n0\n0\n50\n100\n50\n0\n",
"60\n70\n30\n0\n0\n44\n10\n50\n0\n",
"55\n70\n30\n0\n100\n50\n10\n50\n100\n",
"55\n70\n0\n0\n0\n50\n10\n100\n100\n",
"60\n70\n30\n0\n100\n50\n100\n50\n0\n",
"55\n70\n30\n0\n100\n50\n0\n50\n100\n",
"55\n70\n0\n0\n0\n50\n10\n100\n128\n",
"203\n70\n30\n0\n0\n50\n10\n50\n0\n",
"65\n26\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n44\n10\n50\n100\n",
"60\n70\n30\n0\n0\n0\n20\n50\n0\n",
"60\n70\n30\n0\n100\n50\n90\n50\n0\n",
"60\n70\n0\n0\n0\n34\n20\n50\n0\n",
"60\n70\n157\n0\n0\n100\n10\n50\n0\n",
"55\n60\n30\n0\n0\n44\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n20\n50\n0\n",
"55\n26\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n10\n50\n0\n",
"60\n70\n30\n0\n0\n50\n90\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n50\n10\n50\n0\n",
"55\n70\n0\n0\n0\n50\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n50\n0\n",
"55\n70\n30\n0\n0\n0\n10\n50\n0\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have a computer literacy course in your university. In the computer system, the login/logout records of all PCs in a day are stored in a file. Although students may use two or more PCs at a time, no one can log in to a PC which has been logged in by someone who has not logged out of that PC yet.
You are asked to write a program that calculates the total time of a student that he/she used at least one PC in a given time period (probably in a laboratory class) based on the records in the file.
The following are example login/logout records.
* The student 1 logged in to the PC 1 at 12:55
* The student 2 logged in to the PC 4 at 13:00
* The student 1 logged in to the PC 2 at 13:10
* The student 1 logged out of the PC 2 at 13:20
* The student 1 logged in to the PC 3 at 13:30
* The student 1 logged out of the PC 1 at 13:40
* The student 1 logged out of the PC 3 at 13:45
* The student 1 logged in to the PC 1 at 14:20
* The student 2 logged out of the PC 4 at 14:30
* The student 1 logged out of the PC 1 at 14:40
For a query such as "Give usage of the student 1 between 13:00 and 14:30", your program should answer "55 minutes", that is, the sum of 45 minutes from 13:00 to 13:45 and 10 minutes from 14:20 to 14:30, as depicted in the following figure.
<image>
Input
The input is a sequence of a number of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets never exceeds 10.
Each dataset is formatted as follows.
> N M
> r
> record1
> ...
> recordr
> q
> query1
> ...
> queryq
>
The numbers N and M in the first line are the numbers of PCs and the students, respectively. r is the number of records. q is the number of queries. These four are integers satisfying the following.
> 1 ≤ N ≤ 1000, 1 ≤ M ≤ 10000, 2 ≤ r ≤ 1000, 1 ≤ q ≤ 50
Each record consists of four integers, delimited by a space, as follows.
> t n m s
s is 0 or 1. If s is 1, this line means that the student m logged in to the PC n at time t . If s is 0, it means that the student m logged out of the PC n at time t . The time is expressed as elapsed minutes from 0:00 of the day. t , n and m satisfy the following.
> 540 ≤ t ≤ 1260, 1 ≤ n ≤ N , 1 ≤ m ≤ M
You may assume the following about the records.
* Records are stored in ascending order of time t.
* No two records for the same PC has the same time t.
* No PCs are being logged in before the time of the first record nor after that of the last record in the file.
* Login and logout records for one PC appear alternatingly, and each of the login-logout record pairs is for the same student.
Each query consists of three integers delimited by a space, as follows.
> ts te m
It represents "Usage of the student m between ts and te ". ts , te and m satisfy the following.
> 540 ≤ ts < te ≤ 1260, 1 ≤ m ≤ M
Output
For each query, print a line having a decimal integer indicating the time of usage in minutes. Output lines should not have any character other than this number.
Example
Input
4 2
10
775 1 1 1
780 4 2 1
790 2 1 1
800 2 1 0
810 3 1 1
820 1 1 0
825 3 1 0
860 1 1 1
870 4 2 0
880 1 1 0
1
780 870 1
13 15
12
540 12 13 1
600 12 13 0
650 13 15 1
660 12 15 1
665 11 13 1
670 13 15 0
675 11 13 0
680 12 15 0
1000 11 14 1
1060 12 14 1
1060 11 14 0
1080 12 14 0
3
540 700 13
600 1000 15
1000 1200 11
1 1
2
600 1 1 1
700 1 1 0
5
540 600 1
550 650 1
610 620 1
650 750 1
700 800 1
0 0
Output
55
70
30
0
0
50
10
50
0
### Input:
4 2
10
775 1 1 1
780 4 2 1
790 2 1 1
800 2 1 0
810 3 1 1
820 1 1 0
825 3 1 0
860 1 1 1
870 4 2 0
880 1 1 0
1
780 870 1
13 15
12
540 12 13 1
600 12 13 0
650 13 15 1
660 12 15 1
665 11 13 1
670 13 15 0
675 11 13 0
680 12 15 0
1000 11 14 1
1060 12 14 1
1060 11 14 0
1080 12 14 0
3
540 700 13
600 1000 15
1000 1200 11
1 1
2
600 1 1 1
700 1 1 0
5
540 600 1
550 650 1
610 620 1
650 750 1
700 800 1
0 0
### Output:
55
70
30
0
0
50
10
50
0
### Input:
4 2
10
775 1 1 1
780 4 2 1
790 2 1 1
800 2 1 0
810 3 1 1
820 1 1 0
825 3 1 0
860 1 1 1
870 4 2 0
880 1 1 0
1
780 870 1
13 15
12
540 12 13 1
600 12 13 0
650 13 15 1
660 12 15 1
665 11 13 1
670 13 15 0
675 11 13 0
680 12 15 0
1000 11 14 1
1060 12 14 1
1060 11 14 0
1080 12 14 0
3
540 700 13
600 1100 15
1000 1200 11
1 1
2
600 1 1 1
700 1 1 0
5
540 600 1
550 650 1
610 620 1
650 750 1
700 800 1
0 0
### Output:
55
70
30
0
0
50
10
50
0
### Code:
def main(N, M):
member = [[0] * 721 for i in range(M)]
r = int(input())
for _ in range(r):
t, _, m, s = map(int, input().split())
t -= 540
if s == 0:
member[m - 1][t] -= 1
else:
member[m - 1][t] += 1
for i in range(M):
for t in range(1,721):
member[i][t] += member[i][t - 1]
q = int(input())
for i in range(q):
ts, te, m = map(int, input().split())
ts -= 540
te -= 540
ans = 0
#print(member[m-1][ts:te])
for t in range(ts, te):
ans += (member[m-1][t] > 0)
print(ans)
while 1:
n, m = map(int, input().split())
if n == m == 0:
break
main(n,m)
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.