info
large_stringlengths 120
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| question
large_stringlengths 504
10.4k
| avg@8_qwen3_4b_instruct_2507
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|
Carving the cake 2 (Cake 2)
JOI-kun and IOI-chan are twin brothers and sisters. JOI has been enthusiastic about making sweets lately, and JOI tried to bake a cake and eat it today, but when it was baked, IOI who smelled it came, so we decided to divide the cake. became.
The cake is round. We made radial cuts from a point, cut the cake into N pieces, and numbered the pieces counterclockwise from 1 to N. That is, for 1 ≤ i ≤ N, the i-th piece is adjacent to the i − 1st and i + 1st pieces (though the 0th is considered to be the Nth and the N + 1st is considered to be the 1st). The size of the i-th piece was Ai, but I was so bad at cutting that all Ai had different values.
<image>
Figure 1: Cake example (N = 5, A1 = 2, A2 = 8, A3 = 1, A4 = 10, A5 = 9)
I decided to divide these N pieces by JOI-kun and IOI-chan. I decided to divide it as follows:
1. First, JOI chooses and takes one of N.
2. After that, starting with IOI-chan, IOI-chan and JOI-kun alternately take the remaining pieces one by one. However, if you can only take a piece that has already been taken at least one of the pieces on both sides, and there are multiple pieces that can be taken, IOI will choose the largest one and JOI will take it. You can choose what you like.
JOI wants to maximize the total size of the pieces he will finally take.
Task
Given the number N of cake pieces and the size information of N pieces, create a program to find the maximum value of the total size of pieces that JOI can take.
input
Read the following input from standard input.
* The integer N is written on the first line, which means that the cake is cut into N pieces.
* The integer Ai is written on the i-th line (1 ≤ i ≤ N) of the following N lines, which indicates that the size of the i-th piece is Ai.
output
Output an integer representing the maximum value of the total size of pieces that JOI can take to the standard output on one line.
Limits
All input data satisfy the following conditions.
* 1 ≤ N ≤ 20000.
* 1 ≤ Ai ≤ 1 000 000 000.
* Ai are all different.
Input / output example
Input example 1
Five
2
8
1
Ten
9
Output example 1
18
JOI is best to take the pieces as follows.
1. JOI takes the second piece. The size of this piece is 8.
2. IOI takes the first piece. The size of this piece is 2.
3. JOI takes the 5th piece. The size of this piece is 9.
4. IOI takes the 4th piece. The size of this piece is 10.
5. JOI takes the third piece. The size of this piece is 1.
Finally, the total size of the pieces taken by JOI is 8 + 9 + 1 = 18.
Input example 2
8
1
Ten
Four
Five
6
2
9
3
Output example 2
26
Input example 3
15
182243672
10074562
977552215
122668426
685444213
3784162
463324752
560071245
134465220
21447865
654556327
183481051
20041805
405079805
564327789
Output example 3
3600242976
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
5
2
8
1
10
9
Output
18
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
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\"1111222222222222111111111111111111111111222222211222222211111222222211222222222222222222111111111111\\n\", \"1111111221221111111112222222222222222222222222111111122222222212221111111111111111222222211111111122\\n\", \"1111112222222222211111111111222222222222222222111111111111111111111111112222222222222211111111111222\\n\", \"1111122222222222222222222211111111222222221111111111111111111112222222222222222211111111111111111111\\n\", \"1111111111111111111111111111111122222222222222222222222222222222222222222111111111111111111111111111\\n\", \"1111111111111111111111111111111111111111111122222222222222222222222222222222222222222222222222211111\\n\", \"2222222222222222222222222222211111111111111111111111111111111111111111111111111111111111111111111111\\n\", \"2222222222222222222222222221111111111111111111111111222222222222222111111111111111111111111111111112\\n\", \"1121111111111111112222222222222211112222222222222221111111111112222222222222221111111111111111111111\\n\", \"2222222222222222222222222222222222222222222111111111111111111111111111111111111111111111111111111111\\n\", \"1111111112222222222111111111112211111111111111122222222222221111111111111122222222222221111122222222\\n\", \"1111111222222222222222222222222222222111112222221111111111111111111111111111111111111112222222222222\\n\", \"1\\n\", \"1111111112222222222111111111112211111111111111122222222222221111111111111122222222222221111122222222\\n\", \"1\\n\", \"1221112111122222112222221111111111111221112222222221111122211222122211111122211112222222222111222111\\n\", \"1111122222222222222222222211111111222222221111111111111111111112222222222222222211111111111111111111\\n\", \"2222222222222222222222222222211111111111111111111111111111111111111111111111111111111111111111111111\\n\", \"1111111221221111111112222222222222222222222222111111122222222212221111111111111111222222211111111122\\n\", \"1111112222222222211111111111222222222222222222111111111111111111111111112222222222222211111111111222\\n\", \"2222222222222222222222222221111111111111111111111111222222222222222111111111111111111111111111111112\\n\", \"1111111111111111111111111111111111111111111122222222222222222222222222222222222222222222222222211111\\n\", \"1111111222222222222222222222222222222111112222221111111111111111111111111111111111111112222222222222\\n\", \"1111111111111111111111111111111122222222222222222222222222222222222222222111111111111111111111111111\\n\", \"1121111111111111112222222222222211112222222222222221111111111112222222222222221111111111111111111111\\n\", \"2222222222222222222222222222222222222222222111111111111111111111111111111111111111111111111111111111\\n\", \"1111222222222222111111111111111111111111222222211222222211111222222211222222222222222222111111111111\\n\", \"2222111112222211111112222211222221211111112221111222221112222211111111221222211111222222122222111111\\n\", \"1\\n\", \"1211122\\n\", \"11111\\n\", \"22111\\n\", \"21111\\n\", \"1111111111111111111111111111111111111111111111122222222222222222222222222222222222222222222211111111\\n\", \"1111111222222222222222222221111111111111122222222222222222211112221222211111111111111111111111111122\\n\", \"2222222221112222221122211111221112211121112111111112221222222222211111111111112221111122211121112222\\n\", \"21112\\n\", \"1111222\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"11111\\n\", \"1\\n\", \"1\\n\", \"21112\\n\", \"1121122\\n\", \"22111\\n\", \"11111\\n\"]}", "source": "taco"}
|
There are $n$ students standing in a row. Two coaches are forming two teams — the first coach chooses the first team and the second coach chooses the second team.
The $i$-th student has integer programming skill $a_i$. All programming skills are distinct and between $1$ and $n$, inclusive.
Firstly, the first coach will choose the student with maximum programming skill among all students not taken into any team, and $k$ closest students to the left of him and $k$ closest students to the right of him (if there are less than $k$ students to the left or to the right, all of them will be chosen). All students that are chosen leave the row and join the first team. Secondly, the second coach will make the same move (but all students chosen by him join the second team). Then again the first coach will make such move, and so on. This repeats until the row becomes empty (i. e. the process ends when each student becomes to some team).
Your problem is to determine which students will be taken into the first team and which students will be taken into the second team.
-----Input-----
The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \cdot 10^5$) — the number of students and the value determining the range of chosen students during each move, respectively.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$), where $a_i$ is the programming skill of the $i$-th student. It is guaranteed that all programming skills are distinct.
-----Output-----
Print a string of $n$ characters; $i$-th character should be 1 if $i$-th student joins the first team, or 2 otherwise.
-----Examples-----
Input
5 2
2 4 5 3 1
Output
11111
Input
5 1
2 1 3 5 4
Output
22111
Input
7 1
7 2 1 3 5 4 6
Output
1121122
Input
5 1
2 4 5 3 1
Output
21112
-----Note-----
In the first example the first coach chooses the student on a position $3$, and the row becomes empty (all students join the first team).
In the second example the first coach chooses the student on position $4$, and the row becomes $[2, 1]$ (students with programming skills $[3, 4, 5]$ join the first team). Then the second coach chooses the student on position $1$, and the row becomes empty (and students with programming skills $[1, 2]$ join the second team).
In the third example the first coach chooses the student on position $1$, and the row becomes $[1, 3, 5, 4, 6]$ (students with programming skills $[2, 7]$ join the first team). Then the second coach chooses the student on position $5$, and the row becomes $[1, 3, 5]$ (students with programming skills $[4, 6]$ join the second team). Then the first coach chooses the student on position $3$, and the row becomes $[1]$ (students with programming skills $[3, 5]$ join the first team). And then the second coach chooses the remaining student (and the student with programming skill $1$ joins the second team).
In the fourth example the first coach chooses the student on position $3$, and the row becomes $[2, 1]$ (students with programming skills $[3, 4, 5]$ join the first team). Then the second coach chooses the student on position $1$, and the row becomes empty (and students with programming skills $[1, 2]$ join the second team).
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [[[2, -4, 6, -6]], [[7, -3, -10]], [[7, -8, 1, -2]], [[8, 10, -6, -7, 9]], [[-3, 4, -10, 2, -6]], [[2, -6, -4, 1, -8, -2]], [[16, 25, -48, -47, -37, 41, -2]], [[-30, -11, 36, 38, 34, -5, -50]], [[-31, -5, 11, -42, -22, -46, -4, -28]], [[46, 39, -45, -2, -5, -6, -17, -32, 17]], [[-9, -8, -6, -46, 1, -19, 44]], [[-37, -10, -42, 19, -31, -40, -45, 33]], [[-25, -48, -29, -25, 1, 49, -32, -19, -46, 1]], [[-7, -35, -46, -22, 46, 43, -44, -14, 34, -5, -26]], [[-46, -50, -28, -45, -27, -40, 10, 35, 34, 47, -46, -24]], [[-33, -14, 16, 31, 4, 41, -10, -3, -21, -12, -45, 41, -19]], [[-17, 7, -12, 10, 4, -8, -19, -24, 40, 31, -29, 21, -45, 1]], [[-16, 44, -7, -31, 9, -43, -44, -18, 50, 39, -46, -24, 3, -34, -27]]], \"outputs\": [[[-6, -4, 6, 2]], [[-10, -3, 7]], [[-2, -8, 1, 7]], [[-7, -6, 10, 8, 9]], [[-3, -6, -10, 2, 4]], [[-2, -6, -4, -8, 1, 2]], [[-2, -37, -48, -47, 25, 41, 16]], [[-30, -11, -50, -5, 34, 38, 36]], [[-31, -5, -28, -42, -22, -46, -4, 11]], [[-32, -17, -45, -2, -5, -6, 39, 46, 17]], [[-9, -8, -6, -46, -19, 1, 44]], [[-37, -10, -42, -45, -31, -40, 19, 33]], [[-25, -48, -29, -25, -46, -19, -32, 49, 1, 1]], [[-7, -35, -46, -22, -26, -5, -44, -14, 34, 43, 46]], [[-46, -50, -28, -45, -27, -40, -24, -46, 34, 47, 35, 10]], [[-33, -14, -19, -45, -12, -21, -10, -3, 41, 4, 31, 41, 16]], [[-17, -45, -12, -29, -24, -8, -19, 4, 40, 31, 10, 21, 7, 1]], [[-16, -27, -7, -31, -34, -43, -44, -18, -24, -46, 39, 50, 3, 9, 44]]]}", "source": "taco"}
|
# Scenario
With **_Cereal crops_** like wheat or rice, before we can eat the grain kernel, we need to remove that inedible hull, or *to separate the wheat from the chaff*.
___
# Task
**_Given_** a *sequence of n integers* , **_separate_** *the negative numbers (chaff) from positive ones (wheat).*
___
# Notes
* **_Sequence size_** is _at least_ **_3_**
* **_Return_** *a new sequence*, such that **_negative numbers (chaff) come first, then positive ones (wheat)_**.
* In Java , *you're not allowed to modify the input Array/list/Vector*
* **_Have no fear_** , *it is guaranteed that there will be no zeroes* .
* **_Repetition_** of numbers in *the input sequence could occur* , so **_duplications are included when separating_**.
* If a misplaced *positive* number is found in the front part of the sequence, replace it with the last misplaced negative number (the one found near the end of the input). The second misplaced positive number should be swapped with the second last misplaced negative number. *Negative numbers found at the head (begining) of the sequence* , **_should be kept in place_** .
____
# Input >> Output Examples:
```
wheatFromChaff ({7, -8, 1 ,-2}) ==> return ({-2, -8, 1, 7})
```
## **_Explanation_**:
* **_Since_** `7 ` is a **_positive number_** , it should not be located at the beginnig so it needs to be swapped with the **last negative number** `-2`.
____
```
wheatFromChaff ({-31, -5, 11 , -42, -22, -46, -4, -28 }) ==> return ({-31, -5,- 28, -42, -22, -46 , -4, 11})
```
## **_Explanation_**:
* **_Since_**, `{-31, -5} ` are **_negative numbers_** *found at the head (begining) of the sequence* , *so we keep them in place* .
* Since `11` is a positive number, it's replaced by the last negative which is `-28` , and so on till sepration is complete.
____
```
wheatFromChaff ({-25, -48, -29, -25, 1, 49, -32, -19, -46, 1}) ==> return ({-25, -48, -29, -25, -46, -19, -32, 49, 1, 1})
```
## **_Explanation_**:
* **_Since_** `{-25, -48, -29, -25} ` are **_negative numbers_** *found at the head (begining) of the input* , *so we keep them in place* .
* Since `1` is a positive number, it's replaced by the last negative which is `-46` , and so on till sepration is complete.
* Remeber, *duplications are included when separating* , that's why the number `1` appeared twice at the end of the output.
____
# Tune Your Code , There are 250 Assertions , 100.000 element For Each .
# Only O(N) Complexity Solutions Will pass .
____
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"15 7 2\", \"1000 101 10\", \"1100 101 10\", \"1100 111 10\", \"7 2 3\", \"20 7 2\", \"15 3 2\", \"1000 101 3\", \"1100 100 10\", \"1100 101 19\", \"7 1 3\", \"20 13 2\", \"17 3 2\", \"1000 111 3\", \"11 2 3\", \"20 8 2\", \"3 3 2\", \"1000 100 3\", \"11 2 4\", \"20 10 2\", \"3 2 2\", \"1000 001 3\", \"11 2 8\", \"20 10 4\", \"1001 001 3\", \"20 10 5\", \"20 10 3\", \"12 10 3\", \"1011 001 1\", \"12 10 5\", \"19 10 5\", \"0011 000 -2\", \"0001 000 -2\", \"9 7 2\", \"1000 100 17\", \"1000 101 6\", \"1100 001 10\", \"1110 111 10\", \"6 2 3\", \"1001 101 3\", \"1100 111 19\", \"20 9 2\", \"17 3 1\", \"5 2 3\", \"1100 100 3\", \"11 3 4\", \"11 10 2\", \"20 12 4\", \"20 10 1\", \"1101 001 0\", \"12 12 5\", \"24 10 5\", \"1111 000 -2\", \"9 7 3\", \"1010 100 17\", \"1110 111 17\", \"8 2 3\", \"1001 101 6\", \"1100 101 3\", \"8 3 3\", \"3 3 1\", \"0100 100 3\", \"11 4 4\", \"17 10 2\", \"20 20 4\", \"20 14 2\", \"1011 011 2\", \"12 12 3\", \"24 10 9\", \"9 7 4\", \"1010 100 26\", \"1110 101 17\", \"8 2 6\", \"1001 101 8\", \"1000 101 4\", \"13 9 1\", \"0100 100 1\", \"11 8 4\", \"17 10 3\", \"20 7 4\", \"20 14 3\", \"0101 001 1\", \"9 7 8\", \"1010 100 30\", \"1110 100 17\", \"1011 101 8\", \"25 6 1\", \"20 11 4\", \"1010 010 -1\", \"1010 100 34\", \"0110 100 17\", \"1011 111 8\", \"20 11 8\", \"1001 111 8\", \"20 10 8\", \"1001 110 8\", \"0111 011 1\", \"1001 100 8\", \"29 4 1\", \"1000 100 8\", \"4 2 3\", \"10 7 2\", \"1000 100 10\"], \"outputs\": [\"24455\\n\", \"631009281\\n\", \"915151017\\n\", \"890861662\\n\", \"116\\n\", \"907559\\n\", \"32654\\n\", \"836380050\\n\", \"725819821\\n\", \"724720670\\n\", \"128\\n\", \"340928\\n\", \"130872\\n\", \"899630784\\n\", \"2011\\n\", \"812747\\n\", \"4\\n\", \"820261949\\n\", \"1919\\n\", \"606464\\n\", \"6\\n\", \"688423210\\n\", \"936\\n\", \"170352\\n\", \"376846413\\n\", \"112292\\n\", \"304128\\n\", \"536\\n\", \"890724217\\n\", \"161\\n\", \"51841\\n\", \"2048\\n\", \"2\\n\", \"242\\n\", \"719982564\\n\", \"925324135\\n\", \"466428307\\n\", \"440874478\\n\", \"55\\n\", \"480850280\\n\", \"422786764\\n\", \"710226\\n\", \"131072\\n\", \"25\\n\", \"376516295\\n\", \"1479\\n\", \"579\\n\", \"83636\\n\", \"1048576\\n\", \"932856614\\n\", \"42\\n\", \"2332343\\n\", \"245166051\\n\", \"129\\n\", \"41243606\\n\", \"573140266\\n\", \"240\\n\", \"165771780\\n\", \"682542784\\n\", \"188\\n\", \"8\\n\", \"735099638\\n\", \"1040\\n\", \"63088\\n\", \"2452\\n\", \"279040\\n\", \"293995815\\n\", \"189\\n\", \"408568\\n\", \"77\\n\", \"359754313\\n\", \"390561366\\n\", \"138\\n\", \"842042920\\n\", \"214481108\\n\", \"8192\\n\", \"976371285\\n\", \"289\\n\", \"30276\\n\", \"457351\\n\", \"95292\\n\", \"952742563\\n\", \"11\\n\", \"42040707\\n\", \"633696988\\n\", \"936811969\\n\", \"33554432\\n\", \"118832\\n\", \"945362112\\n\", \"584121269\\n\", \"8575690\\n\", \"246047570\\n\", \"24055\\n\", \"471589712\\n\", \"32711\\n\", \"860015187\\n\", \"608377687\\n\", \"609585887\\n\", \"536870912\\n\", \"656321566\\n\", \"11\", \"533\", \"828178524\"]}", "source": "taco"}
|
Snuke has a string x of length N. Initially, every character in x is `0`.
Snuke can do the following two operations any number of times in any order:
* Choose A consecutive characters in x and replace each of them with `0`.
* Choose B consecutive characters in x and replace each of them with `1`.
Find the number of different strings that x can be after Snuke finishes doing operations. This count can be enormous, so compute it modulo (10^9+7).
Constraints
* 1 \leq N \leq 5000
* 1 \leq A,B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the number of different strings that x can be after Snuke finishes doing operations, modulo (10^9+7).
Examples
Input
4 2 3
Output
11
Input
10 7 2
Output
533
Input
1000 100 10
Output
828178524
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n0 0\\n0 0\\n9\\n3\\n1 2\\n2 2\\n1 1\\n2 1\\n3\\n1 2\\n1 1\\n3\\n\", \"1\\n0\\n5\\n1 1\\n3\\n1 1\\n1 1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 5\\n3\\n\", \"2\\n0 0\\n0 0\\n2\\n1 1\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n0 0 0 0\\n0 0 0 0\\n2\\n1 1\\n3\\n\", \"3\\n1 0 1\\n0 1 1\\n1 0 1\\n4\\n3\\n3\\n3\\n3\\n\", \"2\\n1 0\\n1 1\\n6\\n1 2\\n3\\n2 1\\n3\\n1 1\\n3\\n\", \"2\\n1 0\\n0 1\\n1\\n3\\n\", \"2\\n1 1\\n1 0\\n5\\n3\\n1 1\\n3\\n2 1\\n3\\n\", \"2\\n1 0\\n1 0\\n4\\n1 2\\n3\\n1 2\\n3\\n\", \"1\\n1\\n9\\n1 1\\n3\\n1 1\\n1 1\\n3\\n1 1\\n3\\n1 1\\n3\\n\", \"2\\n0 1\\n1 0\\n7\\n3\\n3\\n2 2\\n3\\n2 2\\n2 1\\n3\\n\", \"3\\n0 0 0\\n0 0 1\\n0 1 1\\n3\\n1 2\\n1 3\\n1 1\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"2\\n0 0\\n0 0\\n2\\n1 2\\n3\\n\", \"3\\n1 0 1\\n0 1 1\\n1 0 0\\n4\\n3\\n3\\n3\\n3\\n\", \"2\\n1 1\\n1 0\\n5\\n3\\n2 1\\n3\\n2 1\\n3\\n\", \"2\\n0 1\\n0 0\\n7\\n3\\n3\\n2 2\\n3\\n2 2\\n2 1\\n3\\n\", \"3\\n0 1 1\\n0 1 1\\n1 0 0\\n12\\n3\\n2 3\\n3\\n2 2\\n2 2\\n1 3\\n3\\n3\\n1 2\\n2 1\\n1 1\\n3\\n\", \"2\\n0 1\\n1 0\\n5\\n3\\n2 1\\n3\\n2 1\\n3\\n\", \"2\\n1 1\\n0 0\\n2\\n1 2\\n3\\n\", \"1\\n1\\n9\\n1 1\\n3\\n1 1\\n1 1\\n3\\n2 1\\n3\\n1 1\\n3\\n\", \"2\\n0 0\\n1 0\\n4\\n1 2\\n3\\n1 2\\n3\\n\", \"3\\n1 1 1\\n0 1 1\\n1 0 0\\n12\\n3\\n2 3\\n3\\n2 2\\n2 2\\n2 3\\n3\\n3\\n1 2\\n2 1\\n1 1\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 0\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"2\\n0 1\\n0 0\\n2\\n1 2\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 0\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 5\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n0 1 0 0\\n0 0 0 0\\n2\\n1 1\\n3\\n\", \"2\\n1 0\\n1 1\\n6\\n1 2\\n3\\n2 1\\n3\\n1 2\\n3\\n\", \"2\\n1 0\\n0 0\\n1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"3\\n1 0 1\\n1 1 1\\n1 0 0\\n4\\n3\\n3\\n3\\n3\\n\", \"2\\n1 1\\n1 0\\n5\\n3\\n2 1\\n3\\n2 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"2\\n1 0\\n1 1\\n6\\n1 1\\n3\\n2 1\\n3\\n1 2\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n1 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"2\\n0 0\\n1 0\\n2\\n1 1\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n0 0 0 0\\n0 0 0 0\\n2\\n1 2\\n3\\n\", \"2\\n0 0\\n0 0\\n2\\n2 2\\n3\\n\", \"2\\n0 1\\n0 0\\n2\\n2 2\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n0 1 0 0\\n0 0 0 0\\n2\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"2\\n1 0\\n1 1\\n6\\n1 1\\n3\\n2 2\\n3\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 1 1 0 1\\n0 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"2\\n1 0\\n0 0\\n2\\n1 1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 0\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"3\\n1 1 1\\n0 1 1\\n1 0 0\\n4\\n3\\n3\\n3\\n3\\n\", \"2\\n0 0\\n0 0\\n7\\n3\\n3\\n2 2\\n3\\n2 2\\n2 1\\n3\\n\", \"2\\n0 1\\n1 0\\n5\\n3\\n2 2\\n3\\n2 1\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n1 1 0 0\\n0 0 0 0\\n2\\n1 1\\n3\\n\", \"2\\n1 0\\n1 0\\n6\\n1 2\\n3\\n2 1\\n3\\n1 2\\n3\\n\", \"2\\n0 0\\n0 1\\n1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n0 0 1 0 1\\n1 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 0 0 1 0\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 1\\n0 1 0 0\\n0 0 0 0\\n2\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 0 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 2\\n3\\n\", \"5\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 1 0\\n0 1 0 1 0\\n1 0 1 0 0\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"5\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 0\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n2 3\\n3\\n2 5\\n1 2\\n3\\n\", \"5\\n1 0 1 0 1\\n0 0 0 1 0\\n1 0 1 1 1\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n1 3\\n3\\n2 5\\n1 1\\n3\\n\", \"5\\n1 1 1 0 1\\n0 1 0 1 0\\n1 0 1 0 0\\n0 1 0 1 0\\n1 0 1 0 1\\n7\\n3\\n2 4\\n2 3\\n3\\n2 5\\n1 2\\n3\\n\", \"5\\n1 1 1 0 1\\n0 1 0 1 0\\n1 0 1 0 0\\n0 1 0 1 0\\n0 0 1 0 1\\n7\\n3\\n2 4\\n2 3\\n3\\n2 5\\n1 2\\n3\\n\", \"2\\n0 0\\n0 0\\n9\\n3\\n1 2\\n2 2\\n1 1\\n2 1\\n3\\n1 2\\n1 2\\n3\\n\", \"2\\n0 1\\n0 0\\n2\\n1 1\\n3\\n\", \"4\\n1 1 0 0\\n1 1 0 0\\n0 0 0 0\\n0 0 1 0\\n2\\n1 1\\n3\\n\", \"3\\n1 1 1\\n0 1 1\\n1 0 0\\n12\\n3\\n2 3\\n3\\n2 2\\n2 2\\n1 3\\n3\\n3\\n1 2\\n2 1\\n1 1\\n3\\n\"], \"outputs\": [\"000\", \"11\", \"111\", \"1\", \"1\", \"1111\", \"101\", \"0\", \"101\", \"01\", \"0010\", \"0011\", \"\\n\", \"111\\n\", \"1\\n\", \"0000\\n\", \"101\\n\", \"0011\\n\", \"10110\\n\", \"010\\n\", \"0\\n\", \"0010\\n\", \"10\\n\", \"01001\\n\", \"000\\n\", \"111\\n\", \"1\\n\", \"111\\n\", \"1\\n\", \"101\\n\", \"1\\n\", \"111\\n\", \"0000\\n\", \"101\\n\", \"111\\n\", \"101\\n\", \"111\\n\", \"111\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"111\\n\", \"101\\n\", \"111\\n\", \"0\\n\", \"111\\n\", \"0000\\n\", \"0011\\n\", \"010\\n\", \"1\\n\", \"010\\n\", \"1\\n\", \"111\\n\", \"000\\n\", \"1\\n\", \"111\\n\", \"000\\n\", \"111\\n\", \"000\\n\", \"111\\n\", \"111\\n\", \"000\\n\", \"1\\n\", \"1\\n\", \"01001\"]}", "source": "taco"}
|
Little Chris is a huge fan of linear algebra. This time he has been given a homework about the unusual square of a square matrix.
The dot product of two integer number vectors x and y of size n is the sum of the products of the corresponding components of the vectors. The unusual square of an n × n square matrix A is defined as the sum of n dot products. The i-th of them is the dot product of the i-th row vector and the i-th column vector in the matrix A.
Fortunately for Chris, he has to work only in GF(2)! This means that all operations (addition, multiplication) are calculated modulo 2. In fact, the matrix A is binary: each element of A is either 0 or 1. For example, consider the following matrix A:
<image>
The unusual square of A is equal to (1·1 + 1·0 + 1·1) + (0·1 + 1·1 + 1·0) + (1·1 + 0·1 + 0·0) = 0 + 1 + 1 = 0.
However, there is much more to the homework. Chris has to process q queries; each query can be one of the following:
1. given a row index i, flip all the values in the i-th row in A;
2. given a column index i, flip all the values in the i-th column in A;
3. find the unusual square of A.
To flip a bit value w means to change it to 1 - w, i.e., 1 changes to 0 and 0 changes to 1.
Given the initial matrix A, output the answers for each query of the third type! Can you solve Chris's homework?
Input
The first line of input contains an integer n (1 ≤ n ≤ 1000), the number of rows and the number of columns in the matrix A. The next n lines describe the matrix: the i-th line contains n space-separated bits and describes the i-th row of A. The j-th number of the i-th line aij (0 ≤ aij ≤ 1) is the element on the intersection of the i-th row and the j-th column of A.
The next line of input contains an integer q (1 ≤ q ≤ 106), the number of queries. Each of the next q lines describes a single query, which can be one of the following:
* 1 i — flip the values of the i-th row;
* 2 i — flip the values of the i-th column;
* 3 — output the unusual square of A.
Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.
Output
Let the number of the 3rd type queries in the input be m. Output a single string s of length m, where the i-th symbol of s is the value of the unusual square of A for the i-th query of the 3rd type as it appears in the input.
Examples
Input
3
1 1 1
0 1 1
1 0 0
12
3
2 3
3
2 2
2 2
1 3
3
3
1 2
2 1
1 1
3
Output
01001
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 5 5 7 6 13\\n517 1024 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1334 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 11315 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 1228 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 14921 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 821 746 11315 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 6561 6799 3125\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n844 821 1163 11315 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 6561 10568 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 17\\n844 821 1163 11315 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 9 23\\n517 1024 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 9 23\\n517 270 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 9 23\\n517 270 746 11867 4303 4650\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n695 1024 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 11315 4303 3944\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 6561 4303 5851\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 139 746 11315 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n844 821 746 11315 4303 848\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 746 14367 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 11 6 13\\n913 1334 764 6561 10568 3125\\n0 0 0 0 0 0\", \"2 7 6 7 9 23\\n517 270 746 11867 4303 4650\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 11315 4303 3100\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 139 746 11315 4303 3015\\n0 0 0 0 0 0\", \"2 5 2 11 6 13\\n913 1334 236 6561 10568 3125\\n0 0 0 0 0 0\", \"2 5 2 13 6 13\\n913 1334 236 6561 10568 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 2411 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1502 1228 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n141 1334 746 6561 4303 4028\\n0 0 0 0 0 0\", \"2 7 5 7 10 13\\n141 1334 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1389 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 2535 764 6561 5397 3125\\n0 0 0 0 0 0\", \"2 5 5 2 6 17\\n844 821 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 6561 906 5851\\n0 0 0 0 0 0\", \"2 7 5 7 5 13\\n141 1334 746 6561 3184 3125\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 3 746 14367 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 5 17\\n844 1409 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 173 746 11315 4303 3100\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 139 686 11315 4303 3015\\n0 0 0 0 0 0\", \"3 5 5 7 6 17\\n844 739 1163 11315 4303 2097\\n0 0 0 0 0 0\", \"2 5 2 13 6 13\\n913 1334 236 6681 10568 3125\\n0 0 0 0 0 0\", \"2 5 5 2 6 17\\n844 821 1163 14467 5996 3125\\n0 0 0 0 0 0\", \"2 5 5 8 6 13\\n517 1951 746 11315 4303 3944\\n0 0 0 0 0 0\", \"2 9 5 7 11 13\\n913 1796 746 6561 2237 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n517 1024 746 6561 4303 6238\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 821 746 5007 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 746 11867 4303 5769\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n844 1527 1163 11315 4303 3125\\n0 0 0 0 0 0\", \"4 5 5 7 6 13\\n913 1334 764 7931 10568 3125\\n0 0 0 0 0 0\", \"2 5 6 7 1 23\\n517 1024 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 17\\n1504 821 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 5 7 1 13\\n517 348 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 11\\n517 1024 746 11315 4303 3944\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 746 14367 4303 6178\\n0 0 0 0 0 0\", \"2 5 5 7 5 17\\n844 1467 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 19\\n913 1334 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 2318 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 5 4\\n844 1409 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n913 1334 746 6561 4303 1361\\n0 0 0 0 0 0\", \"2 5 10 7 6 13\\n517 139 686 11315 4303 4959\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n517 1024 1102 6561 4303 6238\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n1415 1334 764 6561 4303 710\\n0 0 0 0 0 0\", \"4 5 5 7 6 13\\n913 1334 764 7931 10568 1739\\n0 0 0 0 0 0\", \"2 5 8 7 6 11\\n517 1024 746 11315 4303 3944\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 524 14367 4303 6178\\n0 0 0 0 0 0\", \"3 5 5 7 1 17\\n844 739 1163 11315 4303 3467\\n0 0 0 0 0 0\", \"4 5 6 7 6 13\\n517 3 746 8081 4303 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n913 1354 746 6561 4303 1361\\n0 0 0 0 0 0\", \"2 5 5 8 10 13\\n517 1951 746 11315 4303 7172\\n0 0 0 0 0 0\", \"2 5 8 7 6 11\\n517 1024 746 3241 4303 3944\\n0 0 0 0 0 0\", \"2 5 10 9 6 13\\n913 553 746 6561 506 3125\\n0 0 0 0 0 0\", \"2 9 6 7 6 13\\n517 1024 524 14367 4303 1932\\n0 0 0 0 0 0\", \"2 5 6 7 6 13\\n517 1024 746 14921 4303 4416\\n0 0 0 0 0 0\", \"2 3 6 7 9 23\\n517 1024 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 6 7 9 23\\n517 270 746 11867 4303 153\\n0 0 0 0 0 0\", \"2 5 6 7 9 23\\n517 56 746 11867 4303 4650\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n517 1024 746 11315 4303 2713\\n0 0 0 0 0 0\", \"4 5 5 7 6 7\\n913 1334 1228 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 3339 4303 5851\\n0 0 0 0 0 0\", \"2 7 6 7 9 23\\n517 521 746 11867 4303 4650\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1791 1228 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n141 1334 746 6561 4303 3987\\n0 0 0 0 0 0\", \"2 5 6 7 6 25\\n517 1389 746 11867 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 2535 764 6561 5397 6232\\n0 0 0 0 0 0\", \"2 5 5 7 6 13\\n913 1334 764 6561 906 7501\\n0 0 0 0 0 0\", \"2 7 5 7 5 4\\n141 1334 746 6561 3184 3125\\n0 0 0 0 0 0\", \"2 5 1 7 5 17\\n844 1409 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"3 5 5 7 6 17\\n844 739 1031 11315 4303 2097\\n0 0 0 0 0 0\", \"2 5 5 2 6 17\\n844 821 1163 28717 5996 3125\\n0 0 0 0 0 0\", \"2 5 2 5 6 13\\n913 1758 236 6681 10568 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n517 537 746 6561 4303 6238\\n0 0 0 0 0 0\", \"4 5 5 7 1 13\\n517 348 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 5 7 5 17\\n844 499 1163 11315 5996 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 19\\n913 1334 746 6561 4303 3958\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n913 1334 140 6561 4303 1361\\n0 0 0 0 0 0\", \"2 5 8 7 6 11\\n517 1024 6 11315 4303 3944\\n0 0 0 0 0 0\", \"1 5 3 7 8 13\\n829 1334 746 6561 4303 3125\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n913 1354 746 12979 4303 1361\\n0 0 0 0 0 0\", \"2 5 5 8 10 13\\n517 1951 746 11315 1865 7172\\n0 0 0 0 0 0\", \"2 9 6 7 6 13\\n517 1401 524 14367 4303 6178\\n0 0 0 0 0 0\", \"2 5 3 7 6 13\\n517 1024 746 6561 4303 3125\\n0 0 0 0 0 0\"], \"outputs\": [\"12\\n116640000\\n\", \"12\\n140332500\\n\", \"12\\n1440000\\n\", \"12\\n420997500\\n\", \"12\\n581280000\\n\", \"12\\n922500\\n\", \"12\\n28066500\\n\", \"12\\n949280000\\n\", \"12\\n1845000\\n\", \"12\\n5613300\\n\", \"48\\n1845000\\n\", \"44\\n949280000\\n\", \"44\\n133492500\\n\", \"44\\n1067940\\n\", \"12\\n58320000\\n\", \"12\\n80640\\n\", \"12\\n2918916\\n\", \"12\\n517500\\n\", \"12\\n47970\\n\", \"12\\n21280000\\n\", \"60\\n5613300\\n\", \"66\\n1067940\\n\", \"12\\n11520\\n\", \"12\\n45540\\n\", \"60\\n16839900\\n\", \"12\\n16839900\\n\", \"12\\n38560000\\n\", \"12\\n5467500\\n\", \"12\\n1459458\\n\", \"6\\n140332500\\n\", \"12\\n3426307500\\n\", \"12\\n23692500\\n\", \"16\\n1845000\\n\", \"12\\n14594580\\n\", \"12\\n70166250\\n\", \"12\\n332500\\n\", \"48\\n3960000\\n\", \"12\\n7740\\n\", \"12\\n91080\\n\", \"48\\n428040\\n\", \"12\\n200200\\n\", \"16\\n40590000\\n\", \"12\\n163800\\n\", \"12\\n204120000\\n\", \"12\\n290946816\\n\", \"12\\n42742500\\n\", \"12\\n7594240\\n\", \"12\\n5715000\\n\", \"12\\n392700\\n\", \"4\\n949280000\\n\", \"48\\n45000\\n\", \"12\\n12757500\\n\", \"60\\n80640\\n\", \"12\\n6571264\\n\", \"48\\n405000\\n\", \"36\\n140332500\\n\", \"12\\n133492500\\n\", \"12\\n3960000\\n\", \"12\\n76340880\\n\", \"12\\n57960\\n\", \"12\\n872840448\\n\", \"12\\n1122660\\n\", \"12\\n1806420\\n\", \"20\\n80640\\n\", \"12\\n19713792\\n\", \"12\\n25579080\\n\", \"12\\n1010000\\n\", \"12\\n167553360\\n\", \"12\\n17550\\n\", \"20\\n59136\\n\", \"12\\n11846250\\n\", \"12\\n1123584\\n\", \"12\\n10230528\\n\", \"22\\n949280000\\n\", \"44\\n427176\\n\", \"44\\n355980\\n\", \"12\\n1301760\\n\", \"6\\n420997500\\n\", \"12\\n36036\\n\", \"66\\n4627740\\n\", \"12\\n60142500\\n\", \"12\\n24810786\\n\", \"20\\n3426307500\\n\", \"12\\n379080\\n\", \"12\\n898128\\n\", \"6\\n70166250\\n\", \"16\\n3960000\\n\", \"48\\n214020\\n\", \"16\\n332407500\\n\", \"12\\n189800\\n\", \"12\\n202298958\\n\", \"6\\n12757500\\n\", \"48\\n3735000\\n\", \"36\\n222062148\\n\", \"12\\n229022640\\n\", \"20\\n16128\\n\", \"12\\n1822500\\n\", \"12\\n1491431760\\n\", \"12\\n52650\\n\", \"12\\n287082096\\n\", \"12\\n116640000\"]}", "source": "taco"}
|
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 1 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 2 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 3\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 1 84 23\\n2 3 58 42\\n2 2 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 27\\n4 5 17 43\\n5 10\\n1 1 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 2 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 0 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 2 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 0 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 1 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 3 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 32\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 16\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 0\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n3 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 0 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 1 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 121\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 1 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 27\\n4 5 17 43\\n5 10\\n1 2 1 77\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 98\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 24\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 143 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 2 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 54\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 3 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 5 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 3\\n3 4 1 13\\n3 2 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 5 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 145 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 2 1 78\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 0 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 88\\n1 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 44\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 3 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 121\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 98\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n1 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 21\\n1 1 84 23\\n2 3 58 45\\n2 5 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 27\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 0 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 0 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 36\\n2 3 2 7\\n2 4 1 46\\n2 5 1 25\\n3 4 1 22\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 143 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 2 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 2 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 0\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n4 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 2 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n2 4 12 52\\n1 1 84 23\\n2 3 58 42\\n2 2 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 27\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n2 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 65\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n2 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 12 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 42\\n1 4 12 1\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n2 4 12 121\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 5\\n1 3 43 43\\n1 4 12 21\\n1 1 84 23\\n2 3 58 45\\n2 5 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 27\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 0 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 153\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 0 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 2\\n5 10\\n2 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 54\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 2 65\\n4 5 1 18\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 3 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 2 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 105\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n2 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 65\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 2 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n2 4 12 121\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n2 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 0\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 1 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 98\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n1 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n2 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 3 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 2 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 105\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 2 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 2\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 4 19\\n3 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 42\\n1 4 12 1\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 32\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 2 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 4 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 2\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 4 19\\n3 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 42\\n1 4 12 1\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 32\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 4 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n2 4 12 121\\n1 5 84 23\\n4 3 58 42\\n2 4 86 99\\n2 5 57 83\\n2 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 14\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n2 4 12 121\\n1 5 84 23\\n4 3 58 42\\n2 4 86 99\\n2 5 57 83\\n2 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 85\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 14\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 15\\n1 3 43 43\\n2 4 12 121\\n1 5 84 23\\n4 3 58 42\\n2 4 86 99\\n2 5 57 83\\n2 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 85\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 14\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 4 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 15\\n1 3 43 43\\n2 4 3 121\\n1 5 84 23\\n4 3 58 42\\n2 4 86 99\\n2 5 57 83\\n2 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 85\\n1 5 1 65\\n4 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 14\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 0 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 3\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 1 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 49\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 16\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 1 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 0 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n4 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 3\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 33\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 16 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 82\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 52\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 2 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 40\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 3\\n3 4 1 13\\n3 2 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n3 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 0 24\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 84\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 4 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 1 1 36\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 61\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 44\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0\", \"3 3\\n1 2 1 8\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n2 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 0\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 1 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 142\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 0 88\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 2 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 42\\n1 5 84 23\\n2 2 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n1 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 0 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\", \"3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0\"], \"outputs\": [\"3\\n5\\n137\\n218\\n\", \"3\\n5\\n162\\n218\\n\", \"3\\n5\\n162\\n207\\n\", \"4\\n5\\n137\\n218\\n\", \"3\\n5\\n162\\n190\\n\", \"3\\n6\\n162\\n207\\n\", \"5\\n5\\n162\\n207\\n\", \"3\\n6\\n168\\n207\\n\", \"3\\n5\\n162\\n173\\n\", \"6\\n5\\n162\\n207\\n\", \"6\\n5\\n162\\n218\\n\", \"3\\n5\\n194\\n173\\n\", \"3\\n5\\n137\\n262\\n\", \"3\\n5\\n162\\n168\\n\", \"3\\n5\\n137\\n190\\n\", \"3\\n5\\n194\\n178\\n\", \"5\\n5\\n162\\n189\\n\", \"3\\n5\\n137\\n176\\n\", \"3\\n5\\n194\\n147\\n\", \"5\\n7\\n162\\n189\\n\", \"3\\n5\\n151\\n207\\n\", \"3\\n4\\n137\\n176\\n\", \"3\\n6\\n162\\n239\\n\", \"5\\n7\\n162\\n194\\n\", \"5\\n8\\n162\\n194\\n\", \"5\\n8\\n162\\n142\\n\", \"6\\n8\\n162\\n142\\n\", \"4\\n8\\n162\\n142\\n\", \"4\\n8\\n165\\n142\\n\", \"4\\n8\\n165\\n200\\n\", \"3\\n6\\n137\\n218\\n\", \"3\\n5\\n162\\n200\\n\", \"3\\n5\\n206\\n207\\n\", \"6\\n5\\n137\\n218\\n\", \"3\\n5\\n137\\n242\\n\", \"5\\n5\\n162\\n252\\n\", \"6\\n5\\n154\\n207\\n\", \"3\\n5\\n162\\n155\\n\", \"3\\n5\\n194\\n151\\n\", \"3\\n6\\n194\\n207\\n\", \"3\\n5\\n173\\n168\\n\", \"5\\n5\\n162\\n218\\n\", \"5\\n7\\n162\\n168\\n\", \"3\\n6\\n128\\n239\\n\", \"3\\n6\\n117\\n218\\n\", \"3\\n4\\n206\\n207\\n\", \"5\\n5\\n162\\n206\\n\", \"3\\n5\\n106\\n218\\n\", \"5\\n5\\n162\\n196\\n\", \"3\\n5\\n137\\n178\\n\", \"3\\n5\\n162\\n166\\n\", \"3\\n4\\n162\\n190\\n\", \"4\\n5\\n148\\n218\\n\", \"3\\n6\\n150\\n239\\n\", \"5\\n7\\n142\\n194\\n\", \"4\\n8\\n89\\n200\\n\", \"3\\n4\\n217\\n207\\n\", \"3\\n5\\n101\\n218\\n\", \"5\\n5\\n238\\n196\\n\", \"3\\n5\\n162\\n151\\n\", \"3\\n5\\n143\\n262\\n\", \"3\\n6\\n194\\n259\\n\", \"3\\n6\\n150\\n250\\n\", \"3\\n4\\n128\\n207\\n\", \"5\\n4\\n162\\n206\\n\", \"3\\n5\\n194\\n259\\n\", \"4\\n6\\n162\\n239\\n\", \"4\\n8\\n89\\n165\\n\", \"4\\n5\\n162\\n239\\n\", \"4\\n8\\n89\\n136\\n\", \"3\\n4\\n128\\n197\\n\", \"3\\n4\\n128\\n229\\n\", \"3\\n4\\n133\\n229\\n\", \"3\\n4\\n222\\n229\\n\", \"3\\n4\\n162\\n218\\n\", \"4\\n5\\n162\\n207\\n\", \"3\\n5\\n142\\n207\\n\", \"3\\n5\\n154\\n218\\n\", \"4\\n6\\n162\\n207\\n\", \"3\\n5\\n235\\n190\\n\", \"3\\n6\\n179\\n207\\n\", \"5\\n6\\n162\\n207\\n\", \"3\\n5\\n162\\n179\\n\", \"3\\n6\\n173\\n207\\n\", \"3\\n5\\n194\\n179\\n\", \"3\\n5\\n204\\n178\\n\", \"3\\n5\\n162\\n178\\n\", \"3\\n5\\n137\\n166\\n\", \"3\\n6\\n162\\n238\\n\", \"3\\n5\\n162\\n239\\n\", \"3\\n6\\n162\\n262\\n\", \"3\\n6\\n162\\n215\\n\", \"9\\n8\\n162\\n194\\n\", \"5\\n8\\n195\\n142\\n\", \"1\\n8\\n162\\n142\\n\", \"2\\n8\\n162\\n142\\n\", \"4\\n8\\n165\\n223\\n\", \"3\\n6\\n137\\n184\\n\", \"3\\n6\\n127\\n207\\n\", \"3\\n5\\n168\\n207\\n\", \"3\\n5\\n137\\n218\"]}", "source": "taco"}
|
King Mercer is the king of ACM kingdom. There are one capital and some cities in his kingdom. Amazingly, there are no roads in the kingdom now. Recently, he planned to construct roads between the capital and the cities, but it turned out that the construction cost of his plan is much higher than expected.
In order to reduce the cost, he has decided to create a new construction plan by removing some roads from the original plan. However, he believes that a new plan should satisfy the following conditions:
* For every pair of cities, there is a route (a set of roads) connecting them.
* The minimum distance between the capital and each city does not change from his original plan.
Many plans may meet the conditions above, but King Mercer wants to know the plan with minimum cost. Your task is to write a program which reads his original plan and calculates the cost of a new plan with the minimum cost.
Input
The input consists of several datasets. Each dataset is formatted as follows.
N M
u1 v1 d1 c1
.
.
.
uM vM dM cM
The first line of each dataset begins with two integers, N and M (1 ≤ N ≤ 10000, 0 ≤ M ≤ 20000). N and M indicate the number of cities and the number of roads in the original plan, respectively.
The following M lines describe the road information in the original plan. The i-th line contains four integers, ui, vi, di and ci (1 ≤ ui, vi ≤ N , ui ≠ vi , 1 ≤ di ≤ 1000, 1 ≤ ci ≤ 1000). ui , vi, di and ci indicate that there is a road which connects ui-th city and vi-th city, whose length is di and whose cost needed for construction is ci.
Each road is bidirectional. No two roads connect the same pair of cities. The 1-st city is the capital in the kingdom.
The end of the input is indicated by a line containing two zeros separated by a space. You should not process the line as a dataset.
Output
For each dataset, print the minimum cost of a plan which satisfies the conditions in a line.
Example
Input
3 3
1 2 1 2
2 3 2 1
3 1 3 2
5 5
1 2 2 2
2 3 1 1
1 4 1 1
4 5 1 1
5 3 1 1
5 10
1 2 32 10
1 3 43 43
1 4 12 52
1 5 84 23
2 3 58 42
2 4 86 99
2 5 57 83
3 4 11 32
3 5 75 21
4 5 23 43
5 10
1 2 1 53
1 3 1 65
1 4 1 24
1 5 1 76
2 3 1 19
2 4 1 46
2 5 1 25
3 4 1 13
3 5 1 65
4 5 1 34
0 0
Output
3
5
137
218
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[7], [25], [50], [100], [1000], [10000]], \"outputs\": [[18], [107], [304], [993], [63589], [4721110]]}", "source": "taco"}
|
Consider a sequence generation that follows the following steps. We will store removed values in variable `res`. Assume `n = 25`:
```Haskell
-> [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] Let's remove the first number => res = [1]. We get..
-> [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Let's remove 2 (so res = [1,2]) and every 2-indexed number. We get..
-> [3,5,7,9,11,13,15,17,19,21,23,25]. Now remove 3, then every 3-indexed number. res = [1,2,3].
-> [5,7,11,13,17,19,23,25]. Now remove 5, and every 5-indexed number. res = [1,2,3,5]. We get..
-> [7,11,13,17,23,25]. Now remove 7 and every 7-indexed. res = [1,2,3,5,7].
But we know that there are no other 7-indexed elements, so we include all remaining numbers in res. So res = [1,2,3,5,7,11,13,17,23,25] and sum(res) = 107.
Note that when we remove every n-indexed number, we must remember that indices start at 0. So for every 3-indexed number above:
[3,5,7,9,11,13,15,17,19,21,23], we remove index0=3, index3= 9, index6=15,index9=21, etc.
Note also that if the length of sequence is greater than x, where x is the first element of the sequence, you should continue the remove step: remove x, and every x-indexed number until the length of sequence is shorter than x. In our example above, we stopped at 7 because the the length of the remaining sequence [7,11,13,17,23,25] is shorter than 7.
```
You will be given a number `n` and your task will be to return the sum of the elements in res, where the maximum element in res is `<= n`.
For example:
```Python
Solve(7) = 18, because this is the sum of res = [1,2,3,5,7].
Solve(25) = 107
```
More examples in the test cases.
Good luck!
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
You are given an array $a_1, a_2, \dots , a_n$, which is sorted in non-decreasing order ($a_i \le a_{i + 1})$.
Find three indices $i$, $j$, $k$ such that $1 \le i < j < k \le n$ and it is impossible to construct a non-degenerate triangle (a triangle with nonzero area) having sides equal to $a_i$, $a_j$ and $a_k$ (for example it is possible to construct a non-degenerate triangle with sides $3$, $4$ and $5$ but impossible with sides $3$, $4$ and $7$). If it is impossible to find such triple, report it.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains one integer $n$ ($3 \le n \le 5 \cdot 10^4$) — the length of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \dots , a_n$ ($1 \le a_i \le 10^9$; $a_{i - 1} \le a_i$) — the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
-----Output-----
For each test case print the answer to it in one line.
If there is a triple of indices $i$, $j$, $k$ ($i < j < k$) such that it is impossible to construct a non-degenerate triangle having sides equal to $a_i$, $a_j$ and $a_k$, print that three indices in ascending order. If there are multiple answers, print any of them.
Otherwise, print -1.
-----Example-----
Input
3
7
4 6 11 11 15 18 20
4
10 10 10 11
3
1 1 1000000000
Output
2 3 6
-1
1 2 3
-----Note-----
In the first test case it is impossible with sides $6$, $11$ and $18$. Note, that this is not the only correct answer.
In the second test case you always can construct a non-degenerate triangle.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
This is the harder version of the problem. In this version, $1 \le n, m \le 2\cdot10^5$. You can hack this problem if you locked it. But you can hack the previous problem only if you locked both problems.
You are given a sequence of integers $a=[a_1,a_2,\dots,a_n]$ of length $n$. Its subsequence is obtained by removing zero or more elements from the sequence $a$ (they do not necessarily go consecutively). For example, for the sequence $a=[11,20,11,33,11,20,11]$: $[11,20,11,33,11,20,11]$, $[11,20,11,33,11,20]$, $[11,11,11,11]$, $[20]$, $[33,20]$ are subsequences (these are just some of the long list); $[40]$, $[33,33]$, $[33,20,20]$, $[20,20,11,11]$ are not subsequences.
Suppose that an additional non-negative integer $k$ ($1 \le k \le n$) is given, then the subsequence is called optimal if: it has a length of $k$ and the sum of its elements is the maximum possible among all subsequences of length $k$; and among all subsequences of length $k$ that satisfy the previous item, it is lexicographically minimal.
Recall that the sequence $b=[b_1, b_2, \dots, b_k]$ is lexicographically smaller than the sequence $c=[c_1, c_2, \dots, c_k]$ if the first element (from the left) in which they differ less in the sequence $b$ than in $c$. Formally: there exists $t$ ($1 \le t \le k$) such that $b_1=c_1$, $b_2=c_2$, ..., $b_{t-1}=c_{t-1}$ and at the same time $b_t<c_t$. For example: $[10, 20, 20]$ lexicographically less than $[10, 21, 1]$, $[7, 99, 99]$ is lexicographically less than $[10, 21, 1]$, $[10, 21, 0]$ is lexicographically less than $[10, 21, 1]$.
You are given a sequence of $a=[a_1,a_2,\dots,a_n]$ and $m$ requests, each consisting of two numbers $k_j$ and $pos_j$ ($1 \le k \le n$, $1 \le pos_j \le k_j$). For each query, print the value that is in the index $pos_j$ of the optimal subsequence of the given sequence $a$ for $k=k_j$.
For example, if $n=4$, $a=[10,20,30,20]$, $k_j=2$, then the optimal subsequence is $[20,30]$ — it is the minimum lexicographically among all subsequences of length $2$ with the maximum total sum of items. Thus, the answer to the request $k_j=2$, $pos_j=1$ is the number $20$, and the answer to the request $k_j=2$, $pos_j=2$ is the number $30$.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 2\cdot10^5$) — the length of the sequence $a$.
The second line contains elements of the sequence $a$: integer numbers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).
The third line contains an integer $m$ ($1 \le m \le 2\cdot10^5$) — the number of requests.
The following $m$ lines contain pairs of integers $k_j$ and $pos_j$ ($1 \le k \le n$, $1 \le pos_j \le k_j$) — the requests.
-----Output-----
Print $m$ integers $r_1, r_2, \dots, r_m$ ($1 \le r_j \le 10^9$) one per line: answers to the requests in the order they appear in the input. The value of $r_j$ should be equal to the value contained in the position $pos_j$ of the optimal subsequence for $k=k_j$.
-----Examples-----
Input
3
10 20 10
6
1 1
2 1
2 2
3 1
3 2
3 3
Output
20
10
20
10
20
10
Input
7
1 2 1 3 1 2 1
9
2 1
2 2
3 1
3 2
3 3
1 1
7 1
7 7
7 4
Output
2
3
2
3
2
3
1
1
3
-----Note-----
In the first example, for $a=[10,20,10]$ the optimal subsequences are: for $k=1$: $[20]$, for $k=2$: $[10,20]$, for $k=3$: $[10,20,10]$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
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10\\n9 10 11\\n10 11 12\\n0 0\"], \"outputs\": [\"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n4\\n4\\n\", \"2\\n3\\n5\\n4\\n\", \"3\\n3\\n3\\n6\\n\", \"3\\n3\\n3\\n5\\n\", \"2\\n3\\n9\\n3\\n\", \"3\\n3\\n4\\n4\\n\", \"2\\n3\\n3\\n5\\n\", \"3\\n3\\n5\\n4\\n\", \"2\\n3\\n4\\n5\\n\", \"2\\n2\\n3\\n4\\n\", \"3\\n3\\n9\\n4\\n\", \"2\\n2\\n3\\n5\\n\", \"2\\n3\\n5\\n10\\n\", \"3\\n3\\n4\\n5\\n\", \"1\\n3\\n5\\n10\\n\", \"2\\n3\\n4\\n8\\n\", \"2\\n3\\n3\\n9\\n\", \"2\\n3\\n5\\n6\\n\", \"3\\n3\\n3\\n9\\n\", \"2\\n3\\n4\\n3\\n\", \"1\\n3\\n3\\n4\\n\", \"1\\n3\\n4\\n8\\n\", \"3\\n3\\n5\\n6\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n4\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n5\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n9\\n4\\n\", \"3\\n3\\n3\\n5\\n\", \"2\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n4\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\\n\", \"2\\n3\\n5\\n4\\n\", \"3\\n3\\n3\\n4\\n\", \"2\\n3\\n3\\n4\"]}", "source": "taco"}
|
The customer telephone support center of the computer sales company called JAG is now in- credibly confused. There are too many customers who request the support, and they call the support center all the time. So, the company wants to figure out how many operators needed to handle this situation.
For simplicity, let us focus on the following simple simulation.
Let N be a number of customers. The i-th customer has id i, and is described by three numbers, Mi, Li and Ki. Mi is the time required for phone support, Li is the maximum stand by time until an operator answers the call, and Ki is the interval time from hanging up to calling back. Let us put these in other words: It takes Mi unit times for an operator to support i-th customer. If the i-th customer is not answered by operators for Li unit times, he hangs up the call. Ki unit times after hanging up, he calls back.
One operator can support only one customer simultaneously. When an operator finish a call, he can immediately answer another call. If there are more than one customer waiting, an operator will choose the customer with the smallest id.
At the beginning of the simulation, all customers call the support center at the same time. The simulation succeeds if operators can finish answering all customers within T unit times.
Your mission is to calculate the minimum number of operators needed to end this simulation successfully.
Input
The input contains multiple datasets. Each dataset has the following format:
N T
M1 L1 K1
.
.
.
MN LN KN
The first line of a dataset contains two positive integers, N and T (1 ≤ N ≤ 1000, 1 ≤ T ≤ 1000). N indicates the number of customers in the dataset, and T indicates the time limit of the simulation.
The following N lines describe the information of customers. The i-th line contains three integers, Mi, Li and Ki (1 ≤ Mi ≤ T , 1 ≤ Li ≤ 1000, 1 ≤ Ki ≤ 1000), describing i-th customer's information. Mi indicates the time required for phone support, Li indicates the maximum stand by time until an operator answers the call, and Ki indicates the is the interval time from hanging up to calling back.
The end of input is indicated by a line containing two zeros. This line is not part of any dataset and hence should not be processed.
Output
For each dataset, print the minimum number of operators needed to end the simulation successfully in a line.
Example
Input
3 300
100 50 150
100 50 150
100 50 150
3 300
100 50 150
100 50 150
200 50 150
9 18
3 1 1
3 1 1
3 1 1
4 100 1
5 100 1
5 100 1
10 5 3
10 5 3
1 7 1000
10 18
1 2 3
2 3 4
3 4 5
4 5 6
5 6 7
6 7 8
7 8 9
8 9 10
9 10 11
10 11 12
0 0
Output
2
3
3
4
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[1], [5], [25], [30], [96], [50], [66], [306], [307], [308]], \"outputs\": [[0], [2], [4], [5], [5], [7], [7], [17], [18], [17]]}", "source": "taco"}
|
Final kata of the series (highly recommended to compute [layers](https://www.codewars.com/kata/progressive-spiral-number-position/) and [branch](https://www.codewars.com/kata/progressive-spiral-number-branch/) first to get a good idea), this is a blatant ripoff of [the one offered on AoC](http://adventofcode.com/2017/day/3).
Given a number, return the Manhattan distance considering the core of the spiral (the `1` cell) as 0 and counting each step up, right, down or left to reach a given cell.
For example, using our beloved 5x5 square:
```
17 16 15 14 13 4 3 2 3 4
18 05 04 03 12 3 2 1 2 3
19 06 01 02 11 => 2 1 0 1 2
20 07 08 09 10 3 2 1 2 3
21 22 23 24 25 4 3 2 3 4
```
And thus your code should behave like this:
```python
distance(1) == 0
distance(5) == 2
distance(25) == 4
distance(30) == 5
distance(50) == 7
```
Just be ready for larger numbers, as usual always positive.
*[Dedicated to [swiftest learner I met in a long while](https://www.codewars.com/users/irbekrm/)]*
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"100 2 8\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n00\\n\", \"40 10 1\\n3662957315\\n8667652926\\n0833069659\\n7030124763\\n0285674766\\n3253847205\\n3183518599\\n6584668288\\n6016531609\\n4094512804\\n8169065529\\n5526028299\\n1251249986\\n3970729176\\n7534232301\\n4643554614\\n8544233598\\n3618335000\\n4458737272\\n2014874848\\n2052050286\\n2523863039\\n3367463306\\n7570627477\\n6504863662\\n5673627493\\n9683553049\\n5087433832\\n4895351652\\n8976415673\\n7744852982\\n8880573285\\n8601062585\\n9914945591\\n6101306342\\n4477024828\\n6711693809\\n9518645171\\n0320790840\\n1660676034\\n\", \"2 2 0\\n02\\n64\\n\", \"10 5 5\\n57903\\n23822\\n16074\\n14758\\n17503\\n85862\\n22741\\n24624\\n91349\\n59483\\n\", \"3 100 2\\n9274856291089022402330510299964972078374631084698909589848378120688833406094439833480605688734822538\\n8559432619222401260831250315191045571941748630289435997646309147962549951488150729159571611224761557\\n7459677994197468453434072563284883271493313149578657711970598092555372522009834711876673556425273784\\n\", \"2 2 3\\n15\\n52\\n\", \"2 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7\\n18\\n70\\n19\\n42\\n74\\n37\\n47\\n43\\n71\\n66\\n25\\n64\\n60\\n45\\n90\\n54\\n38\\n35\\n92\\n79\\n19\\n94\\n76\\n61\\n30\\n49\\n95\\n72\\n57\\n05\\n71\\n10\\n18\\n40\\n63\\n01\\n75\\n44\\n65\\n47\\n27\\n37\\n84\\n30\\n06\\n15\\n55\\n19\\n49\\n00\\n80\\n77\\n20\\n78\\n33\\n67\\n29\\n20\\n98\\n28\\n19\\n00\\n42\\n88\\n11\\n58\\n57\\n69\\n58\\n92\\n90\\n73\\n65\\n09\\n85\\n08\\n93\\n83\\n42\\n54\\n41\\n20\\n66\\n99\\n41\\n01\\n91\\n91\\n39\\n60\\n66\\n82\\n77\\n25\\n02\\n55\\n32\\n64\\n56\\n30\\n\", \"4 3 10\\n194\\n707\\n650\\n633\\n\", \"2 2 10\\n120\\n75\\n\", \"2 100 2\\n0000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000\\n0000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000\\n\", \"100 2 7\\n18\\n70\\n19\\n42\\n74\\n37\\n47\\n43\\n71\\n66\\n25\\n64\\n60\\n45\\n90\\n54\\n38\\n35\\n92\\n79\\n19\\n94\\n76\\n61\\n30\\n49\\n95\\n72\\n57\\n05\\n71\\n10\\n18\\n40\\n63\\n01\\n75\\n51\\n65\\n47\\n27\\n37\\n84\\n30\\n06\\n15\\n55\\n19\\n49\\n00\\n80\\n77\\n20\\n78\\n33\\n67\\n29\\n20\\n98\\n28\\n19\\n00\\n42\\n88\\n11\\n58\\n57\\n69\\n58\\n92\\n90\\n73\\n65\\n09\\n85\\n08\\n93\\n83\\n42\\n54\\n41\\n20\\n66\\n99\\n41\\n01\\n91\\n91\\n39\\n60\\n66\\n82\\n77\\n25\\n02\\n55\\n32\\n64\\n56\\n30\\n\", \"4 3 10\\n194\\n707\\n893\\n633\\n\", \"2 100 3\\n0000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000\\n0000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000\\n\", \"100 2 7\\n18\\n70\\n19\\n42\\n74\\n37\\n47\\n43\\n71\\n66\\n25\\n64\\n60\\n46\\n90\\n54\\n38\\n35\\n92\\n79\\n19\\n94\\n76\\n61\\n30\\n49\\n95\\n72\\n57\\n05\\n71\\n10\\n18\\n40\\n63\\n01\\n75\\n51\\n65\\n47\\n27\\n37\\n84\\n30\\n06\\n15\\n55\\n19\\n49\\n00\\n80\\n77\\n20\\n78\\n33\\n67\\n29\\n20\\n98\\n28\\n19\\n00\\n42\\n88\\n11\\n58\\n57\\n69\\n58\\n92\\n90\\n73\\n65\\n09\\n85\\n08\\n93\\n83\\n42\\n54\\n41\\n20\\n66\\n99\\n41\\n01\\n91\\n91\\n39\\n60\\n66\\n82\\n77\\n25\\n02\\n55\\n32\\n64\\n56\\n30\\n\", \"40 10 1\\n3662957315\\n8667652926\\n0833069659\\n7030124763\\n0285674766\\n2469474265\\n3183518599\\n6584668288\\n6016531609\\n4094512804\\n8169065529\\n4885665490\\n1251249986\\n3970729176\\n7534232301\\n4643554614\\n8544233598\\n3618335000\\n4458737272\\n2014874848\\n2052050286\\n2523863039\\n3367463306\\n7570627477\\n6504863662\\n5673627493\\n9683553049\\n5087433832\\n4895351652\\n8976415673\\n7744852982\\n8880573285\\n8601062585\\n9914945591\\n8230581358\\n8071206142\\n6711693809\\n9518645171\\n0320790840\\n1660676034\\n\", \"100 2 7\\n18\\n70\\n19\\n42\\n74\\n37\\n47\\n43\\n71\\n66\\n25\\n64\\n60\\n45\\n90\\n54\\n38\\n35\\n92\\n79\\n19\\n94\\n76\\n61\\n30\\n49\\n95\\n72\\n57\\n05\\n71\\n10\\n18\\n40\\n63\\n01\\n75\\n44\\n65\\n47\\n27\\n37\\n84\\n30\\n06\\n15\\n55\\n19\\n49\\n00\\n80\\n77\\n20\\n78\\n33\\n67\\n29\\n20\\n98\\n28\\n19\\n00\\n42\\n88\\n11\\n58\\n57\\n69\\n58\\n92\\n96\\n73\\n65\\n09\\n85\\n08\\n93\\n83\\n38\\n54\\n41\\n20\\n66\\n99\\n41\\n01\\n91\\n91\\n39\\n60\\n66\\n82\\n77\\n25\\n02\\n55\\n32\\n64\\n56\\n30\\n\", \"23 2 3\\n00\\n47\\n52\\n36\\n01\\n01\\n39\\n04\\n69\\n93\\n77\\n72\\n33\\n95\\n13\\n50\\n23\\n48\\n79\\n98\\n05\\n63\\n17\\n\", \"40 10 1\\n3662957315\\n8667652926\\n0833069659\\n7030124763\\n0285674766\\n3253847205\\n3183518599\\n6584668288\\n6016531609\\n4094512804\\n8169065529\\n5526028299\\n1251249986\\n3970729176\\n7534232301\\n1762594563\\n8544233598\\n3618335000\\n4458737272\\n2014874848\\n2052050286\\n2523863039\\n3367463306\\n7570627477\\n6504863662\\n5673627493\\n9683553049\\n5087433832\\n4895351652\\n8976415673\\n7744852982\\n8880573285\\n8601062585\\n9914945591\\n6101306342\\n8071206142\\n6711693809\\n9518645171\\n0320790840\\n1660676034\\n\", \"3 4 3\\n9073\\n4768\\n4474\\n\", \"2 2 10\\n98\\n75\\n\", \"3 3 1\\n123\\n456\\n789\\n\", \"3 3 0\\n123\\n456\\n789\\n\"], \"outputs\": [\"0\\n2\\nLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRL\\n\", \"258\\n5\\nRLRRRRLRLRLRRLLLLLRLLRLRRRRRRLRLLLLRLLR\", \"8\\n1\\nR\\n\", \"60\\n5\\nLLRLLRLRL\", \"27\\n9\\nRL\\n\", \"-1\\n\", \"18\\n1\\nR\\n\", \"900\\n2\\nLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRLRL\\n\", \"18\\n3\\nLR\\n\", \"0\\n2\\nL\\n\", \"16\\n37\\nR\\n\", \"-1\\n\", \"45\\n4\\nLLRLRR\", \"21\\n3\\nRLLL\\n\", \"99\\n4\\nRLRLLRLRRRRLL\\n\", \"18\\n4\\nLL\\n\", \"-1\\n\", \"22\\n3\\nLLR\", \"17\\n3\\nLR\\n\", \"140\\n9\\nRLLLRRLLLLRRRLRLLLRLL\", \"18\\n2\\nL\\n\", \"-1\\n\", \"31\\n2\\nLRRL\\n\", \"27\\n3\\nLRR\\n\", \"42\\n4\\nRLLLL\\n\", \"545\\n1\\nRRLRLLRRLLRLRLRRLLRLRRLLRLRLRRLLRRLLRLRLRLRLRRLLRRLRLLRRLRLRLRLLRLRLRRLLRRLRLLRRLRLLRLRLRLRLRLRLRLR\", \"260\\n5\\nRLRRRRLRLRLRRLLLLLRLLRLRRRRRRLRLLLLRLLR\\n\", \"18\\n1\\nR\\n\", \"21\\n3\\nLR\\n\", \"0\\n2\\nL\\n\", \"-1\", \"99\\n4\\nLRRLLRLRRRRRR\\n\", \"23\\n3\\nRL\\n\", \"140\\n9\\nLRLLRLRLLLRRRLRLLLRLL\\n\", \"18\\n2\\nL\\n\", \"27\\n20\\nLLL\\n\", \"15\\n3\\nLL\\n\", \"23\\n2\\nRL\\n\", \"264\\n7\\nRRRLRLLRLRLRRLLLLLRLLRLRRRRRRLRLLLRRRLR\\n\", \"20\\n1\\nRL\\n\", \"12\\n2\\nL\\n\", \"99\\n4\\nRLRLLRLRRRLLL\\n\", \"19\\n2\\nLR\\n\", \"18\\n34\\nL\\n\", \"18\\n2\\nRL\\n\", \"266\\n7\\nRRRLRLLRLRLRRLLLLLRLLRLRRRRRRLRLRLLLLLR\\n\", \"16\\n6\\nLL\\n\", \"258\\n3\\nLLRRLLRLRLRRLRLRRRRLLRLRRRRRRLRLLLLRLLR\\n\", \"66\\n3\\nRLLLRRRLL\\n\", \"21\\n4\\nLR\\n\", \"8\\n2\\nL\\n\", \"15\\n3\\nR\\n\", \"24\\n3\\nLL\\n\", \"99\\n2\\nRRRLLRLRRRRRR\\n\", \"20\\n2\\nRL\\n\", \"22\\n3\\nLLR\\n\", \"144\\n9\\nRLLLRRLLLLRRRLRLLLRLR\\n\", \"18\\n17\\nL\\n\", \"28\\n11\\nLRL\\n\", \"41\\n4\\nRLLLL\\n\", \"540\\n1\\nRRLRLLRRLLRLRLRRLLRLRRLLRLRLRRLLRRLLRLRLRLRLRRLLRRLRLLRRLRLRLRLLRLRLRRLLRRLRLLRLRRLLRLRLRLRLRLRLRLR\\n\", \"11\\n2\\nL\\n\", \"12\\n2\\nRL\\n\", \"15\\n3\\nLR\\n\", \"-1\", \"-1\", \"-1\", \"0\\n2\\nL\\n\", \"-1\", \"-1\", \"0\\n2\\nL\\n\", \"-1\", \"266\\n7\\nRRRLRLLRLRLRRLLLLLRLLRLRRRRRRLRLRLLLLLR\\n\", \"-1\", \"-1\", \"260\\n5\\nRLRRRRLRLRLRRLLLLLRLLRLRRRRRRLRLLLLRLLR\\n\", \"20\\n1\\nRL\\n\", \"-1\\n\", \"16\\n2\\nRL\\n\", \"17\\n3\\nLR\\n\"]}", "source": "taco"}
|
On some square in the lowest row of a chessboard a stands a pawn. It has only two variants of moving: upwards and leftwards or upwards and rightwards. The pawn can choose from which square of the lowest row it can start its journey. On each square lay from 0 to 9 peas. The pawn wants to reach the uppermost row having collected as many peas as possible. As there it will have to divide the peas between itself and its k brothers, the number of peas must be divisible by k + 1. Find the maximal number of peas it will be able to collect and which moves it should make to do it.
The pawn cannot throw peas away or leave the board. When a pawn appears in some square of the board (including the first and last square of the way), it necessarily takes all the peas.
Input
The first line contains three integers n, m, k (2 ≤ n, m ≤ 100, 0 ≤ k ≤ 10) — the number of rows and columns on the chessboard, the number of the pawn's brothers. Then follow n lines containing each m numbers from 0 to 9 without spaces — the chessboard's description. Each square is described by one number — the number of peas in it. The first line corresponds to the uppermost row and the last line — to the lowest row.
Output
If it is impossible to reach the highest row having collected the number of peas divisible by k + 1, print -1.
Otherwise, the first line must contain a single number — the maximal number of peas the pawn can collect given that the number must be divisible by k + 1. The second line must contain a single number — the number of the square's column in the lowest row, from which the pawn must start its journey. The columns are numbered from the left to the right with integral numbers starting from 1. The third line must contain a line consisting of n - 1 symbols — the description of the pawn's moves. If the pawn must move upwards and leftwards, print L, if it must move upwards and rightwards, print R. If there are several solutions to that problem, print any of them.
Examples
Input
3 3 1
123
456
789
Output
16
2
RL
Input
3 3 0
123
456
789
Output
17
3
LR
Input
2 2 10
98
75
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"86232 41348\\n\", \"2 2\\n\", \"100000 17\\n\", \"1 1\\n\", \"4 2\\n\", \"1 99999\\n\", \"4 3\\n\", \"21857 94145\\n\", \"1 29\\n\", \"5444 31525\\n\", \"50664 46559\\n\", \"2 1\\n\", \"7683 65667\\n\", \"4 4\\n\", \"4 1\\n\", \"50000 100000\\n\", \"12345 31\\n\", \"25063 54317\\n\", \"62600 39199\\n\", \"83781 52238\\n\", \"1 2\\n\", \"4 11\\n\", \"5 100\\n\", \"60282 92611\\n\", \"88201 96978\\n\", \"100000 100000\\n\", \"65535 16\\n\", \"3 3\\n\", \"100000 16\\n\", \"128 8\\n\", \"7413 87155\\n\", \"94882 95834\\n\", \"14095 86011\\n\", \"99999 1\\n\", \"85264 15318\\n\", \"3 1\\n\", \"127 7\\n\", \"2 15\\n\", \"78606 36436\\n\", \"60607 63595\\n\", \"86232 6137\\n\", \"100000 34\\n\", \"4 6\\n\", \"1 30\\n\", \"2345 31525\\n\", \"82166 46559\\n\", \"7 1\\n\", \"6 4\\n\", \"42375 100000\\n\", \"12345 17\\n\", \"16183 54317\\n\", \"62600 55451\\n\", \"5 11\\n\", \"73450 92611\\n\", \"58788 16\\n\", \"6 3\\n\", \"153 8\\n\", \"7413 76718\\n\", \"94882 1499\\n\", \"85264 3162\\n\", \"2 3\\n\", \"78606 20511\\n\", \"60607 4830\\n\", \"7704 6137\\n\", \"100000 39\\n\", \"7 6\\n\", \"2 30\\n\", \"2345 3565\\n\", \"82166 44274\\n\", \"1 4\\n\", \"5376 17\\n\", \"18975 54317\\n\", \"42554 55451\\n\", \"2 11\\n\", \"73450 1811\\n\", \"58231 16\\n\", \"2 6\\n\", \"100010 28\\n\", \"13455 76718\\n\", \"37178 1499\\n\", \"85264 413\\n\", \"1 3\\n\", \"78606 23398\\n\", \"60607 1098\\n\", \"7704 1314\\n\", \"7 8\\n\", \"2 58\\n\", \"2345 4659\\n\", \"39129 44274\\n\", \"1 5\\n\", \"5376 20\\n\", \"13113 54317\\n\", \"6 1\\n\", \"100010 16\\n\", \"172 7\\n\", \"5 1\\n\", \"8 1\\n\", \"267 8\\n\", \"172 2\\n\", \"5 2\\n\", \"16 1\\n\", \"3 2\\n\"], \"outputs\": [\"77566161\\n\", \"6\\n\", \"614965071\\n\", \"1\\n\", \"0\\n\", \"833014736\\n\", \"840\\n\", \"689996210\\n\", \"536870911\\n\", \"637906839\\n\", \"425318276\\n\", \"0\\n\", \"298588855\\n\", \"32760\\n\", \"0\\n\", \"821709120\\n\", \"378093434\\n\", \"735545216\\n\", \"366778414\\n\", \"188770162\\n\", \"3\\n\", \"433239206\\n\", \"345449482\\n\", \"814908070\\n\", \"508134449\\n\", \"738698541\\n\", \"558444716\\n\", \"210\\n\", \"0\\n\", \"987517349\\n\", \"340839315\\n\", \"360122315\\n\", \"656508583\\n\", \"0\\n\", \"635855261\\n\", \"0\\n\", \"399589559\\n\", \"73643513\\n\", \"657976765\\n\", \"396334239\\n\", \"189682209\\n\", \"408657483\\n\", \"14295960\\n\", \"73741814\\n\", \"979807969\\n\", \"852884106\\n\", \"0\\n\", \"3603600\\n\", \"7231041\\n\", \"304411089\\n\", \"439396129\\n\", \"829095632\\n\", \"107689893\\n\", \"600389647\\n\", \"536923216\\n\", \"5040\\n\", \"898075930\\n\", \"834089022\\n\", \"504430420\\n\", \"676807722\\n\", \"42\\n\", \"960918236\\n\", \"95356286\\n\", \"610527294\\n\", \"72188603\\n\", \"484156748\\n\", \"9328087\\n\", \"865387213\\n\", \"7209586\\n\", \"15\\n\", \"977388267\\n\", \"502640215\\n\", \"666464083\\n\", \"4188162\\n\", \"208858092\\n\", \"618820764\\n\", \"3906\\n\", \"582315491\\n\", \"533069538\\n\", \"745509389\\n\", \"921020756\\n\", \"7\\n\", \"412781594\\n\", \"304794108\\n\", \"598043829\\n\", \"425271721\\n\", \"184401516\\n\", \"830388303\\n\", \"785601123\\n\", \"31\\n\", \"110888476\\n\", \"33334081\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"6\\n\"]}", "source": "taco"}
|
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecutive elements with xor equal to 0.
The expression <image> means applying the operation of a bitwise xor to numbers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is marked as "^", in Pascal — as "xor".
In this problem you are asked to compute the number of sequences made of n integers from 0 to 2m - 1 that are not a wool sequence. You should print this number modulo 1000000009 (109 + 9).
Input
The only line of input contains two space-separated integers n and m (1 ≤ n, m ≤ 105).
Output
Print the required number of sequences modulo 1000000009 (109 + 9) on the only line of output.
Examples
Input
3 2
Output
6
Note
Sequences of length 3 made of integers 0, 1, 2 and 3 that are not a wool sequence are (1, 3, 1), (1, 2, 1), (2, 1, 2), (2, 3, 2), (3, 1, 3) and (3, 2, 3).
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"5\\n2 1 1 2 5\\n\", \"3\\n4 5 3\\n\", \"2\\n10 10\\n\", \"4\\n1 2 2 1\\n\", \"6\\n3 2 3 3 2 3\\n\", \"1\\n1\\n\", \"14\\n7 7 7 4 3 3 4 5 4 4 5 7 7 7\\n\", \"10\\n1 9 7 6 2 4 7 8 1 3\\n\", \"6\\n1 1 1 1 2 1\\n\", \"7\\n1 1 2 2 3 3 1\\n\", \"4\\n2 2 2 3\\n\", \"7\\n4 1 1 2 4 3 3\\n\", \"4\\n3 1 2 4\\n\", \"3\\n5 5 2\\n\", \"2\\n1 2\\n\", \"7\\n4 1 1 2 3 3 4\\n\", \"8\\n2 2 10 6 4 2 2 4\\n\", \"4\\n3 3 3 4\\n\", \"5\\n1 2 2 1 1\\n\", \"5\\n2 1 1 1 2\\n\", \"4\\n10 10 40 60\\n\", \"4\\n5 3 3 3\\n\", \"7\\n2 2 2 2 2 2 1\\n\", \"5\\n1 1 2 2 1\\n\", \"5\\n3 2 2 3 1\\n\", \"3\\n5 5 4\\n\", \"5\\n3 3 1 1 2\\n\", \"3\\n10 10 9\\n\", \"7\\n9 7 6 5 5 6 7\\n\", \"5\\n1 1 2 3 3\\n\", \"5\\n2 2 2 2 1\\n\", \"5\\n5 4 4 4 5\\n\", \"3\\n5 5 3\\n\", \"13\\n5 2 2 1 1 2 5 2 1 1 2 2 5\\n\", \"8\\n9 7 6 5 5 6 7 8\\n\", \"5\\n4 3 3 4 1\\n\", \"4\\n4 4 4 3\\n\", \"5\\n10 9 5 3 7\\n\", \"5\\n1 2 1 2 5\\n\", \"4\\n2 1 4 5\\n\", \"4\\n2 10 1 1\\n\", \"5\\n1 2 2 1 5\\n\", \"3\\n2 2 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3 3 2 3\\n\", \"4\\n10 10 40 76\\n\", \"10\\n1 9 7 6 2 4 8 8 1 3\\n\", \"5\\n1 2 1 2 10\\n\", \"5\\n1 6 1 4 6\\n\", \"5\\n5 6 1 1 2\\n\", \"4\\n3 4 3 4\\n\", \"7\\n1 0 2 2 3 3 1\\n\", \"4\\n1 3 2 1\\n\", \"8\\n9 7 6 5 5 6 7 6\\n\", \"5\\n3 2 4 4 5\\n\", \"3\\n10 10 18\\n\", \"5\\n0 1 2 3 3\\n\", \"6\\n1 1 1 2 2 1\\n\", \"4\\n3 1 2 2\\n\", \"5\\n2 1 2 2 1\\n\", \"4\\n2 2 2 4\\n\", \"5\\n10 10 9 9 8\\n\", \"4\\n5 5 3 3\\n\", \"10\\n5 2 2 6 0 7 8 1 5 5\\n\", \"3\\n10 5 4\\n\", \"14\\n8 7 7 4 3 3 4 5 4 4 5 7 7 7\\n\", \"5\\n3 3 2 1 2\\n\", \"3\\n5 3 2\\n\", \"9\\n5 4 3 3 2 2 2 1 5\\n\", \"5\\n2 2 2 1 1\\n\", \"10\\n5 5 1 2 2 1 3 5 1 1\\n\", \"5\\n1 2 2 1 3\\n\", \"7\\n1 1 1 2 3 3 4\\n\", \"5\\n4 2 2 2 1\\n\", \"5\\n0 1 6 4 4\\n\", \"5\\n10 9 5 3 11\\n\", \"10\\n10 9 8 7 7 10 8 9 10 11\\n\", \"5\\n5 4 4 1 5\\n\", \"5\\n3 2 3 3 1\\n\", \"5\\n2 2 1 1 2\\n\", \"4\\n2 12 1 1\\n\", \"4\\n1 1 3 6\\n\", \"8\\n2 2 10 6 4 3 2 4\\n\", \"4\\n2 1 3 5\\n\", \"4\\n1 1 4 5\\n\", \"3\\n0 5 3\\n\", \"5\\n1 0 4 4 6\\n\", \"4\\n4 7 4 3\\n\", \"2\\n2 2\\n\", \"2\\n10 14\\n\", \"3\\n4 4 3\\n\", \"5\\n2 2 1 2 5\\n\", \"1\\n4\\n\", \"13\\n5 0 2 1 1 2 5 2 1 1 2 3 5\\n\", \"7\\n2 2 2 2 0 4 1\\n\", \"4\\n2 3 1 1\\n\", \"7\\n4 0 1 4 4 3 3\\n\", \"5\\n1 5 3 4 1\\n\", \"20\\n16 1 2 3 5 7 7 9 4 9 9 4 9 7 7 5 3 2 5 10\\n\", \"6\\n11 2 3 3 2 3\\n\", \"4\\n10 10 21 76\\n\", \"10\\n0 9 7 6 2 4 8 8 1 3\\n\", \"5\\n1 2 1 4 10\\n\", \"5\\n1 6 1 4 3\\n\", \"5\\n4 6 1 1 2\\n\", \"4\\n3 4 3 8\\n\", \"7\\n1 0 2 2 3 3 2\\n\", \"2\\n10 10\\n\", \"3\\n4 5 3\\n\", \"5\\n2 1 1 2 5\\n\"], \"outputs\": [\"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\", \"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\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", 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|
Vova's family is building the Great Vova Wall (named by Vova himself). Vova's parents, grandparents, grand-grandparents contributed to it. Now it's totally up to Vova to put the finishing touches.
The current state of the wall can be respresented by a sequence $a$ of $n$ integers, with $a_i$ being the height of the $i$-th part of the wall.
Vova can only use $2 \times 1$ bricks to put in the wall (he has infinite supply of them, however).
Vova can put bricks only horizontally on the neighbouring parts of the wall of equal height. It means that if for some $i$ the current height of part $i$ is the same as for part $i + 1$, then Vova can put a brick there and thus increase both heights by 1. Obviously, Vova can't put bricks in such a way that its parts turn out to be off the borders (to the left of part $1$ of the wall or to the right of part $n$ of it).
Note that Vova can't put bricks vertically.
Vova is a perfectionist, so he considers the wall completed when: all parts of the wall has the same height; the wall has no empty spaces inside it.
Can Vova complete the wall using any amount of bricks (possibly zero)?
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of parts in the wall.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) — the initial heights of the parts of the wall.
-----Output-----
Print "YES" if Vova can complete the wall using any amount of bricks (possibly zero).
Print "NO" otherwise.
-----Examples-----
Input
5
2 1 1 2 5
Output
YES
Input
3
4 5 3
Output
NO
Input
2
10 10
Output
YES
-----Note-----
In the first example Vova can put a brick on parts 2 and 3 to make the wall $[2, 2, 2, 2, 5]$ and then put 3 bricks on parts 1 and 2 and 3 bricks on parts 3 and 4 to make it $[5, 5, 5, 5, 5]$.
In the second example Vova can put no bricks in the wall.
In the third example the wall is already complete.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"9\\n9 4\\n7 5\\n4 1\\n6 5\\n5 2\\n3 1\\n2 1\\n8 3\\n3\\n9 7 2\\n1 6 4\\n8 4 1\\n\", \"7\\n3 4\\n2 3\\n6 5\\n2 7\\n5 2\\n1 2\\n6\\n5 6 2\\n3 2 4\\n5 1 1\\n2 4 3\\n3 7 4\\n6 5 2\\n\", \"3\\n2 3\\n2 1\\n3\\n3 2 3\\n3 1 2\\n1 2 4\\n\", \"7\\n2 7\\n4 2\\n6 5\\n2 1\\n1 3\\n5 4\\n5\\n1 4 2\\n7 3 1\\n3 2 1\\n1 2 3\\n6 3 1\\n\", \"5\\n3 2\\n5 3\\n4 1\\n1 2\\n7\\n1 2 4\\n2 4 2\\n5 2 1\\n4 2 2\\n3 5 1\\n4 2 2\\n3 1 3\\n\", \"5\\n4 2\\n2 1\\n1 3\\n1 5\\n1\\n3 5 4\\n\", \"8\\n1 2\\n2 8\\n2 4\\n5 6\\n1 3\\n7 6\\n5 4\\n7\\n2 3 2\\n5 8 2\\n3 2 2\\n6 4 2\\n5 4 3\\n3 6 2\\n5 4 3\\n\", \"5\\n3 5\\n2 1\\n2 4\\n1 3\\n6\\n2 4 4\\n4 1 1\\n2 1 1\\n2 3 1\\n2 5 1\\n5 2 1\\n\", \"6\\n1 2\\n2 3\\n1 6\\n5 1\\n2 4\\n3\\n2 5 1\\n4 6 2\\n2 5 1\\n\", \"4\\n1 2\\n3 1\\n3 4\\n7\\n4 2 1\\n1 2 3\\n4 1 3\\n3 1 3\\n4 1 4\\n4 3 1\\n4 2 2\\n\", \"8\\n3 5\\n3 2\\n6 2\\n5 8\\n1 4\\n1 7\\n1 2\\n2\\n2 3 3\\n1 7 4\\n\", \"4\\n4 3\\n2 1\\n2 3\\n4\\n4 3 3\\n4 3 3\\n1 3 1\\n4 2 3\\n\", \"4\\n1 2\\n4 2\\n3 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\"-1\\n\", \"4 4 \\n\", \"-1\\n\", \"4 2 1 4 3 4 \\n\", \"1 1 1 1 1 1 1 1 1 \\n\", \"1 \\n\", \"3 \\n\", \"1 4 2 1 1 1 4 \\n\", \"4 \\n\", \"2 2 1 4 4 2 2 1 \\n\", \"1 1 1 1 1 \\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4 4 1 4 1 4 1 4 3 \\n\", \"1 1 1 1 2 \\n\", \"2 2 1 1 2 2 \\n\", \"1 1 1 1 \\n\", \"3 1 2 2 2 2 2 2 \\n\", \"4 1 2 4 4 3 4 \\n\", \"1 4 1 1 4 \\n\", \"1 1 1 1 1 1 1 \\n\", \"2 3 3 2 1 \\n\", \"2 2 1 2 2 \\n\", \"-1\\n\", \"2 3 1 1 3 3 1 2 1 \\n\", \"3 3 \\n\", \"-1\\n\", \"-1\\n\", \"4 2 3 2 \\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1 1 \\n\", \"-1\\n\", \"1 2 1 1 1 \\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1 1 1 1 2 \\n\", \"-1\\n\", \"1 1 1 \\n\", \"-1\\n\", \"1 1 1 1 1 1 1 \\n\", \"2 4 2 2 1 2 1 \\n\", \"1 2 2 4 \\n\", \"3 4 1 1 1 \\n\", \"-1\\n\", \"1 1 1 1 1 1 \\n\", \"1 3 1 1 1 1 3 \\n\", \"-1\\n\", \"2\\n2\\n\", \"3 4 2 1 1 1\\n\", \"1 2 2 3 1 2\\n\", \"-1\\n\", \"2 3 3 2 2 1 3\\n\", \"1 1 4 1\\n\", \"2 1 2 1 2\\n\", \"1 1 1 1 1 1 1 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|
There are n railway stations in Berland. They are connected to each other by n-1 railway sections. The railway network is connected, i.e. can be represented as an undirected tree.
You have a map of that network, so for each railway section you know which stations it connects.
Each of the n-1 sections has some integer value of the scenery beauty. However, these values are not marked on the map and you don't know them. All these values are from 1 to 10^6 inclusive.
You asked m passengers some questions: the j-th one told you three values:
* his departure station a_j;
* his arrival station b_j;
* minimum scenery beauty along the path from a_j to b_j (the train is moving along the shortest path from a_j to b_j).
You are planning to update the map and set some value f_i on each railway section — the scenery beauty. The passengers' answers should be consistent with these values.
Print any valid set of values f_1, f_2, ..., f_{n-1}, which the passengers' answer is consistent with or report that it doesn't exist.
Input
The first line contains a single integer n (2 ≤ n ≤ 5000) — the number of railway stations in Berland.
The next n-1 lines contain descriptions of the railway sections: the i-th section description is two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), where x_i and y_i are the indices of the stations which are connected by the i-th railway section. All the railway sections are bidirected. Each station can be reached from any other station by the railway.
The next line contains a single integer m (1 ≤ m ≤ 5000) — the number of passengers which were asked questions. Then m lines follow, the j-th line contains three integers a_j, b_j and g_j (1 ≤ a_j, b_j ≤ n; a_j ≠ b_j; 1 ≤ g_j ≤ 10^6) — the departure station, the arrival station and the minimum scenery beauty along his path.
Output
If there is no answer then print a single integer -1.
Otherwise, print n-1 integers f_1, f_2, ..., f_{n-1} (1 ≤ f_i ≤ 10^6), where f_i is some valid scenery beauty along the i-th railway section.
If there are multiple answers, you can print any of them.
Examples
Input
4
1 2
3 2
3 4
2
1 2 5
1 3 3
Output
5 3 5
Input
6
1 2
1 6
3 1
1 5
4 1
4
6 1 3
3 4 1
6 5 2
1 2 5
Output
5 3 1 2 1
Input
6
1 2
1 6
3 1
1 5
4 1
4
6 1 1
3 4 3
6 5 3
1 2 4
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
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|
Problem
There are $ 2 $ teams, Team UKU and Team Ushi. Initially, Team UKU has $ N $ people and Team Uku has $ M $ people. Team UKU and Team Ushi decided to play a game called "U & U". "U & U" has a common score for $ 2 $ teams, and the goal is to work together to minimize the common score. In "U & U", everyone's physical strength is $ 2 $ at first, and the common score is $ 0 $, and the procedure is as follows.
1. Each person in Team UKU makes exactly $ 1 $ attacks on someone in Team UKU for $ 1 $. The attacked person loses $ 1 $ in health and leaves the team when he or she reaches $ 0 $. At this time, when the number of team members reaches $ 0 $, the game ends. If the game is not over when everyone on Team UKU has just completed $ 1 $ attacks, $ 1 $ will be added to the common score and proceed to $ 2 $.
2. Similarly, team members make $ 1 $ each and just $ 1 $ attacks on someone in Team UKU. The attacked person loses $ 1 $ in health and leaves the team when he or she reaches $ 0 $. At this time, when the number of team UKUs reaches $ 0 $, the game ends. If the game isn't over when everyone on the team has just finished $ 1 $ attacks, $ 1 $ will be added to the common score and back to $ 1 $.
Given the number of team UKUs and the number of teams, find the minimum possible common score at the end of the "U & U" game.
Constraints
The input satisfies the following conditions.
* $ 1 \ le N, M \ le 10 ^ {18} $
* $ N $ and $ M $ are integers
Input
The input is given in the following format.
$ N $ $ M $
An integer $ N $ representing the number of team UKUs and an integer $ M $ representing the number of team members are given, separated by blanks.
Output
Print the lowest score on the $ 1 $ line.
Examples
Input
20 10
Output
0
Input
10 20
Output
1
Input
64783 68943
Output
4
Input
1000000000000000000 1000000000000000000
Output
2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 6\\n1 4 3\\n\", \"5 400\\n3 1 4 1 5\\n\", \"6 20\\n10 4 3 10 25 2\\n\", \"1 400\\n3 1 4 1 5\", \"3 6\\n1 7 3\", \"3 6\\n1 5 2\", \"3 7\\n1 5 0\", \"4 590\\n0 1 1 1 5\", \"5 1135\\n1 1 1 2 5\", \"1 734\\n3 1 4 1 5\", \"3 6\\n1 7 2\", \"1 734\\n3 1 4 0 5\", \"1 1126\\n3 1 4 0 5\", \"3 6\\n1 5 0\", \"1 1126\\n0 1 4 0 5\", \"1 586\\n0 1 4 0 5\", \"3 7\\n0 5 0\", \"1 586\\n0 1 4 -1 5\", \"3 7\\n0 5 -1\", \"1 586\\n0 1 3 -1 5\", \"2 7\\n0 5 -1\", \"1 586\\n0 1 1 -1 5\", \"2 7\\n0 6 -1\", \"1 586\\n0 2 1 -1 5\", \"2 7\\n0 6 0\", \"1 586\\n0 2 1 -2 5\", \"2 7\\n0 3 0\", \"1 586\\n-1 2 1 -2 5\", \"2 7\\n0 1 0\", \"1 988\\n-1 2 1 -2 5\", \"0 7\\n0 1 0\", \"1 590\\n-1 2 1 -2 5\", \"0 7\\n0 2 0\", \"1 590\\n-1 1 1 -2 5\", \"0 7\\n0 2 1\", \"1 590\\n-1 1 1 0 5\", \"0 7\\n0 1 1\", \"1 590\\n0 1 1 0 5\", \"0 6\\n0 1 1\", \"2 590\\n0 1 1 0 5\", \"2 590\\n0 1 1 1 5\", \"4 1135\\n0 1 1 1 5\", \"4 1135\\n1 1 1 1 5\", \"4 1135\\n1 1 1 2 5\", \"5 1135\\n1 1 1 2 9\", \"5 84\\n1 1 1 2 9\", \"5 84\\n1 1 1 4 9\", \"5 400\\n3 1 4 2 5\", \"3 6\\n1 4 1\", \"6 20\\n10 4 5 10 25 2\", \"1 400\\n3 1 4 1 4\", \"3 6\\n0 7 3\", \"1 734\\n3 1 4 1 10\", \"3 6\\n2 7 2\", \"1 734\\n3 0 4 0 5\", \"3 6\\n1 4 2\", \"1 1126\\n0 1 4 0 9\", \"3 6\\n1 7 0\", \"1 1126\\n0 1 3 0 5\", \"1 586\\n0 1 1 0 5\", \"3 12\\n0 5 0\", \"1 586\\n1 1 4 -1 5\", \"3 6\\n0 5 -1\", \"1 330\\n0 1 3 -1 5\", \"2 7\\n0 0 -1\", \"1 451\\n0 1 1 -1 5\", \"2 7\\n0 9 -1\", \"1 586\\n0 2 2 -1 5\", \"2 7\\n-1 6 0\", \"0 586\\n0 2 1 -2 5\", \"2 7\\n0 0 0\", \"1 586\\n-1 2 1 -3 5\", \"2 7\\n-1 1 0\", \"1 988\\n-1 2 1 -2 0\", \"0 13\\n0 1 0\", \"1 226\\n-1 2 1 -2 5\", \"1 7\\n0 2 0\", \"1 590\\n-1 1 1 -3 5\", \"0 7\\n0 4 1\", \"1 590\\n-1 1 1 0 6\", \"0 7\\n0 1 2\", \"0 590\\n0 1 1 0 5\", \"0 6\\n0 1 0\", \"2 590\\n0 0 1 0 5\", \"2 590\\n0 1 1 1 1\", \"4 590\\n0 1 2 1 5\", \"4 1135\\n0 2 1 1 5\", \"4 1135\\n1 1 0 1 5\", \"4 1135\\n0 1 1 2 5\", \"5 1135\\n2 1 1 2 5\", \"5 1135\\n1 1 1 2 18\", \"5 84\\n0 1 1 2 9\", \"0 84\\n1 1 1 4 9\", \"5 400\\n3 1 5 2 5\", \"3 6\\n1 3 1\", \"6 20\\n10 4 5 10 25 3\", \"0 400\\n3 1 4 1 4\", \"3 6\\n0 7 4\", \"1 734\\n3 2 4 1 10\", \"3 6\\n2 7 0\", \"1 734\\n3 1 3 0 5\", \"3 6\\n1 6 2\", \"2 1126\\n0 1 4 0 9\", \"5 400\\n3 1 4 1 5\", \"3 6\\n1 4 3\", \"6 20\\n10 4 3 10 25 2\"], \"outputs\": [\"1\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"0\\n\", \"5\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"5\", \"1\", \"3\"]}", "source": "taco"}
|
AtCoDeer the deer has N cards with positive integers written on them. The number on the i-th card (1≤i≤N) is a_i.
Because he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.
Then, for each card i, he judges whether it is unnecessary or not, as follows:
- If, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.
- Otherwise, card i is NOT unnecessary.
Find the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary.
-----Constraints-----
- All input values are integers.
- 1≤N≤5000
- 1≤K≤5000
- 1≤a_i≤10^9 (1≤i≤N)
-----Partial Score-----
- 300 points will be awarded for passing the test set satisfying N,K≤400.
-----Input-----
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
-----Output-----
Print the number of the unnecessary cards.
-----Sample Input-----
3 6
1 4 3
-----Sample Output-----
1
There are two good sets: {2,3} and {1,2,3}.
Card 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.
For card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.
Neither is card 3 for a similar reason, hence the answer is 1.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"1010\\n1110\", \"1\\n1\", \"11010\\n11001\", \"0100100\\n1111101\", \"1010\\n1111\", \"0100100\\n1100000\", \"1010\\n0000\", \"0100100\\n0000001\", \"11010\\n11011\", \"0100100\\n0111111\", \"1010\\n1010\", \"11010\\n10011\", \"0100100\\n0101111\", \"1010\\n1011\", \"11010\\n10111\", \"0100100\\n0101110\", \"1010\\n1001\", \"11010\\n10110\", \"0100100\\n0101100\", \"1010\\n0001\", \"11010\\n11110\", \"0100100\\n0101011\", \"1010\\n0011\", \"11010\\n11010\", \"0100100\\n0101010\", \"1010\\n1000\", \"11010\\n01010\", \"0100100\\n0100010\", \"1010\\n0100\", \"11010\\n01110\", \"0100100\\n0100000\", \"1010\\n0010\", \"11010\\n10010\", \"1010\\n0110\", \"11010\\n00011\", \"0100100\\n1100100\", \"1010\\n0111\", \"11010\\n00111\", \"0100100\\n1000100\", \"1010\\n0101\", \"11010\\n00101\", \"0100100\\n1000101\", \"1010\\n1101\", \"11010\\n01101\", \"0100100\\n1100101\", \"11010\\n01100\", \"0100100\\n1100001\", \"11010\\n01111\", \"0100100\\n0100001\", \"11010\\n01011\", \"0100100\\n0110001\", \"11010\\n00010\", \"11010\\n00000\", \"0100100\\n0000101\", \"11010\\n10000\", \"0100100\\n0100101\", \"11010\\n00001\", \"0100100\\n0100111\", \"11010\\n00100\", \"0100100\\n0000111\", \"11010\\n00110\", \"0100100\\n0001101\", \"11010\\n01001\", \"0100100\\n1001101\", \"11010\\n01000\", \"0100100\\n1001100\", \"11010\\n11000\", \"0100100\\n1101101\", \"11010\\n11111\", \"0100100\\n1000001\", \"11010\\n11100\", \"0100100\\n1000011\", \"11010\\n10100\", \"0100100\\n1100011\", \"11010\\n10101\", \"0100100\\n1110011\", \"11010\\n11101\", \"0100100\\n0110011\", \"0100100\\n0110111\", \"0100100\\n1110111\", \"0100100\\n1110110\", \"0100100\\n1100110\", \"0100100\\n1100111\", \"0100100\\n1111110\", \"0100100\\n0111011\", \"0100100\\n1111011\", \"0100100\\n0110101\", \"0100100\\n1110101\", \"0100100\\n1000111\", \"0100100\\n1101111\", \"0100100\\n1101011\", \"0100100\\n1001011\", \"0100100\\n1001111\", \"0100100\\n0000011\", \"0100100\\n0010101\", \"0100100\\n0010001\", \"0100100\\n0010111\", \"0100100\\n0011111\", \"0100100\\n1011111\", \"0100100\\n0111101\", \"1010\\n1100\", \"1\\n0\", \"11010\\n10001\", \"0100100\\n1111111\"], \"outputs\": [\"1\\n\", \"0\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"5\\n\", \"-1\\n\", \"6\\n\", \"1\\n\", \"4\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"4\\n\", \"3\\n\", \"0\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"-1\\n\", \"4\\n\", \"5\\n\", \"1\\n\", \"6\\n\", \"2\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"6\\n\", \"3\\n\", \"6\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"6\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"3\\n\", \"3\", \"-1\", \"4\", \"5\"]}", "source": "taco"}
|
You have two strings A = A_1 A_2 ... A_n and B = B_1 B_2 ... B_n of the same length consisting of 0 and 1.
You can transform A using the following operations in any order and as many times as you want:
* Shift A by one character to the left (i.e., if A = A_1 A_2 ... A_n, replace A with A_2 A_3 ... A_n A_1).
* Shift A by one character to the right (i.e., if A = A_1 A_2 ... A_n, replace A with A_n A_1 A_2 ... A_{n-1}).
* Choose any i such that B_i = 1. Flip A_i (i.e., set A_i = 1 - A_i).
You goal is to make strings A and B equal.
Print the smallest number of operations required to achieve this, or -1 if the goal is unreachable.
Constraints
* 1 \leq |A| = |B| \leq 2,000
* A and B consist of 0 and 1.
Input
Input is given from Standard Input in the following format:
A
B
Output
Print the smallest number of operations required to make strings A and B equal, or -1 if the goal is unreachable.
Examples
Input
1010
1100
Output
3
Input
1
0
Output
-1
Input
11010
10001
Output
4
Input
0100100
1111111
Output
5
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 4 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 4\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 1 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 5 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 2 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 74\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 1\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 4 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 3 2 9 6\\n2 9\\n1 3 3 3 3 3 2 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 3 6 1 1 3 1 3 1 1 1 3 1 2 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 63\\n4 2\\n6 6 6 5 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 74\\n4 2\\n6 6 6 7 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 5\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 2 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 0 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 1\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 2 1 3\\n\", \"7\\n1 2\\n1 1\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 12 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 1 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 5\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 2 3 3 6 1 1 3 1 3 1 1 6 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 2 2 2 3 6\\n3 3\\n1 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 3 6 1 1 3 1 3 1 1 1 3 1 2 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 0\\n2 2\\n1 4 2 1\\n4 2\\n50 60 50 9 1 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 2 2 2 3 6\\n3 3\\n1 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 2 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 3 6 1 1 3 1 3 1 1 1 3 1 2 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 0\\n2 2\\n1 4 2 1\\n4 2\\n50 60 50 9 1 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 2 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 1 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 5\\n2 9\\n1 4 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 2 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 1 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 4 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 5 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 3 1\\n4 2\\n50 50 50 9 1 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 4 3 1 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 8 2 2 9 6\\n2 9\\n1 3 2 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 1\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 63\\n4 2\\n6 6 6 5 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 2 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 74\\n4 2\\n6 6 6 7 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 5 4 6 1 1 3 1 3 1 1 3 3 2 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 2 2 2 3 6\\n3 3\\n1 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 0\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 3 6 1 1 3 1 3 1 1 1 3 1 2 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 2 2 2 3 6\\n3 3\\n1 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 2 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 4 3 3 6 1 1 3 1 3 1 1 1 3 1 2 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 3\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 1 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 2 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 6 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 5 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n2 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 5\\n2 9\\n1 4 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 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2\\n1 2 8 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 0 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 2 3 3 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 3\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 56 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 6 3 4 6 1 1 3 1 3 1 1 3 3 1 1 3\\n\", \"7\\n1 2\\n1 2\\n3 2\\n1 0 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 1 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 6 6 2 2 9 6\\n2 9\\n1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 2 1 3\\n\", \"7\\n1 2\\n1 1\\n3 2\\n1 1 2 2 3 6\\n3 3\\n3 4 4 1 1 1 1 1 2\\n2 2\\n1 2 2 1\\n4 2\\n50 50 50 50 3 50 50 50\\n4 2\\n6 6 12 6 2 2 9 6\\n2 9\\n1 4 3 1 3 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\"1\\n1\\n0\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n7\\n\", \"0\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n2\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n3\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n12\\n\", \"1\\n0\\n4\\n0\\n1\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n0\\n0\\n1\\n7\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n3\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n3\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n1\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n4\\n\", \"1\\n2\\n0\\n0\\n0\\n0\\n12\\n\", \"0\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n7\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n2\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n4\\n0\\n0\\n1\\n7\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n9\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n7\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n8\\n\", \"1\\n1\\n4\\n0\\n1\\n0\\n1\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n3\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n1\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n4\\n\", \"1\\n2\\n0\\n0\\n0\\n0\\n12\\n\", \"1\\n0\\n2\\n0\\n1\\n0\\n1\\n\", \"1\\n1\\n3\\n0\\n1\\n1\\n1\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n7\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n4\\n\", \"1\\n1\\n0\\n0\\n0\\n0\\n9\\n\", \"1\\n1\\n4\\n0\\n0\\n1\\n7\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n9\\n\", \"1\\n0\\n4\\n0\\n0\\n1\\n3\\n\", \"1\\n1\\n4\\n0\\n0\\n0\\n5\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n8\\n\", \"1\\n1\\n4\\n0\\n1\\n1\\n1\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n0\\n\", \"1\\n1\\n4\\n1\\n0\\n0\\n1\\n\", \"1\\n1\\n2\\n0\\n0\\n0\\n4\\n\", \"1\\n0\\n4\\n0\\n0\\n0\\n1\\n\"]}", "source": "taco"}
|
It is the hard version of the problem. The only difference is that in this version $1 \le n \le 300$.
In the cinema seats can be represented as the table with $n$ rows and $m$ columns. The rows are numbered with integers from $1$ to $n$. The seats in each row are numbered with consecutive integers from left to right: in the $k$-th row from $m (k - 1) + 1$ to $m k$ for all rows $1 \le k \le n$.
$1$
$2$
$\cdots$
$m - 1$
$m$
$m + 1$
$m + 2$
$\cdots$
$2 m - 1$
$2 m$
$2m + 1$
$2m + 2$
$\cdots$
$3 m - 1$
$3 m$
$\vdots$
$\vdots$
$\ddots$
$\vdots$
$\vdots$
$m (n - 1) + 1$
$m (n - 1) + 2$
$\cdots$
$n m - 1$
$n m$
The table with seats indices
There are $nm$ people who want to go to the cinema to watch a new film. They are numbered with integers from $1$ to $nm$. You should give exactly one seat to each person.
It is known, that in this cinema as lower seat index you have as better you can see everything happening on the screen. $i$-th person has the level of sight $a_i$. Let's define $s_i$ as the seat index, that will be given to $i$-th person. You want to give better places for people with lower sight levels, so for any two people $i$, $j$ such that $a_i < a_j$ it should be satisfied that $s_i < s_j$.
After you will give seats to all people they will start coming to their seats. In the order from $1$ to $nm$, each person will enter the hall and sit in their seat. To get to their place, the person will go to their seat's row and start moving from the first seat in this row to theirs from left to right. While moving some places will be free, some will be occupied with people already seated. The inconvenience of the person is equal to the number of occupied seats he or she will go through.
Let's consider an example: $m = 5$, the person has the seat $4$ in the first row, the seats $1$, $3$, $5$ in the first row are already occupied, the seats $2$ and $4$ are free. The inconvenience of this person will be $2$, because he will go through occupied seats $1$ and $3$.
Find the minimal total inconvenience (the sum of inconveniences of all people), that is possible to have by giving places for all people (all conditions should be satisfied).
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 300$) — the number of rows and places in each row respectively.
The second line of each test case contains $n \cdot m$ integers $a_1, a_2, \ldots, a_{n \cdot m}$ ($1 \le a_i \le 10^9$), where $a_i$ is the sight level of $i$-th person.
It's guaranteed that the sum of $n \cdot m$ over all test cases does not exceed $10^5$.
-----Output-----
For each test case print a single integer — the minimal total inconvenience that can be achieved.
-----Examples-----
Input
7
1 2
1 2
3 2
1 1 2 2 3 3
3 3
3 4 4 1 1 1 1 1 2
2 2
1 1 2 1
4 2
50 50 50 50 3 50 50 50
4 2
6 6 6 6 2 2 9 6
2 9
1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3
Output
1
0
4
0
0
0
1
-----Note-----
In the first test case, there is a single way to give seats: the first person sits in the first place and the second person — in the second. The total inconvenience is $1$.
In the second test case the optimal seating looks like this:
In the third test case the optimal seating looks like this:
The number in a cell is the person's index that sits on this place.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[3], [4], [100], [97], [101], [120], [130]], \"outputs\": [[[2, 5]], [[3, 5]], [[97, 101]], [[89, 101]], [[97, 103]], [[113, 127]], [[127, 131]]]}", "source": "taco"}
|
We need a function ```prime_bef_aft()``` that gives the largest prime below a certain given value ```n```,
```befPrime or bef_prime``` (depending on the language),
and the smallest prime larger than this value,
```aftPrime/aft_prime``` (depending on the language).
The result should be output in a list like the following:
```python
prime_bef_aft(n) == [befPrime, aftPrime]
```
If n is a prime number it will give two primes, n will not be included in the result.
Let's see some cases:
```python
prime_bef_aft(100) == [97, 101]
prime_bef_aft(97) == [89, 101]
prime_bef_aft(101) == [97, 103]
```
Range for the random tests:
```1000 <= n <= 200000```
(The extreme and special case n = 2 will not be considered for the tests. Thanks Blind4Basics)
Happy coding!!
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 3\\n1000000 1000000 1000000\\n2 1\\n1 3\\n3 2\\n\", \"4 3\\n10 10 5 1\\n2 1\\n3 1\\n3 4\\n\", \"4 3\\n1 2 8 6\\n1 3\\n1 4\\n3 4\\n\", \"6 8\\n69 36 41 23 91 35\\n1 2\\n3 1\\n3 2\\n1 4\\n3 4\\n3 5\\n5 4\\n4 6\\n\", \"6 7\\n85 2 34 6 83 61\\n1 2\\n2 3\\n4 2\\n4 3\\n1 5\\n4 5\\n6 3\\n\", \"6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n2 6\\n6 3\\n\", \"6 6\\n33 76 98 59 4 69\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n\", \"4 4\\n9 3 3 1\\n1 2\\n3 1\\n3 2\\n4 3\\n\", \"4 3\\n5 3 4 4\\n2 1\\n4 1\\n3 4\\n\", \"4 3\\n5 1 10 1\\n2 1\\n3 2\\n1 4\\n\", \"6 5\\n59 69 52 38 93 53\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n\", \"6 8\\n64 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 4\\n\", \"4 5\\n4 10 3 9\\n1 2\\n3 1\\n3 2\\n2 4\\n4 3\\n\", \"4 2\\n2 9 8 4\\n1 3\\n4 2\\n\", \"6 10\\n17 5 55 24 55 74\\n1 3\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n\", \"3 3\\n1 1 999999\\n1 2\\n2 3\\n3 1\\n\", \"3 3\\n1000000 1000000 1000000\\n1 2\\n2 3\\n1 3\\n\", \"6 6\\n39 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 6\\n\", \"6 8\\n36 19 99 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n1 5\\n5 4\\n1 6\\n6 2\\n\", \"3 0\\n1 1 1\\n\", \"4 3\\n5 5 9 6\\n3 2\\n1 4\\n3 4\\n\", \"3 3\\n100000 100000 100001\\n1 2\\n2 3\\n3 1\\n\", \"6 11\\n95 81 74 94 60 69\\n3 2\\n1 4\\n4 2\\n3 4\\n1 5\\n5 2\\n5 3\\n1 6\\n2 6\\n3 6\\n4 6\\n\", \"3 3\\n999999 1 1\\n1 2\\n2 3\\n3 1\\n\", \"4 0\\n9 8 2 10\\n\", \"4 3\\n6 8 10 1\\n2 3\\n1 4\\n3 4\\n\", \"4 3\\n16 10 5 1\\n2 1\\n3 1\\n3 4\\n\", \"6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n\", \"6 6\\n33 76 98 59 4 18\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n\", \"6 5\\n59 69 52 38 93 52\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n\", \"6 8\\n64 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n\", \"4 5\\n4 10 3 9\\n1 2\\n4 1\\n3 2\\n2 4\\n4 3\\n\", \"6 10\\n17 5 55 24 55 74\\n1 4\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n\", \"6 6\\n39 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n\", \"6 8\\n36 19 53 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n1 5\\n5 4\\n1 6\\n6 2\\n\", \"4 5\\n4 10 3 9\\n1 2\\n4 1\\n4 2\\n2 4\\n4 3\\n\", \"6 6\\n38 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n\", \"6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n\", \"6 6\\n43 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n\", \"6 6\\n43 26 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n\", \"6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n6 5\\n6 2\\n6 3\\n6 1\\n\", \"6 7\\n85 2 34 6 83 61\\n1 2\\n2 3\\n4 2\\n4 3\\n1 3\\n4 5\\n6 3\\n\", \"3 3\\n0 1 999999\\n1 2\\n2 3\\n3 1\\n\", \"6 6\\n39 15 73 82 37 19\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 6\\n\", \"6 8\\n36 19 99 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n2 5\\n5 4\\n1 6\\n6 2\\n\", \"3 3\\n1 1 3\\n1 2\\n2 3\\n3 1\\n\", \"6 6\\n33 116 98 59 4 18\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n\", \"6 5\\n94 69 52 38 93 52\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n\", \"6 8\\n104 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n\", \"6 10\\n29 5 55 24 55 74\\n1 4\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n\", \"4 4\\n9 3 3 1\\n1 2\\n2 1\\n3 2\\n4 3\\n\", \"4 3\\n5 1 10 0\\n2 1\\n3 2\\n1 4\\n\", \"3 3\\n1 1 999999\\n1 2\\n2 3\\n2 1\\n\", \"4 0\\n9 12 2 10\\n\", \"4 3\\n6 8 10 1\\n2 1\\n1 4\\n3 4\\n\", \"6 6\\n92 56 15 83 30 28\\n2 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n\", \"6 6\\n33 76 98 59 4 18\\n1 2\\n3 2\\n5 1\\n3 5\\n4 5\\n6 5\\n\", \"4 3\\n1 1 10 0\\n2 1\\n3 2\\n1 4\\n\", \"6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n\", \"4 0\\n9 23 2 10\\n\", \"4 3\\n6 8 10 1\\n2 1\\n2 4\\n3 4\\n\", \"6 6\\n92 56 15 83 30 28\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n\", \"4 0\\n9 0 2 10\\n\", \"4 3\\n5 8 10 1\\n2 1\\n2 4\\n3 4\\n\", \"6 6\\n92 56 15 83 30 21\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n\", \"6 8\\n64 44 5 31 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n\", \"4 0\\n9 0 2 7\\n\", \"6 6\\n92 44 15 83 30 21\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n\", \"6 8\\n64 44 5 36 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n\", \"4 0\\n9 0 2 0\\n\", \"6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n\", \"4 0\\n9 0 3 0\\n\", \"6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n1 5\\n6 5\\n6 2\\n6 3\\n6 1\\n\", \"4 3\\n3 1 10 1\\n2 1\\n3 2\\n1 4\\n\", \"6 5\\n59 69 52 38 93 53\\n4 2\\n1 5\\n6 1\\n4 6\\n5 2\\n\", \"6 8\\n64 44 5 31 14 16\\n1 4\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 4\\n\", \"4 2\\n0 9 8 4\\n1 3\\n4 2\\n\", \"3 0\\n0 1 1\\n\", \"4 3\\n5 9 9 6\\n3 2\\n1 4\\n3 4\\n\", \"4 0\\n9 8 2 17\\n\", \"3 2\\n2 3 3\\n2 3\\n2 1\\n\", \"4 3\\n28 10 5 1\\n2 1\\n3 1\\n3 4\\n\", \"6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 1\\n\", \"4 3\\n5 0 10 0\\n2 1\\n3 2\\n1 4\\n\", \"4 3\\n2 8 10 1\\n2 1\\n1 4\\n3 4\\n\", \"6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n2 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n\", \"4 4\\n1 1 1 1\\n1 2\\n2 3\\n3 4\\n4 1\\n\", \"3 3\\n1 2 3\\n1 2\\n2 3\\n3 1\\n\", \"3 2\\n2 3 4\\n2 3\\n2 1\\n\"], \"outputs\": [\"3000000\", \"-1\", \"15\", \"133\", \"42\", \"-1\", \"113\", \"15\", \"-1\", \"-1\", \"205\", \"85\", \"17\", \"-1\", \"115\", \"1000001\", \"3000000\", \"94\", \"132\", \"-1\", \"-1\", \"300001\", \"215\", \"1000001\", \"-1\", \"-1\", \"-1\\n\", \"135\\n\", \"113\\n\", \"204\\n\", \"85\\n\", \"22\\n\", \"96\\n\", \"94\\n\", \"132\\n\", \"23\\n\", \"93\\n\", \"124\\n\", \"98\\n\", \"109\\n\", \"78\\n\", \"42\\n\", \"1000000\\n\", \"73\\n\", \"79\\n\", \"5\\n\", \"153\\n\", \"239\\n\", \"125\\n\", \"108\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"124\\n\", \"-1\\n\", \"-1\\n\", \"124\\n\", \"-1\\n\", \"124\\n\", \"-1\\n\", \"98\\n\", \"-1\\n\", \"-1\\n\", \"85\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\", \"6\", \"-1\"]}", "source": "taco"}
|
A little boy Gerald entered a clothes shop and found out something very unpleasant: not all clothes turns out to match. For example, Gerald noticed that he looks rather ridiculous in a smoking suit and a baseball cap.
Overall the shop sells n clothing items, and exactly m pairs of clothing items match. Each item has its price, represented by an integer number of rubles. Gerald wants to buy three clothing items so that they matched each other. Besides, he wants to spend as little money as possible. Find the least possible sum he can spend.
Input
The first input file line contains integers n and m — the total number of clothing items in the shop and the total number of matching pairs of clothing items (<image>).
Next line contains n integers ai (1 ≤ ai ≤ 106) — the prices of the clothing items in rubles.
Next m lines each contain a pair of space-separated integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi). Each such pair of numbers means that the ui-th and the vi-th clothing items match each other. It is guaranteed that in each pair ui and vi are distinct and all the unordered pairs (ui, vi) are different.
Output
Print the only number — the least possible sum in rubles that Gerald will have to pay in the shop. If the shop has no three clothing items that would match each other, print "-1" (without the quotes).
Examples
Input
3 3
1 2 3
1 2
2 3
3 1
Output
6
Input
3 2
2 3 4
2 3
2 1
Output
-1
Input
4 4
1 1 1 1
1 2
2 3
3 4
4 1
Output
-1
Note
In the first test there only are three pieces of clothing and they all match each other. Thus, there is only one way — to buy the 3 pieces of clothing; in this case he spends 6 roubles.
The second test only has three pieces of clothing as well, yet Gerald can't buy them because the first piece of clothing does not match the third one. Thus, there are no three matching pieces of clothing. The answer is -1.
In the third example there are 4 pieces of clothing, but Gerald can't buy any 3 of them simultaneously. The answer is -1.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 151 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 7 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 15 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 , 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 7 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 13 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 15 + 81 / 24 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 7 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 1 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 151 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 9 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 7 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 9 - 0 - 8 * 2\\n19: 8 / (2 - 3 + 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / 2( - 3 * 7)\\n1153: 10 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 , 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 , 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 14\\n0:\", \"5: 3 - 3\\n17: 1 , 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 , 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 0 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 , 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 89 + 81 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 4 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 4 * 2\\n29: 8 / (2 - 6 ) 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) , 7\\n11: 1 / 8 - 5 . 4 * 2\\n29: 8 / (2 - 6 ) 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 11 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 4 / 7 + ( 83 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 * 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 0 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 151 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 0 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 17 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 7 - 8 * 2\\n19: 8 . (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 . 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 15 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 , 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 . 7 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 21 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 15 + 81 / 24 ) + 11\\n0:\", \"5: 3 - 3\\n17: 0 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 1 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 151 / 22 ) + 4\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 10\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 9 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 24 ) + 18\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 7 + ( 50 + 81 / 6 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 20 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 0 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 5 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n18: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / 2( - 3 * 7)\\n1153: 10 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 1 - 5 - 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 ) (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 0 / 7 + ( 50 + 81 / 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 12 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 15 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (3 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 + 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 0 5 * )2 + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 14\\n0:\", \"5: 3 - 3\\n17: 1 , 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 . 7 + ( 50 + 81 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * )2 + 7\\n11: 1 / 8 , 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 9\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 0 7 + ( 50 + 81 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 0 * 2( + 3 / 5 * 2) + 7\\n11: 1 / 8 , 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 261 / 24 ) , 14\\n0:\", \"5: 3 - 0\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 89 + 81 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 , 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7)\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 1 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 8 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 3 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) + 3\\n11: 1 / 8 - 5 . 4 * 2\\n29: 8 / (2 - 6 * 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 * 2) + 7\\n11: 1 / 8 - 5 . 4 * 2\\n29: 6 / (2 - 6 ) 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 3 - 3\\n18: 1 + 3 ) (2 + 3 / 1 ) 2) , 7\\n11: 1 / 8 - 5 . 4 * 2\\n29: 8 / (2 - 6 ) 7(\\n1153: 5 * 3 / 7 + ( 89 + 4 . 24 ) * 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 15 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 11 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 0 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 4 / 7 + ( 83 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 * 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 1 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * 2( + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 15 + 81 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 0 + 3 * (2 + 3 / 5 * 2) , 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 151 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 0 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 49 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 0 8 - 7 - 8 * 2\\n19: 8 . (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 , 0 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 . 7 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 0 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 , ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 1 * 7)\\n1153: 10 * 3 / 7 + ( 76 + 151 / 22 ) + 4\\n0:\", \"5: 2 - 3\\n17: 0 + 3 * (2 + 3 / 5 * 2) * 10\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 ) 4 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 0 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 20 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 0 / 8 - 5 - 8 * 2\\n19: 8 . (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 50 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 5 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 0 / 5 + ( 50 + 81 / 6 ) + 14\\n0:\", \"5: 2 - 3\\n18: 1 + 3 * (2 + 3 / 5 * 2) * 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 . 2( - 3 * 7)\\n1153: 10 ) 0 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\", \"5: 3 - 3\\n17: 1 + 3 * (2 + 3 / 1 * 2) + 7\\n11: 1 / 1 - 5 - 8 * 2\\n29: 8 / (2 - 3 * 7)\\n1153: 5 * 3 / 7 + ( 27 + 81 / 24 ) + 11\\n0:\", \"5: 2 - 3\\n17: 1 + 3 ) (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 3\\n19: 8 / (2 - 3 * 7)\\n1153: 18 * 0 / 5 + ( 50 + 132 / 24 ) + 14\\n0:\", \"5: 2 - 3\\n17: 1 + 3 * (2 + 3 / 5 * 2) + 7\\n11: 1 / 8 - 5 - 8 * 2\\n19: 8 / (2 - 3 * 7)\\n1153: 10 * 3 / 7 + ( 50 + 81 / 22 ) + 11\\n0:\"], \"outputs\": [\"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*4/7+(50+81/22)+11 = 587 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+14 = 957 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+151/22)+11 = 1023 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-8*2 = 2 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-7-8*2 = 6 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-8*2 = 2 (mod 11)\\nNG\\n10*3/7+(15+81/24)+11 = 919 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1,3*(2+3/5*2)+7 = 1 (mod 17)\\n1/8-7-8*2 = 6 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-13*2 = 3 (mod 11)\\nNG\\n10*3/7+(15+81/24)+11 = 919 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*0/7+(50+81/24)+14 = 788 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-1*7) = 6 (mod 19)\\n10*3/7+(50+151/22)+11 = 1023 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/9-0-8*2 = 0 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/7+(50+81/24)+14 = 788 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)0/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/9-0-8*2 = 0 (mod 11)\\n8/(2-3+7) = 14 (mod 19)\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n5*3/7+(50+81/24)+11 = 293 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+81/24)+14 = 788 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/2(-3*7) = 4 (mod 19)\\n10)0/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)+11 = 293 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)*11 = 1104 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*2)+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)*11 = 1104 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1,3*(2+3/1*2)+7 = 1 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)*11 = 1104 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+261/24)+14 = 219 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1,3*(2+3/1*2)+7 = 1 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81.24)*11 = 792 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+261/24),14 = 205 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1,3*(2+3/1*2)+7 = 1 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(50+81.24)*11 = 792 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8,5-8*3 = 7 (mod 11)\\nNG\\n10*0/5+(50+261/24),14 = 205 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(50+81.24)*11 = 792 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+0*2(+3/5*)2+7 = 1 (mod 17)\\n1/8,5-8*3 = 7 (mod 11)\\nNG\\n10*0/5+(50+261/24),14 = 205 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(89+81.24)*11 = 831 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 14 (mod 18)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2)+7 = 4 (mod 18)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2)+7 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2)+7 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n8/(2-6)7( = 27 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2),7 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n8/(2-6)7( = 27 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/11+(50+81/22)+11 = 15 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*4/7+(83+81/22)+11 = 620 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1*3*(2+3/5*2)+7 = 3 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*2)+7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+14 = 957 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n0+3*(2+3/5*2)+7 = 3 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+151/22)+11 = 1023 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+0/5*2)+7 = 14 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-8*2 = 2 (mod 11)\\nNG\\n10*3/7+(50+81/17)+11 = 913 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-7-8*2 = 6 (mod 11)\\n8.(2-3*7) = 8 (mod 19)\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2.3 = 2 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-8*2 = 2 (mod 11)\\nNG\\n10*3/7+(15+81/24)+11 = 919 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1,3*(2+3/5*2)+7 = 1 (mod 17)\\n1/8.7-8*2 = 7 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-21*2 = 9 (mod 11)\\nNG\\n10*3/7+(15+81/24)+11 = 919 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n0+3*(2+3/5*2)+7 = 3 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/24)+11 = 954 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-1*7) = 6 (mod 19)\\n10*3/7+(50+151/22)+4 = 1016 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*10 = 12 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/9-0-8*2 = 0 (mod 11)\\nNG\\n10*3/7+(50+81/24)+18 = 961 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/7+(50+81/6)+14 = 654 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n20)0/7+(50+81/22)+11 = 20 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n0/8-5-8*2 = 1 (mod 11)\\nNG\\n5*3/7+(50+81/24)+11 = 293 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+5*(2+3/5*2)+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+81/24)+14 = 788 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 18)\\n1/8-5-8*2 = 8 (mod 11)\\n8/2(-3*7) = 4 (mod 19)\\n10)0/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/1-5-8*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)+11 = 293 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3)(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*0/7+(50+81/24)*11 = 443 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*2)+7 = 7 (mod 17)\\n1/8-5-12*3 = 10 (mod 11)\\nNG\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.15*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(50+81/24)*11 = 1104 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\n8/(3-3*7) = 8 (mod 19)\\n10*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\n8/(2-3+7) = 14 (mod 19)\\n10*0/5+(50+261/24)+14 = 219 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+305*)2+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+261/24),14 = 205 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1,3*(2+3/1*2)+7 = 1 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3.7+(50+81.24)*11 = 15 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*)2+7 = 7 (mod 17)\\n1/8,5-8*3 = 7 (mod 11)\\nNG\\n10*0/5+(50+261/24),9 = 205 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*307+(50+81.24)*11 = 513 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+0*2(+3/5*2)+7 = 1 (mod 17)\\n1/8,5-8*3 = 7 (mod 11)\\nNG\\n10*0/5+(50+261/24),14 = 205 (mod 1153)\\n\", \"3-0 = 3 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(89+81.24)*11 = 831 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2,3/1*2)+7 = 7 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7) = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+1/1*2)+7 = 3 (mod 17)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 14 (mod 18)\\n1/8-5.8*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+3.24)*11 = 753 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2)+3 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n8/(2-6*7( = 23 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1*2)+7 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n6/(2-6)7( = 13 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3)(2+3/1)2),7 = 4 (mod 18)\\n1/8-5.4*2 = 2 (mod 11)\\n8/(2-6)7( = 27 (mod 29)\\n5*3/7+(89+4.24)*11 = 754 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-15*2 = 5 (mod 11)\\nNG\\n10*3/11+(50+81/22)+11 = 15 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-0-8*2 = 2 (mod 11)\\nNG\\n10*4/7+(83+81/22)+11 = 620 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1*3*(2+3/5*2)+7 = 3 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*1/7+(50+81/24)+11 = 457 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*2(+3/5*2)+7 = 7 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(15+81/24)+14 = 922 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n0+3*(2+3/5*2),7 = 13 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+151/22)+11 = 1023 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+0/5*2)+7 = 14 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+49/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n108-7-8*2 = 8 (mod 11)\\n8.(2-3*7) = 8 (mod 19)\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1,0*(2+3/5*2)+7 = 1 (mod 17)\\n1/8.7-8*2 = 7 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n0+3*(2+3/5*2)+7 = 3 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7,(50+81/24)+11 = 169 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\n8/(2-1*7) = 6 (mod 19)\\n10*3/7+(76+151/22)+4 = 1042 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n0+3*(2+3/5*2)*10 = 11 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10)4/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 17)\\n108-5-8*2 = 10 (mod 11)\\nNG\\n20)0/7+(50+81/22)+11 = 20 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n0/8-5-8*2 = 1 (mod 11)\\n8.(2-3*7) = 8 (mod 19)\\n5*3/7+(50+81/24)+11 = 293 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+5*(2+3/5*2)+7 = 7 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n10*0/5+(50+81/6)+14 = 654 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)*7 = 7 (mod 18)\\n1/8-5-8*2 = 8 (mod 11)\\n8.2(-3*7) = 8 (mod 19)\\n10)0/7+(50+81/22)+11 = 10 (mod 1153)\\n\", \"3-3 = 0 (mod 5)\\n1+3*(2+3/1*2)+7 = 15 (mod 17)\\n1/1-5-8*2 = 2 (mod 11)\\n8/(2-3*7) = 24 (mod 29)\\n5*3/7+(27+81/24)+11 = 270 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3)(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*3 = 0 (mod 11)\\nNG\\n18*0/5+(50+132/24)+14 = 646 (mod 1153)\\n\", \"2-3 = 4 (mod 5)\\n1+3*(2+3/5*2)+7 = 4 (mod 17)\\n1/8-5-8*2 = 8 (mod 11)\\nNG\\n10*3/7+(50+81/22)+11 = 915 (mod 1153)\"]}", "source": "taco"}
|
The reciprocal of all non-zero real numbers is real, but the reciprocal of an integer is not necessarily an integer. This is the reason why 3/2 * 2 = 2 even though 3.0 / 2.0 * 2.0 = 3.0 in C language. However, if you consider integers with the same remainder after dividing by a prime number as the same, you can make all integers other than 0 have the reciprocal.
Write x ≡ y (mod p) when the remainders of the integers x and y divided by p are equal. If p is a prime number and we consider such x and y to be the same, then all integers n are x ≡ n (mod p) for any integer x from 0 to p−1. You can see that we should consider a world consisting only of the set {0, 1, 2, ..., p−1}.
Addition, subtraction, multiplication and division in this world are as follows.
* The value of the addition x + y is the number z from 0 to p−1, which is x + y ≡ z (mod p).
* The value of the subtraction x−y is x−y ≡ x + m (mod p) for the number m (which corresponds to y) from 0 to p−1, which is y + m ≡ 0 (mod p). It is obtained from the fact that. For example, when p = 5, then 4 + 1 ≡ 0 (mod 5). At this time, the value of 2-4 becomes 3 from 2-4 ≡ 2 + 1 ≡ 3 (mod 5).
* The value of multiplication x * y is the number z from 0 to p−1, which is x * y ≡ z (mod p).
* The value of division x / y is x / y ≡ x * d (mod p) for the number d from 0 to p−1, which is y * d ≡ 1 (mod p) (this is the reciprocal of y). ). For example, when p = 5, 3 is the reciprocal of 2 from 2 * 3 ≡ 1 (mod 5). Then, from 1/2 ≡ 1 * 3 ≡ 3 (mod 5), the value of 1/2 becomes 3.
In this way, all four arithmetic operations of addition, subtraction, multiplication and division fall within the range of 0 to p-1. At this time, the set {0,1, ..., p−1} is called a finite field of p. Within this finite field, you can construct arithmetic expressions using addition, subtraction, multiplication, division, numbers from 0 to p-1, and parentheses.
We can see that all non-zero elements of the finite field of p have reciprocals from the famous theorem ap−1 ≡ 1 (mod p) called Fermat's Little Theorem (where p is a prime number and a and p are prime numbers). Coprime). Because all the elements x of the finite field of p are relatively prime to p, this theorem gives x * xp-2 ≡ 1 (mod p) and xp-2 is the reciprocal of x.
Now, when you are given a prime number and an expression, create a calculator program that calculates the expression with a finite field of that prime number.
input
The input consists of multiple datasets. The end of the input is indicated by a line 0: with only 0 followed by a colon. Each dataset is given in the following format.
p: exp
The dataset is one row, where p (2 ≤ p ≤ 46000) is a prime number and exp is an arithmetic expression. exp consists of addition, subtraction, multiplication and division (+,-, *, /, respectively), parentheses, and numbers from 0 to p-1. One or more spaces can appear before and after operators, numbers, parentheses, etc. The length of exp does not exceed 100,000.
The number of datasets does not exceed 1000.
output
The calculation result is output for each data set. The output format is as follows.
exp = val (mod p)
val is the result of the arithmetic exp on a finite field of p. However, if division by 0 is included, NG is output. Also, do not leave spaces before and after the addition, subtraction, multiplication, division, parentheses, and numbers that appear in exp. However, leave one space before and after the =. Also, leave a space between val and the opening parenthesis, and between mod and p.
Example
Input
5: 2 - 3
17: 1 + 3 * (2 + 3 / 5 * 2) + 7
11: 1 / 8 - 5 - 8 * 2
19: 8 / (2 - 3 * 7)
1153: 10 * 3 / 7 + ( 50 + 81 / 22 ) + 11
0:
Output
2-3 = 4 (mod 5)
1+3*(2+3/5*2)+7 = 4 (mod 17)
1/8-5-8*2 = 8 (mod 11)
NG
10*3/7+(50+81/22)+11 = 915 (mod 1153)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 1\\n1 2\\n3 4\\n2 3\", \"10 10\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 9\\n1 8\\n3 4\\n3 4\\n2 7\", \"3 2\\n1 2\\n2 2\", \"4 3\\n1 2\\n3 4\\n2 2\", \"6 1\\n1 2\", \"1 1\\n1 2\\n3 4\\n2 3\", \"10 10\\n8 9\\n2 8\\n7 6\\n4 9\\n7 8\\n2 9\\n1 8\\n3 4\\n3 4\\n2 7\", \"3 0\\n1 2\\n2 2\", \"10 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 8\\n1 8\\n3 4\\n3 4\\n3 7\", \"7 1\\n1 2\", \"7 0\\n1 2\", \"4 0\\n1 8\\n4 2\", \"5 0\\n1 8\\n4 3\", \"13 0\\n-3 0\", \"22 0\\n-3 0\", \"28 0\\n-3 0\", \"11 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n3 4\\n6 4\\n3 7\", \"16 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n3 4\\n6 4\\n3 7\", \"8 0\\n1 8\\n4 3\", \"21 0\\n-3 0\", \"9 0\\n-3 0\", \"42 0\\n-3 0\", \"6 0\\n-4 1\", \"11 0\\n1 3\", \"19 0\\n-3 0\", \"10 0\\n-4 1\", \"33 0\\n-8 2\", \"14 0\\n-1 0\", \"11 2\\n8 5\\n4 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n3 4\\n6 5\\n3 7\", \"24 1\\n8 9\\n2 8\\n5 6\\n4 9\\n7 3\\n2 11\\n1 8\\n3 4\\n1 4\\n3 7\", \"48 0\\n0 3\", \"24 2\\n8 9\\n2 8\\n5 5\\n4 9\\n7 3\\n2 11\\n1 8\\n3 4\\n1 4\\n3 7\", \"23 0\\n2 2\", \"13 1\\n2 10\\n6 0\", \"11 3\\n8 5\\n4 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n4 7\\n6 5\\n3 7\", \"14 1\\n5 9\\n2 13\\n7 6\\n4 9\\n4 8\\n2 13\\n0 12\\n3 3\\n3 1\\n3 10\", \"12 0\\n-1 0\\n8 2\", \"17 0\\n-1 -1\\n8 4\", \"10 10\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 8\\n1 8\\n3 4\\n3 4\\n3 7\", \"4 3\\n1 2\\n3 4\\n1 2\", \"1 1\\n1 1\\n3 4\\n2 3\", \"3 0\\n1 3\\n2 2\", \"10 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n3 4\\n3 4\\n3 7\", \"1 1\\n1 0\\n3 4\\n2 3\", \"2 0\\n1 3\\n2 2\", \"10 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 11\\n1 8\\n3 4\\n6 4\\n3 7\", \"7 0\\n1 4\", \"1 1\\n1 0\\n0 4\\n2 3\", \"1 0\\n1 3\\n2 2\", \"10 1\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 11\\n2 8\\n3 4\\n6 4\\n3 7\", \"7 0\\n0 4\", \"1 1\\n2 0\\n0 4\\n2 3\", \"1 0\\n1 4\\n2 2\", \"7 0\\n0 8\", \"1 1\\n2 0\\n1 4\\n2 3\", \"1 0\\n1 8\\n2 2\", \"7 0\\n-1 8\", \"1 1\\n2 0\\n1 4\\n2 4\", \"1 0\\n1 8\\n4 2\", \"7 0\\n-2 8\", \"1 1\\n1 0\\n1 4\\n2 4\", \"2 0\\n1 8\\n4 2\", \"7 0\\n-2 3\", \"1 1\\n1 0\\n1 4\\n0 4\", \"7 0\\n-2 0\", \"1 1\\n1 0\\n1 2\\n0 4\", \"4 0\\n1 8\\n4 3\", \"7 0\\n-3 0\", \"1 1\\n1 0\\n1 0\\n0 4\", \"0 1\\n1 0\\n1 0\\n0 4\", \"2 0\\n1 8\\n4 3\", \"0 1\\n1 0\\n1 0\\n0 6\", \"2 0\\n2 8\\n4 3\", \"0 1\\n2 0\\n1 0\\n0 6\", \"2 0\\n2 8\\n4 0\", \"28 0\\n-6 0\", \"0 1\\n2 1\\n1 0\\n0 6\", \"2 0\\n2 8\\n4 1\", \"28 0\\n-6 1\", \"0 2\\n2 1\\n1 0\\n0 6\", \"2 0\\n3 8\\n4 1\", \"28 0\\n-4 1\", \"0 2\\n2 2\\n1 0\\n0 6\", \"3 0\\n3 8\\n4 1\", \"28 0\\n-4 2\", \"4 0\\n3 8\\n4 1\", \"28 0\\n-4 3\", \"4 0\\n3 10\\n4 1\", \"4 0\\n3 10\\n4 0\", \"10 10\\n8 9\\n2 8\\n4 6\\n4 9\\n7 14\\n2 8\\n1 8\\n3 4\\n3 4\\n2 7\", \"2 1\\n1 2\", \"3 2\\n0 2\\n2 2\", \"6 1\\n1 4\", \"1 1\\n1 2\\n3 4\\n2 2\", \"10 10\\n8 9\\n2 8\\n7 6\\n4 9\\n7 8\\n3 9\\n1 8\\n3 4\\n3 4\\n2 7\", \"3 0\\n1 1\\n2 2\", \"10 1\\n8 9\\n2 8\\n4 6\\n4 9\\n4 8\\n2 8\\n1 8\\n3 4\\n3 4\\n3 7\", \"1 1\\n0 1\\n3 4\\n2 3\", \"3 0\\n1 3\\n1 2\", \"7 0\\n1 3\", \"3 2\\n1 2\\n1 2\", \"4 3\\n1 2\\n3 4\\n2 3\", \"10 10\\n8 9\\n2 8\\n4 6\\n4 9\\n7 8\\n2 8\\n1 8\\n3 4\\n3 4\\n2 7\", \"3 1\\n1 2\"], \"outputs\": [\"5\\n\", \"9\\n\", \"1\\n\", \"2\\n\", \"14\\n\", \"0\\n\", \"7\\n\", \"3\\n\", \"44\\n\", \"20\\n\", \"21\\n\", \"6\\n\", \"10\\n\", \"78\\n\", \"231\\n\", \"378\\n\", \"54\\n\", \"119\\n\", \"28\\n\", \"210\\n\", \"36\\n\", \"861\\n\", \"15\\n\", \"55\\n\", \"171\\n\", \"45\\n\", \"528\\n\", \"91\\n\", \"52\\n\", \"275\\n\", \"1128\\n\", \"273\\n\", \"253\\n\", \"77\\n\", \"49\\n\", \"90\\n\", \"66\\n\", \"136\\n\", \"5\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"44\\n\", \"0\\n\", \"1\\n\", \"44\\n\", \"21\\n\", \"0\\n\", \"0\\n\", \"44\\n\", \"21\\n\", \"0\\n\", \"0\\n\", \"21\\n\", \"0\\n\", \"0\\n\", \"21\\n\", \"0\\n\", \"0\\n\", \"21\\n\", \"0\\n\", \"1\\n\", \"21\\n\", \"0\\n\", \"21\\n\", \"0\\n\", \"6\\n\", \"21\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"378\\n\", \"0\\n\", \"1\\n\", \"378\\n\", \"0\\n\", \"1\\n\", \"378\\n\", \"0\\n\", \"3\\n\", \"378\\n\", \"6\\n\", \"378\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"0\\n\", \"1\\n\", \"14\\n\", \"0\\n\", \"10\\n\", \"3\\n\", \"44\\n\", \"0\\n\", \"3\\n\", \"21\\n\", \"0\", \"1\", \"5\", \"2\"]}", "source": "taco"}
|
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 1\\n1 2\\n\", \"2 2\\n1 2\\n\", \"3 1\\n3 2\\n3 1\\n\", \"5 2\\n2 1\\n2 3\\n5 3\\n4 1\\n\", \"4 4\\n3 2\\n4 3\\n2 1\\n\", \"21 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n10 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n14 21\\n\", \"6 5\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n\", \"4 4\\n1 2\\n1 3\\n1 4\\n\", \"4 3\\n1 2\\n1 3\\n1 4\\n\", \"3 2\\n3 2\\n3 1\\n\", \"5 2\\n2 1\\n2 3\\n5 3\\n4 2\\n\", \"6 1\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n\", \"4 4\\n1 2\\n1 3\\n2 4\\n\", \"21 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n14 21\\n\", \"21 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n8 10\\n10 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n14 21\\n\", \"7 3\\n1 2\\n1 3\\n4 2\\n6 5\\n6 3\\n6 7\\n\", \"6 2\\n2 4\\n1 3\\n1 4\\n1 5\\n1 6\\n\", \"21 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 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20\\n11 21\\n\", \"3 2\\n3 1\\n2 1\\n\", \"21 1\\n1 4\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n21 20\\n11 21\\n\", \"4 4\\n3 2\\n4 3\\n4 1\\n\", \"4 2\\n1 2\\n2 3\\n1 4\\n\", \"6 1\\n2 4\\n1 3\\n1 4\\n1 5\\n1 6\\n\", \"6 1\\n1 2\\n2 3\\n1 4\\n1 5\\n2 6\\n\", \"21 1\\n1 2\\n2 3\\n2 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n14 21\\n\", \"21 1\\n1 4\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n5 14\\n4 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n14 21\\n\", \"6 1\\n1 2\\n1 3\\n3 4\\n1 5\\n1 6\\n\", \"21 1\\n1 4\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n5 14\\n14 15\\n14 16\\n19 17\\n14 18\\n14 19\\n14 20\\n11 21\\n\", \"3 3\\n3 1\\n2 1\\n\", \"21 1\\n1 4\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n3 11\\n11 12\\n12 13\\n1 14\\n14 15\\n14 16\\n14 17\\n14 18\\n14 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|
Two players, Red and Blue, are at it again, and this time they're playing with crayons! The mischievous duo is now vandalizing a rooted tree, by coloring the nodes while playing their favorite game.
The game works as follows: there is a tree of size n, rooted at node 1, where each node is initially white. Red and Blue get one turn each. Red goes first.
In Red's turn, he can do the following operation any number of times:
* Pick any subtree of the rooted tree, and color every node in the subtree red.
However, to make the game fair, Red is only allowed to color k nodes of the tree. In other words, after Red's turn, at most k of the nodes can be colored red.
Then, it's Blue's turn. Blue can do the following operation any number of times:
* Pick any subtree of the rooted tree, and color every node in the subtree blue. However, he's not allowed to choose a subtree that contains a node already colored red, as that would make the node purple and no one likes purple crayon.
Note: there's no restriction on the number of nodes Blue can color, as long as he doesn't color a node that Red has already colored.
After the two turns, the score of the game is determined as follows: let w be the number of white nodes, r be the number of red nodes, and b be the number of blue nodes. The score of the game is w ⋅ (r - b).
Red wants to maximize this score, and Blue wants to minimize it. If both players play optimally, what will the final score of the game be?
Input
The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ k ≤ n) — the number of vertices in the tree and the maximum number of red nodes.
Next n - 1 lines contains description of edges. The i-th line contains two space separated integers u_i and v_i (1 ≤ u_i, v_i ≤ n; u_i ≠ v_i) — the i-th edge of the tree.
It's guaranteed that given edges form a tree.
Output
Print one integer — the resulting score if both Red and Blue play optimally.
Examples
Input
4 2
1 2
1 3
1 4
Output
1
Input
5 2
1 2
2 3
3 4
4 5
Output
6
Input
7 2
1 2
1 3
4 2
3 5
6 3
6 7
Output
4
Input
4 1
1 2
1 3
1 4
Output
-1
Note
In the first test case, the optimal strategy is as follows:
* Red chooses to color the subtrees of nodes 2 and 3.
* Blue chooses to color the subtree of node 4.
At the end of this process, nodes 2 and 3 are red, node 4 is blue, and node 1 is white. The score of the game is 1 ⋅ (2 - 1) = 1.
In the second test case, the optimal strategy is as follows:
* Red chooses to color the subtree of node 4. This colors both nodes 4 and 5.
* Blue does not have any options, so nothing is colored blue.
At the end of this process, nodes 4 and 5 are red, and nodes 1, 2 and 3 are white. The score of the game is 3 ⋅ (2 - 0) = 6.
For the third test case:
<image>
The score of the game is 4 ⋅ (2 - 1) = 4.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"aba\", \"abbabba\"], [\"aba\", \"abaa\"], [\"aba\", \"a\"], [\"a\", \"a\"], [\"a\", \"aaa\"], [\"abcdefgh\", \"hgfedcba\"]], \"outputs\": [[9], [4], [3], [1], [3], [64]]}", "source": "taco"}
|
# Task
You are given two string `a` an `s`. Starting with an empty string we can do the following two operations:
```
append the given string a to the end of the current string.
erase one symbol of the current string.```
Your task is to find the least number of operations needed to construct the given string s. Assume that all the letters from `s` appear in `a` at least once.
# Example
For `a = "aba", s = "abbaab"`, the result should be `6`.
Coinstruction:
`"" -> "aba" -> "ab" -> "ababa" -> "abba" -> "abbaaba" -> "abbaab".`
So, the result is 6.
For `a = "aba", s = "a"`, the result should be `3`.
Coinstruction:
`"" -> "aba" -> "ab" -> "a".`
So, the result is 3.
For `a = "aba", s = "abaa"`, the result should be `4`.
Coinstruction:
`"" -> "aba" -> "abaaba" -> "abaab" -> "abaa".`
So, the result is 4.
# Input/Output
- `[input]` string `a`
string to be appended. Contains only lowercase English letters.
1 <= a.length <= 20
- `[input]` string `s`
desired string containing only lowercase English letters.
1 <= s.length < 1000
- `[output]` an integer
minimum number of operations
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
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\"1\\n1\\n\", \"3\\n1 2 3\\n\"], \"outputs\": [\"-1\\n\", \"3\\n\", \"-1\\n\", \"23450\\n\", \"-1\\n\", \"25165\\n\", \"-1\\n\", \"23078\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"868\\n\", \"-1\\n\", \"1150\\n\", \"-1\\n\", \"2502\\n\", \"-1\\n\", \"1598\\n\", \"-1\\n\", \"3448\\n\", \"32\\n\", \"15\\n\", \"-1\\n\", \"27000\\n\", \"-1\\n\", \"278\\n\", \"-1\\n\", \"34000\\n\", \"34\\n\", \"57\\n\", \"92\\n\", \"98\\n\", \"15\\n\", \"21\\n\", \"22\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"6\\n\", \"868\\n\", \"34\\n\", \"1598\\n\", \"34000\\n\", \"-1\\n\", \"-1\\n\", \"278\\n\", \"92\\n\", \"-1\\n\", \"32\\n\", \"22\\n\", \"25165\\n\", \"-1\\n\", \"21\\n\", \"2502\\n\", \"4\\n\", \"23078\\n\", \"4\\n\", \"-1\\n\", \"-1\\n\", \"3448\\n\", \"-1\\n\", \"3\\n\", \"1150\\n\", \"23450\\n\", \"-1\\n\", \"98\\n\", \"-1\\n\", \"-1\\n\", \"27000\\n\", \"57\\n\", \"-1\\n\", \"15\\n\", \"-1\\n\", \"-1\\n\", \"6\\n\", \"4\\n\", \"15\\n\", \"945\\n\", \"34\\n\", \"1598\\n\", \"34000\\n\", 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|
Two pirates Polycarpus and Vasily play a very interesting game. They have n chests with coins, the chests are numbered with integers from 1 to n. Chest number i has a_{i} coins.
Polycarpus and Vasily move in turns. Polycarpus moves first. During a move a player is allowed to choose a positive integer x (2·x + 1 ≤ n) and take a coin from each chest with numbers x, 2·x, 2·x + 1. It may turn out that some chest has no coins, in this case the player doesn't take a coin from this chest. The game finishes when all chests get emptied.
Polycarpus isn't a greedy scrooge. Polycarpys is a lazy slob. So he wonders in what minimum number of moves the game can finish. Help Polycarpus, determine the minimum number of moves in which the game can finish. Note that Polycarpus counts not only his moves, he also counts Vasily's moves.
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 100) — the number of chests with coins. The second line contains a sequence of space-separated integers: a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 1000), where a_{i} is the number of coins in the chest number i at the beginning of the game.
-----Output-----
Print a single integer — the minimum number of moves needed to finish the game. If no sequence of turns leads to finishing the game, print -1.
-----Examples-----
Input
1
1
Output
-1
Input
3
1 2 3
Output
3
-----Note-----
In the first test case there isn't a single move that can be made. That's why the players won't be able to empty the chests.
In the second sample there is only one possible move x = 1. This move should be repeated at least 3 times to empty the third chest.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"100\\n9 13 6 72 98 70 5 100 26 75 25 87 35 10 95 31 41 80 91 38 61 64 29 71 52 63 24 74 14 56 92 85 12 73 59 23 3 39 30 42 68 47 16 18 8 93 96 67 48 89 53 77 49 62 44 33 83 57 81 55 28 76 34 36 88 37 17 11 40 90 46 84 94 60 4 51 69 21 50 82 97 1 54 2 65 32 15 22 79 27 99 78 20 43 7 86 45 19 66 58\\n\", \"100\\n98 62 49 47 84 1 77 88 76 85 21 50 2 92 72 66 100 99 78 58 33 83 27 89 71 97 64 94 4 13 17 8 32 20 79 44 12 56 7 9 43 6 26 57 18 23 39 69 30 55 16 96 35 91 11 68 67 31 38 90 40 48 25 41 54 82 15 22 37 51 81 65 60 34 24 14 5 87 74 19 46 3 80 45 61 86 10 28 52 73 29 42 70 53 93 95 63 75 59 36\\n\", \"15\\n2 3 4 5 1 7 8 9 10 6 12 13 14 15 11\\n\", \"100\\n53 12 13 98 57 83 52 61 69 54 13 92 91 27 16 91 86 75 93 29 16 59 14 2 37 74 34 30 98 17 3 72 83 93 21 72 52 89 57 58 60 29 94 16 45 20 76 64 78 67 76 68 41 47 50 36 9 75 79 11 10 88 71 22 36 60 44 19 79 43 49 24 6 57 8 42 51 58 60 2 84 48 79 55 74 41 89 10 45 70 76 29 53 9 82 93 24 40 94 56\\n\", 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|
As you have noticed, there are lovely girls in Arpa’s land.
People in Arpa's land are numbered from 1 to n. Everyone has exactly one crush, i-th person's crush is person with the number crushi.
<image>
Someday Arpa shouted Owf loudly from the top of the palace and a funny game started in Arpa's land. The rules are as follows.
The game consists of rounds. Assume person x wants to start a round, he calls crushx and says: "Oww...wwf" (the letter w is repeated t times) and cuts off the phone immediately. If t > 1 then crushx calls crushcrushx and says: "Oww...wwf" (the letter w is repeated t - 1 times) and cuts off the phone immediately. The round continues until some person receives an "Owf" (t = 1). This person is called the Joon-Joon of the round. There can't be two rounds at the same time.
Mehrdad has an evil plan to make the game more funny, he wants to find smallest t (t ≥ 1) such that for each person x, if x starts some round and y becomes the Joon-Joon of the round, then by starting from y, x would become the Joon-Joon of the round. Find such t for Mehrdad if it's possible.
Some strange fact in Arpa's land is that someone can be himself's crush (i.e. crushi = i).
Input
The first line of input contains integer n (1 ≤ n ≤ 100) — the number of people in Arpa's land.
The second line contains n integers, i-th of them is crushi (1 ≤ crushi ≤ n) — the number of i-th person's crush.
Output
If there is no t satisfying the condition, print -1. Otherwise print such smallest t.
Examples
Input
4
2 3 1 4
Output
3
Input
4
4 4 4 4
Output
-1
Input
4
2 1 4 3
Output
1
Note
In the first sample suppose t = 3.
If the first person starts some round:
The first person calls the second person and says "Owwwf", then the second person calls the third person and says "Owwf", then the third person calls the first person and says "Owf", so the first person becomes Joon-Joon of the round. So the condition is satisfied if x is 1.
The process is similar for the second and the third person.
If the fourth person starts some round:
The fourth person calls himself and says "Owwwf", then he calls himself again and says "Owwf", then he calls himself for another time and says "Owf", so the fourth person becomes Joon-Joon of the round. So the condition is satisfied when x is 4.
In the last example if the first person starts a round, then the second person becomes the Joon-Joon, and vice versa.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
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100\\n815 283\\n6\\n106 21\\n68 55\\n2 77\\n19 13\\n83 42\\n2 1\\n0\", \"4\\n1 1\\n3 1\\n4 1\\n2 1\\n3\\n5 3\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n26 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 78\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 1\\n3 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1001\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 25\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 2\\n3 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 10\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 78\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 1\\n3 1\\n4 1\\n4 2\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1101\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 150\\n6\\n74 78\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 2\\n3 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1001\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 137\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 2\\n3 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 21\\n53 55\\n77 77\\n12 13\\n39 22\\n1 1\\n0\", \"4\\n1 2\\n1 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n78 21\\n53 55\\n77 77\\n12 13\\n54 42\\n1 1\\n0\", \"4\\n1 1\\n3 1\\n4 1\\n4 2\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1001\\n10\\n5 62\\n10 115\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 150\\n6\\n74 78\\n53 55\\n77 153\\n12 13\\n39 42\\n1 1\\n0\", \"4\\n1 2\\n3 1\\n4 1\\n2 1\\n3\\n10 2\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 21\\n53 55\\n77 77\\n15 13\\n54 42\\n1 1\\n0\", \"4\\n1 2\\n3 1\\n4 1\\n2 1\\n3\\n5 2\\n1 2\\n1 2\\n1\\n1000 1100\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n14 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n78 21\\n53 55\\n77 77\\n12 13\\n54 42\\n1 1\\n0\", \"4\\n1 1\\n3 1\\n4 1\\n2 1\\n3\\n5 3\\n1 2\\n1 2\\n1\\n1000 1000\\n10\\n5 62\\n10 68\\n15 72\\n20 73\\n25 75\\n30 77\\n35 79\\n40 82\\n45 100\\n815 283\\n6\\n74 78\\n53 55\\n77 77\\n12 13\\n39 42\\n1 1\\n0\"], \"outputs\": [\"14\\n14\\n3000\\n2013\\n522\\n\", \"14\\n14\\n3001\\n2013\\n522\\n\", \"14\\n14\\n3001\\n1880\\n522\\n\", \"16\\n14\\n3001\\n1880\\n522\\n\", \"15\\n14\\n3000\\n2013\\n522\\n\", \"17\\n14\\n3001\\n1880\\n522\\n\", \"15\\n14\\n3000\\n2013\\n581\\n\", \"15\\n14\\n3000\\n2013\\n465\\n\", \"15\\n14\\n3000\\n2013\\n480\\n\", \"15\\n14\\n3000\\n2013\\n484\\n\", \"14\\n14\\n3001\\n2013\\n500\\n\", \"15\\n14\\n3000\\n1990\\n522\\n\", \"17\\n14\\n3001\\n1925\\n522\\n\", \"15\\n22\\n3000\\n2013\\n480\\n\", \"15\\n14\\n3100\\n2013\\n484\\n\", \"17\\n14\\n3001\\n1925\\n519\\n\", 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\"14\\n14\\n3001\\n2013\\n531\\n\", \"15\\n14\\n3001\\n1880\\n474\\n\", \"14\\n14\\n3000\\n2013\\n471\\n\", \"15\\n14\\n3001\\n2013\\n522\\n\", \"11\\n14\\n\", \"17\\n14\\n3101\\n1931\\n519\\n\", \"14\\n22\\n3000\\n1975\\n481\\n\", \"17\\n14\\n3100\\n2013\\n534\\n\", \"16\\n24\\n3000\\n2013\\n506\\n\", \"16\\n24\\n3000\\n2072\\n590\\n\", \"14\\n16\\n3000\\n2054\\n522\\n\", \"13\\n14\\n3001\\n2013\\n531\\n\", \"15\\n14\\n3001\\n1880\\n515\\n\", \"14\\n22\\n3000\\n1913\\n481\\n\", \"17\\n14\\n3100\\n2048\\n534\\n\", \"15\\n22\\n3000\\n2013\\n474\\n\", \"16\\n24\\n3000\\n2013\\n507\\n\", \"13\\n14\\n3101\\n2013\\n531\\n\", \"17\\n14\\n3001\\n1880\\n515\\n\", \"14\\n22\\n3000\\n1913\\n471\\n\", \"17\\n12\\n3100\\n2048\\n534\\n\", \"15\\n24\\n3000\\n2045\\n590\\n\", \"12\\n14\\n3101\\n2013\\n531\\n\", \"17\\n14\\n3001\\n1910\\n515\\n\", \"17\\n13\\n3100\\n2048\\n534\\n\", \"15\\n22\\n3000\\n2013\\n451\\n\", \"15\\n24\\n3000\\n2045\\n479\\n\", \"14\\n14\\n\", \"17\\n13\\n3100\\n2019\\n534\\n\", \"15\\n22\\n3000\\n2013\\n452\\n\", \"14\\n15\\n\", \"17\\n13\\n3100\\n2019\\n533\\n\", \"15\\n22\\n3000\\n2072\\n452\\n\", \"15\\n24\\n3000\\n2045\\n494\\n\", \"17\\n13\\n3100\\n1866\\n533\\n\", \"15\\n22\\n3000\\n2072\\n382\\n\", \"15\\n24\\n3000\\n2050\\n494\\n\", \"15\\n22\\n3000\\n2072\\n395\\n\", \"17\\n24\\n3000\\n2050\\n494\\n\", \"15\\n22\\n3000\\n2112\\n395\\n\", \"17\\n24\\n3000\\n2050\\n489\\n\", \"15\\n22\\n3000\\n2135\\n395\\n\", \"16\\n24\\n3000\\n2050\\n489\\n\", \"16\\n24\\n3000\\n2054\\n489\\n\", \"14\\n24\\n3000\\n2054\\n489\\n\", \"13\\n24\\n3000\\n2054\\n489\\n\", \"13\\n24\\n3000\\n2052\\n489\\n\", \"14\\n15\\n3000\\n2013\\n522\\n\", \"14\\n14\\n3001\\n2013\\n469\\n\", \"15\\n14\\n3000\\n1975\\n522\\n\", \"17\\n14\\n3101\\n1880\\n522\\n\", \"15\\n14\\n3001\\n2013\\n581\\n\", \"15\\n14\\n3000\\n2013\\n445\\n\", \"13\\n14\\n3000\\n2013\\n484\\n\", \"17\\n14\\n3001\\n1925\\n598\\n\", \"15\\n22\\n3000\\n2013\\n483\\n\", \"15\\n14\\n3100\\n1995\\n484\\n\", \"14\\n15\\n3000\\n2013\\n522\"]}", "source": "taco"}
|
At the school where the twins Ami and Mami attend, the summer vacation has already begun, and a huge amount of homework has been given this year as well. However, the two of them were still trying to go out without doing any homework today. It is obvious that you will see crying on the last day of summer vacation as it is, so you, as a guardian, decided not to leave the house until you finished your homework of reading impressions today with your heart as a demon.
Well-prepared you have already borrowed all the assignment books from the library. However, according to library rules, only one book is borrowed for each book. By the way, for educational reasons, I decided to ask them to read all the books and write their impressions without cooperating with each other. In addition, since the deadline for returning books is near, I decided to have them finish reading all the books as soon as possible. And you decided to think about how to do your homework so that you can finish your homework as soon as possible under those conditions. Here, the time when both the twins finish their work is considered as the time when they finish reading the book and the time when they finish their homework.
Since there is only one book for each book, two people cannot read the same book at the same time. In addition, due to adult circumstances, once you start reading a book, you cannot interrupt it, and once you start writing an impression about a book, you cannot interrupt it. Of course, I can't write my impressions about a book I haven't read. Since Ami and Mami are twins, the time it takes to read each book and the time it takes to write an impression are common to both of them.
For example, suppose that there are three books, and the time it takes to read each book and the time it takes to write an impression are as follows.
| Time to read a book | Time to write an impression
--- | --- | ---
Book 1 | 5 | 3
Book 2 | 1 | 2
Book 3 | 1 | 2
In this case, if you proceed with your homework as shown in Figure C-1, you can finish reading all the books in time 10 and finish your homework in time 15. In the procedure shown in Fig. C-2, the homework is completed in time 14, but it cannot be adopted this time because the time to finish reading the book is not the shortest. Also, as shown in Fig. C-3, two people cannot read the same book at the same time, interrupt reading of a book as shown in Fig. C-4, or write an impression of a book that has not been read.
<image>
Figure C-1: An example of how to get the homework done in the shortest possible time
<image>
Figure C-2: An example where the time to finish reading a book is not the shortest
<image>
Figure C-3: An example of two people reading the same book at the same time
<image>
Figure C-4: An example of writing an impression of a book that has not been read or interrupting work.
Considering the circumstances of various adults, let's think about how to proceed so that the homework can be completed as soon as possible for the twins who want to go out to play.
Input
The input consists of multiple datasets. The format of each data set is as follows.
N
r1 w1
r2 w2
...
rN wN
N is an integer representing the number of task books, and can be assumed to be 1 or more and 1,000 or less.
The following N lines represent information about the task book. Each line contains two integers separated by spaces, ri (1 ≤ ri ≤ 1,000) is the time it takes to read the i-th book, and wi (1 ≤ wi ≤ 1,000) is the impression of the i-th book. Represents the time it takes to write.
N = 0 indicates the end of input. This is not included in the dataset.
Output
For each dataset, output the minimum time to finish writing all the impressions on one line when the time to finish reading all the books by two people is minimized.
Sample Input
Four
1 1
3 1
4 1
twenty one
3
5 3
1 2
1 2
1
1000 1000
Ten
5 62
10 68
15 72
20 73
25 75
30 77
35 79
40 82
45 100
815 283
6
74 78
53 55
77 77
12 13
39 42
1 1
0
Output for Sample Input
14
15
3000
2013
522
Example
Input
4
1 1
3 1
4 1
2 1
3
5 3
1 2
1 2
1
1000 1000
10
5 62
10 68
15 72
20 73
25 75
30 77
35 79
40 82
45 100
815 283
6
74 78
53 55
77 77
12 13
39 42
1 1
0
Output
14
15
3000
2013
522
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Everything is great about Ilya's city, except the roads. The thing is, the only ZooVille road is represented as n holes in a row. We will consider the holes numbered from 1 to n, from left to right.
Ilya is really keep on helping his city. So, he wants to fix at least k holes (perharps he can fix more) on a single ZooVille road.
The city has m building companies, the i-th company needs ci money units to fix a road segment containing holes with numbers of at least li and at most ri. The companies in ZooVille are very greedy, so, if they fix a segment containing some already fixed holes, they do not decrease the price for fixing the segment.
Determine the minimum money Ilya will need to fix at least k holes.
Input
The first line contains three integers n, m, k (1 ≤ n ≤ 300, 1 ≤ m ≤ 105, 1 ≤ k ≤ n). The next m lines contain the companies' description. The i-th line contains three integers li, ri, ci (1 ≤ li ≤ ri ≤ n, 1 ≤ ci ≤ 109).
Output
Print a single integer — the minimum money Ilya needs to fix at least k holes.
If it is impossible to fix at least k holes, print -1.
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
10 4 6
7 9 11
6 9 13
7 7 7
3 5 6
Output
17
Input
10 7 1
3 4 15
8 9 8
5 6 8
9 10 6
1 4 2
1 4 10
8 10 13
Output
2
Input
10 1 9
5 10 14
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
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|
This is the easy version of the problem. The only difference is that in this version k = 0.
There is an array a_1, a_2, …, a_n of n positive integers. You should divide it into a minimal number of continuous segments, such that in each segment there are no two numbers (on different positions), whose product is a perfect square.
Moreover, it is allowed to do at most k such operations before the division: choose a number in the array and change its value to any positive integer. But in this version k = 0, so it is not important.
What is the minimum number of continuous segments you should use if you will make changes optimally?
Input
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains two integers n, k (1 ≤ n ≤ 2 ⋅ 10^5, k = 0).
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7).
It's guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case print a single integer — the answer to the problem.
Example
Input
3
5 0
18 6 2 4 1
5 0
6 8 1 24 8
1 0
1
Output
3
2
1
Note
In the first test case the division may be as follows:
* [18, 6]
* [2, 4]
* [1]
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"82\\n\", \"49\\n\", \"35\\n\", \"79\\n\", \"92\\n\", \"57\\n\", \"100\\n\", \"75\\n\", \"56\\n\", \"41\\n\", \"16\\n\", \"25\\n\", \"8\\n\", \"74\\n\", \"90\\n\", \"44\\n\", \"13\\n\", \"64\\n\", \"70\\n\", \"7\\n\", \"9\\n\", \"4\\n\", \"72\\n\", \"69\\n\", \"2\\n\", \"29\\n\", \"68\\n\", \"86\\n\", \"27\\n\", \"63\\n\", \"14\\n\", \"66\\n\", \"98\\n\", \"87\\n\", \"36\\n\", \"42\\n\", \"67\\n\", \"60\\n\", \"39\\n\", \"85\\n\", \"46\\n\", \"5\\n\", \"19\\n\", \"6\\n\", \"38\\n\", \"94\\n\", \"91\\n\", \"58\\n\", \"88\\n\", \"33\\n\", \"28\\n\", \"77\\n\", \"50\\n\", \"3\\n\", \"18\\n\", \"59\\n\", \"40\\n\", \"93\\n\", \"62\\n\", \"15\\n\", \"78\\n\", \"23\\n\", \"80\\n\", \"73\\n\", \"54\\n\", \"37\\n\", \"65\\n\", \"11\\n\", \"76\\n\", \"22\\n\", \"21\\n\", \"81\\n\", \"61\\n\", \"95\\n\", \"17\\n\", \"20\\n\", \"26\\n\", \"99\\n\", \"97\\n\", \"45\\n\", \"24\\n\", \"51\\n\", \"43\\n\", \"34\\n\", \"48\\n\", \"55\\n\", \"96\\n\", \"52\\n\", \"71\\n\", \"53\\n\", \"47\\n\", \"12\\n\", \"84\\n\", \"83\\n\", \"31\\n\", \"30\\n\", \"89\\n\", \"32\\n\", \"001\\n\", \"010\\n\", \"011\\n\", \"1\\n\", \"10\\n\"], \"outputs\": [\"10 10\\n\", \"8 8\\n\", \"6 6\\n\", \"9 9\\n\", \"10 10\\n\", \"8 8\\n\", \"11 11\\n\", \"9 9\\n\", \"8 8\\n\", \"7 7\\n\", \"5 5\\n\", \"6 6\\n\", \"3 3\\n\", \"9 9\\n\", \"10 10\\n\", \"7 7\\n\", \"4 4\\n\", \"9 9\\n\", \"9 9\\n\", \"3 3\\n\", \"4 4\\n\", \"4 2\\n\", \"9 9\\n\", \"9 9\\n\", \"2 2\\n\", \"6 6\\n\", \"9 9\\n\", \"10 10\\n\", \"6 6\\n\", \"8 8\\n\", \"4 4\\n\", \"9 9\\n\", \"10 10\\n\", \"10 10\\n\", \"7 7\\n\", \"7 7\\n\", \"9 9\\n\", \"8 8\\n\", \"7 7\\n\", \"10 10\\n\", \"7 7\\n\", \"3 3\\n\", \"5 5\\n\", \"3 3\\n\", \"7 7\\n\", \"10 10\\n\", \"10 10\\n\", \"8 8\\n\", \"10 10\\n\", \"6 6\\n\", \"6 6\\n\", \"9 9\\n\", \"8 8\\n\", \"2 2\\n\", \"5 5\\n\", \"8 8\\n\", \"7 7\\n\", \"10 10\\n\", \"8 8\\n\", \"4 4\\n\", \"9 9\\n\", \"5 5\\n\", \"9 9\\n\", \"9 9\\n\", \"8 8\\n\", \"7 7\\n\", \"9 9\\n\", \"4 4\\n\", \"9 9\\n\", \"5 5\\n\", \"5 5\\n\", \"10 10\\n\", \"8 8\\n\", \"10 10\\n\", \"5 5\\n\", \"5 5\\n\", \"6 6\\n\", \"10 10\\n\", \"10 10\\n\", \"7 7\\n\", \"5 5\\n\", \"8 8\\n\", \"7 7\\n\", \"6 6\\n\", \"7 7\\n\", \"8 8\\n\", \"10 10\\n\", \"8 8\\n\", \"9 9\\n\", \"8 8\\n\", \"7 7\\n\", \"4 4\\n\", \"10 10\\n\", \"10 10\\n\", \"6 6\\n\", \"6 6\\n\", \"10 10\\n\", \"6 6\\n\", \"-1\\n\", \"4 4\\n\", \"4 4\\n\", \"-1\\n\", \"4 4\\n\"]}", "source": "taco"}
|
Given an integer x, find 2 integers a and b such that:
* 1 ≤ a,b ≤ x
* b divides a (a is divisible by b).
* a ⋅ b>x.
* a/b<x.
Input
The only line contains the integer x (1 ≤ x ≤ 100).
Output
You should output two integers a and b, satisfying the given conditions, separated by a space. If no pair of integers satisfy the conditions above, print "-1" (without quotes).
Examples
Input
10
Output
6 3
Input
1
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
There are N stones arranged in a row. The i-th stone from the left is painted in the color C_i.
Snuke will perform the following operation zero or more times:
* Choose two stones painted in the same color. Repaint all the stones between them, with the color of the chosen stones.
Find the number of possible final sequences of colors of the stones, modulo 10^9+7.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq C_i \leq 2\times 10^5(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1
:
C_N
Output
Print the number of possible final sequences of colors of the stones, modulo 10^9+7.
Examples
Input
5
1
2
1
2
2
Output
3
Input
6
4
2
5
4
2
4
Output
5
Input
7
1
3
1
2
3
3
2
Output
5
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Eugeny has array a = a_1, a_2, ..., a_{n}, consisting of n integers. Each integer a_{i} equals to -1, or to 1. Also, he has m queries: Query number i is given as a pair of integers l_{i}, r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n). The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum a_{l}_{i} + a_{l}_{i} + 1 + ... + a_{r}_{i} = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
-----Input-----
The first line contains integers n and m (1 ≤ n, m ≤ 2·10^5). The second line contains n integers a_1, a_2, ..., a_{n} (a_{i} = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers l_{i}, r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n).
-----Output-----
Print m integers — the responses to Eugene's queries in the order they occur in the input.
-----Examples-----
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"2 2\\n\", \"2 3\\n\", \"3 3\\n\", \"20 68\\n\", \"1 1\\n\", \"1 2\\n\", \"1 3\\n\", \"2 1\\n\", \"2 2\\n\", \"3 1\\n\", \"3 2\\n\", \"68 42\\n\", \"1 35\\n\", \"25 70\\n\", \"59 79\\n\", \"65 63\\n\", \"46 6\\n\", \"28 82\\n\", \"98 98\\n\", \"98 99\\n\", \"98 100\\n\", \"99 98\\n\", \"99 99\\n\", \"99 100\\n\", \"100 98\\n\", \"100 99\\n\", \"100 100\\n\", \"3 4\\n\", \"1 1\\n\", \"59 79\\n\", \"2 1\\n\", \"1 2\\n\", \"3 2\\n\", \"100 100\\n\", \"3 4\\n\", \"99 100\\n\", \"98 98\\n\", \"25 70\\n\", \"20 68\\n\", \"1 3\\n\", \"98 100\\n\", \"98 99\\n\", \"100 98\\n\", \"1 35\\n\", \"46 6\\n\", \"99 99\\n\", \"100 99\\n\", \"99 98\\n\", \"3 1\\n\", \"28 82\\n\", \"65 63\\n\", \"68 42\\n\", \"46 79\\n\", \"25 66\\n\", \"4 2\\n\", \"5 4\\n\", \"26 68\\n\", \"1 5\\n\", \"1 45\\n\", \"46 10\\n\", \"28 100\\n\", \"1 6\\n\", \"50 79\\n\", \"8 2\\n\", \"4 4\\n\", \"26 66\\n\", \"1 7\\n\", \"46 9\\n\", \"50 50\\n\", \"2 4\\n\", \"2 7\\n\", \"71 9\\n\", \"64 50\\n\", \"38 9\\n\", \"13 50\\n\", \"39 9\\n\", \"39 10\\n\", \"31 10\\n\", \"59 84\\n\", \"20 82\\n\", \"2 6\\n\", \"10 100\\n\", \"98 52\\n\", \"57 99\\n\", \"100 18\\n\", \"99 34\\n\", \"54 82\\n\", \"46 1\\n\", \"5 5\\n\", \"38 66\\n\", \"12 68\\n\", \"7 1\\n\", \"46 2\\n\", \"50 16\\n\", \"3 7\\n\", \"4 14\\n\", \"26 28\\n\", \"2 10\\n\", \"83 9\\n\", \"36 50\\n\", \"1 10\\n\", \"64 66\\n\", \"66 9\\n\", \"13 5\\n\", \"25 9\\n\", \"23 10\\n\", \"20 10\\n\", \"3 84\\n\", \"14 82\\n\", \"4 6\\n\", \"24 52\\n\", \"3 5\\n\", \"12 45\\n\", \"13 1\\n\", \"30 2\\n\", \"6 7\\n\", \"8 14\\n\", \"83 18\\n\", \"67 50\\n\", \"2 3\\n\", \"3 3\\n\", \"2 2\\n\"], \"outputs\": [\"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Malvika\\n\", \"Akshat\\n\", \"Malvika\\n\"]}", "source": "taco"}
|
After winning gold and silver in IOI 2014, Akshat and Malvika want to have some fun. Now they are playing a game on a grid made of n horizontal and m vertical sticks.
An intersection point is any point on the grid which is formed by the intersection of one horizontal stick and one vertical stick.
In the grid shown below, n = 3 and m = 3. There are n + m = 6 sticks in total (horizontal sticks are shown in red and vertical sticks are shown in green). There are n·m = 9 intersection points, numbered from 1 to 9.
[Image]
The rules of the game are very simple. The players move in turns. Akshat won gold, so he makes the first move. During his/her move, a player must choose any remaining intersection point and remove from the grid all sticks which pass through this point. A player will lose the game if he/she cannot make a move (i.e. there are no intersection points remaining on the grid at his/her move).
Assume that both players play optimally. Who will win the game?
-----Input-----
The first line of input contains two space-separated integers, n and m (1 ≤ n, m ≤ 100).
-----Output-----
Print a single line containing "Akshat" or "Malvika" (without the quotes), depending on the winner of the game.
-----Examples-----
Input
2 2
Output
Malvika
Input
2 3
Output
Malvika
Input
3 3
Output
Akshat
-----Note-----
Explanation of the first sample:
The grid has four intersection points, numbered from 1 to 4.
[Image]
If Akshat chooses intersection point 1, then he will remove two sticks (1 - 2 and 1 - 3). The resulting grid will look like this.
[Image]
Now there is only one remaining intersection point (i.e. 4). Malvika must choose it and remove both remaining sticks. After her move the grid will be empty.
In the empty grid, Akshat cannot make any move, hence he will lose.
Since all 4 intersection points of the grid are equivalent, Akshat will lose no matter which one he picks.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"6\\n010000\\n000001\\n\", \"10\\n1111100000\\n0000011111\\n\", \"8\\n10101010\\n01010101\\n\", \"10\\n1111100000\\n1111100001\\n\", \"12\\n011001010101\\n111001010101\\n\", \"9\\n111110000\\n111100000\\n\", \"5\\n10100\\n01010\\n\", \"10\\n1010111110\\n1011101101\\n\", \"3\\n000\\n000\\n\", \"5\\n11011\\n10111\\n\", \"10\\n0111101111\\n0111111110\\n\", \"10\\n1100000100\\n0010000011\\n\", \"10\\n1010111110\\n1011101101\\n\", \"12\\n011001010101\\n111001010101\\n\", \"10\\n1100000100\\n0010000011\\n\", \"10\\n0111101111\\n0111111110\\n\", \"3\\n000\\n000\\n\", \"5\\n10100\\n01010\\n\", \"5\\n11011\\n10111\\n\", \"9\\n111110000\\n111100000\\n\", \"10\\n1010011110\\n1011101101\\n\", \"9\\n111010000\\n111100000\\n\", \"10\\n1010011110\\n1001101101\\n\", \"10\\n1111100000\\n0010011101\\n\", \"10\\n1111100000\\n0011011001\\n\", \"10\\n1100100100\\n0010000011\\n\", \"10\\n0111001111\\n0111111110\\n\", \"3\\n000\\n001\\n\", \"5\\n10100\\n01110\\n\", \"5\\n01011\\n10111\\n\", \"6\\n010000\\n000000\\n\", \"10\\n1111100000\\n0000011101\\n\", \"8\\n10101010\\n01011101\\n\", \"10\\n0100100100\\n0010000011\\n\", \"3\\n100\\n000\\n\", \"5\\n10101\\n01110\\n\", \"5\\n01011\\n00111\\n\", \"9\\n111011000\\n111100000\\n\", \"10\\n1010011110\\n1001111101\\n\", \"10\\n0100100100\\n0010010011\\n\", \"5\\n10101\\n00110\\n\", \"5\\n01010\\n00111\\n\", \"10\\n1111100000\\n0011011101\\n\", \"10\\n1010011110\\n1001111100\\n\", \"10\\n0100100110\\n0010010011\\n\", \"5\\n01010\\n00101\\n\", \"10\\n0010011110\\n1001111100\\n\", \"10\\n0100110110\\n0010010011\\n\", \"5\\n01010\\n10101\\n\", \"10\\n0110011110\\n1001111100\\n\", \"5\\n11010\\n10101\\n\", \"10\\n0110111110\\n1001111100\\n\", \"5\\n11010\\n10001\\n\", \"10\\n0110111110\\n1001111101\\n\", \"10\\n0110111111\\n1001111101\\n\", \"10\\n1010111110\\n1011111101\\n\", \"12\\n011101010101\\n111001010101\\n\", \"10\\n1100000100\\n0010000001\\n\", \"10\\n0111111111\\n0111111110\\n\", \"3\\n010\\n000\\n\", \"5\\n10100\\n00010\\n\", \"5\\n11011\\n10011\\n\", \"9\\n111010000\\n111100001\\n\", \"6\\n010001\\n000001\\n\", \"10\\n1011100000\\n0000011111\\n\", \"8\\n10101011\\n01010101\\n\", \"10\\n1100100100\\n1010000011\\n\", \"5\\n10101\\n11110\\n\", \"9\\n111010000\\n011100000\\n\", \"10\\n1010011100\\n1001101101\\n\", \"10\\n0110100100\\n0010000011\\n\", \"3\\n010\\n001\\n\", \"5\\n10101\\n01100\\n\", \"5\\n11011\\n00111\\n\", \"9\\n111011000\\n111100001\\n\", \"10\\n1110100000\\n0000011101\\n\", \"5\\n10101\\n00111\\n\", \"5\\n01010\\n00011\\n\", \"10\\n1110011110\\n1001111100\\n\", \"10\\n0100100111\\n0010010011\\n\", \"5\\n01010\\n00001\\n\", \"10\\n0010011110\\n1001111000\\n\", \"10\\n0100100110\\n0010000011\\n\", \"10\\n0110011110\\n1001011100\\n\", \"5\\n11000\\n10101\\n\", \"5\\n11010\\n10011\\n\", \"10\\n0110101110\\n1001111101\\n\", \"10\\n1010111110\\n0011111101\\n\", \"12\\n011101010101\\n101001010101\\n\", \"3\\n010\\n100\\n\", \"5\\n10100\\n00110\\n\", \"6\\n010001\\n100001\\n\", \"8\\n10001011\\n01010101\\n\", \"10\\n1100100100\\n1010001011\\n\", \"9\\n111010000\\n011101000\\n\", \"10\\n1010111100\\n1001101101\\n\", \"3\\n010\\n101\\n\", \"10\\n1111100000\\n1111100001\\n\", \"6\\n010000\\n000001\\n\", \"10\\n1111100000\\n0000011111\\n\", \"8\\n10101010\\n01010101\\n\"], \"outputs\": [\"1\", \"5\", \"1\", \"-1\", \"-1\", \"-1\", \"1\", \"2\", \"0\", \"1\", \"1\", \"2\", \"2\\n\", \"-1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\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\", \"-1\\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\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"4\\n\", \"1\\n\", \"1\\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\", \"1\\n\", \"2\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"1\\n\", \"5\\n\", \"1\\n\"]}", "source": "taco"}
|
Naman has two binary strings $s$ and $t$ of length $n$ (a binary string is a string which only consists of the characters "0" and "1"). He wants to convert $s$ into $t$ using the following operation as few times as possible.
In one operation, he can choose any subsequence of $s$ and rotate it clockwise once.
For example, if $s = 1\textbf{1}101\textbf{00}$, he can choose a subsequence corresponding to indices ($1$-based) $\{2, 6, 7 \}$ and rotate them clockwise. The resulting string would then be $s = 1\textbf{0}101\textbf{10}$.
A string $a$ is said to be a subsequence of string $b$ if $a$ can be obtained from $b$ by deleting some characters without changing the ordering of the remaining characters.
To perform a clockwise rotation on a sequence $c$ of size $k$ is to perform an operation which sets $c_1:=c_k, c_2:=c_1, c_3:=c_2, \ldots, c_k:=c_{k-1}$ simultaneously.
Determine the minimum number of operations Naman has to perform to convert $s$ into $t$ or say that it is impossible.
-----Input-----
The first line contains a single integer $n$ $(1 \le n \le 10^6)$ — the length of the strings.
The second line contains the binary string $s$ of length $n$.
The third line contains the binary string $t$ of length $n$.
-----Output-----
If it is impossible to convert $s$ to $t$ after any number of operations, print $-1$.
Otherwise, print the minimum number of operations required.
-----Examples-----
Input
6
010000
000001
Output
1
Input
10
1111100000
0000011111
Output
5
Input
8
10101010
01010101
Output
1
Input
10
1111100000
1111100001
Output
-1
-----Note-----
In the first test, Naman can choose the subsequence corresponding to indices $\{2, 6\}$ and rotate it once to convert $s$ into $t$.
In the second test, he can rotate the subsequence corresponding to all indices $5$ times. It can be proved, that it is the minimum required number of operations.
In the last test, it is impossible to convert $s$ into $t$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 5\\n..XXX\\n...X.\\n...X.\\n...X.\\n5\\n1 3\\n3 3\\n4 5\\n5 5\\n1 5\\n\", \"1 1\\nX\\n1\\n1 1\\n\", \"1 1\\n.\\n1\\n1 1\\n\", \"3 3\\n..X\\n.X.\\nX..\\n10\\n1 3\\n1 3\\n1 3\\n2 3\\n1 3\\n1 2\\n1 3\\n2 2\\n2 3\\n2 2\\n\", \"3 3\\n...\\nXXX\\nXX.\\n10\\n2 3\\n1 2\\n2 2\\n1 3\\n2 3\\n1 2\\n1 3\\n1 3\\n2 3\\n1 1\\n\", \"3 3\\nXX.\\nXX.\\nX..\\n10\\n2 3\\n2 2\\n2 3\\n1 3\\n2 3\\n1 1\\n2 3\\n1 2\\n3 3\\n2 3\\n\", \"3 3\\n.XX\\nX..\\nXXX\\n10\\n2 2\\n1 1\\n1 2\\n1 3\\n1 3\\n2 3\\n1 2\\n2 3\\n1 3\\n1 2\\n\", \"3 3\\nXX.\\n...\\n.XX\\n10\\n1 3\\n1 3\\n1 2\\n1 2\\n3 3\\n1 3\\n2 3\\n3 3\\n2 3\\n2 2\\n\", \"3 3\\n..X\\n.XX\\nXXX\\n10\\n1 2\\n1 1\\n2 2\\n1 2\\n1 3\\n1 2\\n1 3\\n2 2\\n2 3\\n2 2\\n\", \"3 3\\nX.X\\nXX.\\n..X\\n10\\n1 3\\n1 2\\n1 2\\n3 3\\n1 2\\n1 2\\n3 3\\n1 1\\n1 3\\n2 3\\n\", \"3 3\\n.X.\\nX..\\nX.X\\n10\\n1 2\\n1 1\\n2 3\\n1 2\\n2 2\\n1 3\\n1 2\\n3 3\\n2 3\\n2 3\\n\", \"3 3\\nX.X\\n.XX\\n...\\n10\\n1 3\\n1 2\\n2 3\\n2 3\\n2 2\\n3 3\\n3 3\\n1 3\\n1 2\\n1 3\\n\", \"3 3\\nXX.\\nXXX\\nXX.\\n10\\n2 2\\n3 3\\n3 3\\n2 3\\n2 3\\n1 2\\n1 3\\n1 1\\n1 3\\n1 2\\n\", \"3 3\\nX.X\\n..X\\nXXX\\n10\\n3 3\\n1 2\\n3 3\\n1 2\\n1 3\\n1 2\\n1 1\\n2 3\\n2 3\\n1 2\\n\", \"3 3\\n..X\\nX.X\\n..X\\n10\\n2 3\\n2 2\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n1 1\\n1 2\\n1 1\\n\", \"3 3\\nXXX\\nXX.\\nXX.\\n10\\n1 3\\n1 2\\n1 2\\n1 3\\n3 3\\n2 2\\n2 3\\n2 3\\n2 3\\n2 2\\n\", \"3 3\\n...\\nX.X\\n..X\\n10\\n2 3\\n3 3\\n2 3\\n1 2\\n3 3\\n1 1\\n1 2\\n2 3\\n1 1\\n1 2\\n\", \"3 3\\nXX.\\nXXX\\n..X\\n10\\n1 2\\n1 2\\n2 3\\n1 3\\n1 1\\n2 3\\n1 3\\n1 1\\n2 3\\n2 2\\n\", \"3 3\\nX..\\n..X\\nXX.\\n10\\n1 3\\n2 2\\n1 2\\n1 2\\n2 3\\n1 3\\n1 1\\n2 2\\n1 3\\n1 1\\n\", \"3 3\\n..X\\nX..\\n...\\n10\\n3 3\\n1 3\\n1 3\\n3 3\\n1 3\\n2 3\\n3 3\\n3 3\\n2 3\\n1 2\\n\", \"3 3\\n.XX\\n..X\\n.X.\\n10\\n2 3\\n1 3\\n2 3\\n2 3\\n1 3\\n1 1\\n2 2\\n1 2\\n3 3\\n1 2\\n\", \"3 3\\n.XX\\nX..\\nXXX\\n10\\n1 2\\n1 1\\n2 3\\n1 2\\n2 3\\n2 3\\n1 3\\n2 3\\n3 3\\n2 3\\n\", \"3 3\\nXXX\\nX..\\nX..\\n10\\n2 2\\n1 2\\n2 2\\n2 3\\n2 2\\n3 3\\n1 1\\n2 3\\n2 2\\n1 3\\n\"], \"outputs\": [\"YES\\nYES\\nNO\\nYES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nNO\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\n\", \"NO\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nYES\\nNO\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nNO\\nNO\\nNO\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nNO\\nYES\\nNO\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\n\", \"NO\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nYES\\nYES\\nNO\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\n\"]}", "source": "taco"}
|
The problem statement looms below, filling you with determination.
Consider a grid in which some cells are empty and some cells are filled. Call a cell in this grid exitable if, starting at that cell, you can exit the grid by moving up and left through only empty cells. This includes the cell itself, so all filled in cells are not exitable. Note that you can exit the grid from any leftmost empty cell (cell in the first column) by going left, and from any topmost empty cell (cell in the first row) by going up.
Let's call a grid determinable if, given only which cells are exitable, we can exactly determine which cells are filled in and which aren't.
You are given a grid $a$ of dimensions $n \times m$ , i. e. a grid with $n$ rows and $m$ columns. You need to answer $q$ queries ($1 \leq q \leq 2 \cdot 10^5$). Each query gives two integers $x_1, x_2$ ($1 \leq x_1 \leq x_2 \leq m$) and asks whether the subgrid of $a$ consisting of the columns $x_1, x_1 + 1, \ldots, x_2 - 1, x_2$ is determinable.
-----Input-----
The first line contains two integers $n, m$ ($1 \leq n, m \leq 10^6$, $nm \leq 10^6$) — the dimensions of the grid $a$.
$n$ lines follow. The $y$-th line contains $m$ characters, the $x$-th of which is 'X' if the cell on the intersection of the the $y$-th row and $x$-th column is filled and "." if it is empty.
The next line contains a single integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.
$q$ lines follow. Each line contains two integers $x_1$ and $x_2$ ($1 \leq x_1 \leq x_2 \leq m$), representing a query asking whether the subgrid of $a$ containing the columns $x_1, x_1 + 1, \ldots, x_2 - 1, x_2$ is determinable.
-----Output-----
For each query, output one line containing "YES" if the subgrid specified by the query is determinable and "NO" otherwise. The output is case insensitive (so "yEs" and "No" will also be accepted).
-----Examples-----
Input
4 5
..XXX
...X.
...X.
...X.
5
1 3
3 3
4 5
5 5
1 5
Output
YES
YES
NO
YES
NO
-----Note-----
For each query of the example, the corresponding subgrid is displayed twice below: first in its input format, then with each cell marked as "E" if it is exitable and "N" otherwise.
For the first query:
..X EEN
... EEE
... EEE
... EEE
For the second query:
X N
. E
. E
. E
Note that you can exit the grid by going left from any leftmost cell (or up from any topmost cell); you do not need to reach the top left corner cell to exit the grid.
For the third query:
XX NN
X. NN
X. NN
X. NN
This subgrid cannot be determined only from whether each cell is exitable, because the below grid produces the above "exitability grid" as well:
XX
XX
XX
XX
For the fourth query:
X N
. E
. E
. E
For the fifth query:
..XXX EENNN
...X. EEENN
...X. EEENN
...X. EEENN
This query is simply the entire grid. It cannot be determined only from whether each cell is exitable because the below grid produces the above "exitability grid" as well:
..XXX
...XX
...XX
...XX
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n1 3 1 4 5\\n\", \"4\\n4 2 2 4\\n\", \"2\\n1 1\\n\", \"5\\n100 1 100 1 100\\n\", \"4\\n2 3 4 2\\n\", \"4\\n2 1 3 3\\n\", \"5\\n1 5 5 1 4\\n\", \"4\\n2 3 4 2\\n\", \"4\\n2 1 3 3\\n\", \"8\\n4 2 5 5 1 2 5 2\\n\", \"5\\n1 5 5 1 4\\n\", \"4\\n1 3 4 2\\n\", \"4\\n2 1 5 3\\n\", \"8\\n7 2 5 5 1 2 5 2\\n\", \"5\\n1 3 1 4 7\\n\", \"8\\n7 2 5 5 1 2 2 2\\n\", \"5\\n0 5 5 1 4\\n\", \"4\\n4 2 2 7\\n\", \"2\\n1 2\\n\", \"4\\n1 3 8 2\\n\", \"4\\n2 2 5 3\\n\", \"8\\n7 2 5 5 2 2 5 2\\n\", \"5\\n0 5 6 1 4\\n\", \"5\\n2 3 1 4 7\\n\", \"4\\n4 2 0 7\\n\", \"2\\n1 4\\n\", \"4\\n1 4 8 2\\n\", \"4\\n3 2 5 3\\n\", \"5\\n0 10 6 1 4\\n\", \"5\\n2 3 0 4 7\\n\", \"4\\n4 2 0 3\\n\", \"2\\n1 0\\n\", \"4\\n0 4 8 2\\n\", \"4\\n3 1 5 3\\n\", \"5\\n0 10 6 1 8\\n\", \"4\\n2 2 0 3\\n\", \"4\\n-1 4 8 2\\n\", \"4\\n3 0 5 3\\n\", \"5\\n0 10 6 1 3\\n\", \"4\\n2 4 0 3\\n\", \"4\\n-1 4 8 3\\n\", \"4\\n3 1 5 1\\n\", \"5\\n1 10 6 1 3\\n\", \"4\\n1 4 0 3\\n\", \"4\\n-1 4 8 5\\n\", \"4\\n3 0 5 1\\n\", \"5\\n1 19 6 1 3\\n\", \"4\\n1 7 0 3\\n\", \"4\\n-1 5 8 5\\n\", \"5\\n1 19 10 1 3\\n\", \"4\\n1 7 0 0\\n\", \"4\\n-1 3 8 5\\n\", \"5\\n1 16 10 1 3\\n\", \"5\\n1 16 10 0 3\\n\", \"5\\n1 30 10 0 3\\n\", \"5\\n1 30 10 0 0\\n\", \"5\\n1 2 10 0 0\\n\", \"5\\n0 2 10 0 0\\n\", \"5\\n0 2 6 0 0\\n\", \"5\\n0 2 6 0 1\\n\", \"5\\n0 2 5 0 1\\n\", \"5\\n0 2 8 0 1\\n\", \"5\\n-1 2 8 0 1\\n\", \"5\\n-1 4 8 0 1\\n\", \"4\\n2 3 4 4\\n\", \"4\\n2 2 3 3\\n\", \"8\\n4 3 5 5 1 2 5 2\\n\", \"5\\n1 5 5 1 1\\n\", \"5\\n1 1 1 4 5\\n\", \"5\\n110 1 100 1 100\\n\", \"4\\n3 2 2 4\\n\", \"2\\n0 0\\n\", \"4\\n1 3 4 0\\n\", \"4\\n2 1 5 6\\n\", \"5\\n0 5 2 1 4\\n\", \"5\\n2 3 1 7 7\\n\", \"4\\n1 2 2 7\\n\", \"2\\n2 2\\n\", \"4\\n1 4 0 2\\n\", \"4\\n2 0 5 3\\n\", \"8\\n7 2 5 5 3 2 5 2\\n\", \"5\\n0 5 6 1 1\\n\", \"5\\n2 3 1 4 3\\n\", \"4\\n4 2 0 5\\n\", \"4\\n1 4 8 3\\n\", \"4\\n3 3 5 3\\n\", \"5\\n-1 10 6 1 4\\n\", \"5\\n2 6 0 4 7\\n\", \"4\\n4 2 1 3\\n\", \"4\\n-1 8 8 3\\n\", \"5\\n1 3 1 4 5\\n\", \"5\\n100 1 100 1 100\\n\", \"4\\n4 2 2 4\\n\", \"2\\n1 1\\n\"], \"outputs\": [\"3\", \"1\", \"1\", \"2\", \"1\", \"2\", \"2\", \"1\", \"2\", \"4\", \"2\", \"1\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\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\", \"3\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"3\", \"2\", \"1\", \"1\"]}", "source": "taco"}
|
There are $n$ beautiful skyscrapers in New York, the height of the $i$-th one is $h_i$. Today some villains have set on fire first $n - 1$ of them, and now the only safety building is $n$-th skyscraper.
Let's call a jump from $i$-th skyscraper to $j$-th ($i < j$) discrete, if all skyscrapers between are strictly lower or higher than both of them. Formally, jump is discrete, if $i < j$ and one of the following conditions satisfied: $i + 1 = j$ $\max(h_{i + 1}, \ldots, h_{j - 1}) < \min(h_i, h_j)$ $\max(h_i, h_j) < \min(h_{i + 1}, \ldots, h_{j - 1})$.
At the moment, Vasya is staying on the first skyscraper and wants to live a little longer, so his goal is to reach $n$-th skyscraper with minimal count of discrete jumps. Help him with calcualting this number.
-----Input-----
The first line contains a single integer $n$ ($2 \le n \le 3 \cdot 10^5$) — total amount of skyscrapers.
The second line contains $n$ integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le 10^9$) — heights of skyscrapers.
-----Output-----
Print single number $k$ — minimal amount of discrete jumps. We can show that an answer always exists.
-----Examples-----
Input
5
1 3 1 4 5
Output
3
Input
4
4 2 2 4
Output
1
Input
2
1 1
Output
1
Input
5
100 1 100 1 100
Output
2
-----Note-----
In the first testcase, Vasya can jump in the following way: $1 \rightarrow 2 \rightarrow 4 \rightarrow 5$.
In the second and third testcases, we can reach last skyscraper in one jump.
Sequence of jumps in the fourth testcase: $1 \rightarrow 3 \rightarrow 5$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"100 5\\n101 101 5 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 90\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 0 5 1\\n45 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n101 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 82 90\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 0 5 1\\n45 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 2\\n-30 0 500 5\\n0 0\", \"100 5\\n001 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 82 90\\n-110 108 10 2\\n10 11\\n15 -1 5 1\\n25 0 5 1\\n35 0 5 1\\n45 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n111 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 63 82 90\\n-110 108 10 2\\n10 11\\n15 -1 5 1\\n25 0 5 1\\n35 0 5 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n111 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 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90\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 1 5 1\\n35 -1 5 1\\n53 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n36 0 5 1\\n-20 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n101 101 5 5\\n110 110 3 3\\n-112 -30 5 11\\n-208 160 82 90\\n-93 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 0 5 1\\n45 0 5 1\\n55 0 5 2\\n65 0 5 1\\n81 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n111 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 293 82 90\\n-110 159 10 2\\n10 11\\n15 -1 5 1\\n25 0 5 1\\n35 0 5 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 2\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n101 111 5 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 90\\n-110 87 14 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 -1 5 1\\n45 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n36 0 5 0\\n-20 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n101 101 5 5\\n110 110 3 3\\n-112 -30 5 11\\n-208 155 82 90\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 0 5 2\\n45 0 5 1\\n55 0 5 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5\\n0 0\", \"100 5\\n111 101 5 5\\n110 010 2 3\\n-112 -100 5 11\\n-208 160 109 90\\n-110 159 10 2\\n10 11\\n15 -1 5 1\\n25 0 5 1\\n56 0 5 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 1\\n83 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n101 111 5 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 102\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 -1 5 2\\n45 0 10 1\\n55 0 5 1\\n65 0 0 1\\n75 0 5 1\\n73 0 5 1\\n36 0 5 0\\n-20 0 5 20\\n-30 0 500 5\\n0 0\", \"100 5\\n111 101 5 5\\n110 110 0 3\\n-112 -100 5 11\\n-208 160 109 90\\n-110 159 10 2\\n10 11\\n15 -1 5 2\\n25 0 5 1\\n35 0 5 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 1\\n83 0 5 1\\n85 0 5 1\\n95 -1 5 1\\n-19 0 5 20\\n-30 0 500 5\\n0 0\", \"110 5\\n101 111 5 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 102\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 -1 5 2\\n45 0 10 1\\n55 0 5 1\\n65 0 5 1\\n30 0 5 1\\n85 0 5 1\\n36 0 5 0\\n-20 0 5 20\\n-30 0 107 5\\n0 0\", \"100 5\\n101 111 9 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 102\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 -1 5 2\\n21 0 10 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 0\\n85 0 5 1\\n36 0 5 0\\n-20 0 5 20\\n-30 0 107 5\\n0 0\", \"100 5\\n111 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 109 90\\n-110 159 10 2\\n10 11\\n15 -1 5 2\\n25 0 5 1\\n35 0 5 1\\n118 0 5 1\\n55 0 5 1\\n65 0 5 1\\n149 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 -1 5 20\\n-30 1 500 5\\n0 0\", \"100 5\\n110 101 5 3\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 109 90\\n-110 159 10 2\\n10 11\\n15 -1 5 2\\n25 0 5 1\\n35 0 6 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 1\\n83 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-19 -1 5 20\\n-30 1 500 5\\n0 0\", \"100 5\\n010 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 109 172\\n-110 159 10 2\\n10 11\\n15 -1 5 2\\n25 0 5 1\\n35 0 5 1\\n65 0 5 1\\n55 0 5 1\\n65 0 5 1\\n83 0 5 1\\n85 -1 5 1\\n95 0 5 1\\n-19 -1 5 20\\n-30 1 500 5\\n0 0\", \"100 5\\n110 101 5 5\\n110 110 2 3\\n-112 -100 5 11\\n-208 160 109 90\\n-110 159 10 2\\n10 11\\n15 -1 5 0\\n26 0 5 1\\n35 0 5 1\\n65 0 5 1\\n55 0 5 2\\n65 0 5 1\\n83 0 5 1\\n85 -1 5 1\\n95 0 5 1\\n-19 -1 5 20\\n-30 1 500 5\\n0 0\", \"100 5\\n101 101 5 5\\n110 110 2 3\\n-112 -100 9 11\\n-208 160 82 90\\n-110 108 10 2\\n10 11\\n15 0 5 1\\n25 0 5 1\\n35 0 5 1\\n45 0 5 1\\n55 0 5 1\\n65 0 5 1\\n75 0 5 1\\n85 0 5 1\\n95 0 5 1\\n-20 0 5 20\\n-30 0 500 5\\n0 0\"], \"outputs\": [\"1\\n1\\n\", \"1\\n0\\n\", \"2\\n1\\n\", \"0\\n1\\n\", \"1\\n2\\n\", \"0\\n2\\n\", \"1\\n3\\n\", \"0\\n0\\n\", \"0\\n3\\n\", \"1\\n4\\n\", \"2\\n2\\n\", \"0\\n4\\n\", \"3\\n2\\n\", \"3\\n3\\n\", \"2\\n3\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n0\\n\", \"2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"0\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"0\\n1\\n\", \"1\\n1\\n\", \"0\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\"]}", "source": "taco"}
|
In 40XX, the Earth was invaded by aliens! Already most of the Earth has been dominated by aliens, leaving Tsuruga Castle Fortress as the only remaining defense base. Suppression units are approaching the Tsuruga Castle Fortress one after another.
<image>
But hope remains. The ultimate defense force weapon, the ultra-long-range penetrating laser cannon, has been completed. The downside is that it takes a certain distance to reach its power, and enemies that are too close can just pass through. Enemies who have invaded the area where power does not come out have no choice but to do something with other forces. The Defense Forces staff must know the number to deal with the invading UFOs, but it is unlikely to be counted well because there are too many enemies. So the staff ordered you to have a program that would output the number of UFOs that weren't shot down by the laser. Create a program by the time the battle begins and help protect the Tsuruga Castle Fortress.
Enemy UFOs just rush straight toward the base of the laser cannon (the UFOs are treated to slip through each other and do not collide). The laser cannon begins firing at the center of the nearest UFO one minute after the initial state, and then continues firing the laser every minute under the same conditions. The laser penetrates, and the UFO beyond it can be shot down with the laser just scratching it. However, this laser has a range where it is not powerful, and it is meaningless to aim a UFO that has fallen into that range, so it is designed not to aim. How many UFOs invaded the area where the power of the laser did not come out when it was shot down as much as possible?
Create a program that inputs the radius R of the range where the power of the laser does not come out and the information of the invading UFO, and outputs how many UFOs are invading without being shot down. The information on the incoming UFO consists of the number of UFOs N, the initial coordinates of each UFO (x0, y0), the radius r of each UFO, and the speed v of each UFO.
The origin of the coordinates (0, 0) is the position of the laser cannon. The distance between the laser cannon and the UFO is given by the distance from the origin to the center of the UFO, and UFOs with this distance less than or equal to R are within the range where the power of the laser does not come out. Consider that there are no cases where there are multiple targets to be aimed at at the same time. All calculations are considered on a plane and all inputs are given as integers.
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:
R N
x01 y01 r1 v1
x02 y02 r2 v2
::
x0N y0N rN vN
The first line gives the radius R (1 ≤ R ≤ 500) and the number of UFOs N (1 ≤ N ≤ 100) within the range of laser power. The following N lines give the i-th UFO information x0i, y0i (-100 ≤ x0i, y0i ≤ 1000), ri, vi (1 ≤ ri, vi ≤ 500).
The number of datasets does not exceed 50.
Output
For each input dataset, it prints the number of UFOs that have invaded the area where the laser power does not come out on one line.
Example
Input
100 5
101 101 5 5
110 110 2 3
-112 -100 9 11
-208 160 82 90
-110 108 10 2
10 11
15 0 5 1
25 0 5 1
35 0 5 1
45 0 5 1
55 0 5 1
65 0 5 1
75 0 5 1
85 0 5 1
95 0 5 1
-20 0 5 20
-30 0 500 5
0 0
Output
1
1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[5, 6], [19, 20], [6, 20], [15, 20], [8, 20], [9, 8], [4, 10], [12, 12], [7, 10], [4, 12]], \"outputs\": [[19], [208], [195], [204], [197], [36], [48], [77], [51], [69]]}", "source": "taco"}
|
Your task is to return the number of visible dots on a die after it has been rolled(that means the total count of dots that would not be touching the table when rolled)
6, 8, 10, 12, 20 sided dice are the possible inputs for "numOfSides"
topNum is equal to the number that is on top, or the number that was rolled.
for this exercise, all opposite faces add up to be 1 more than the total amount of sides
Example: 6 sided die would have 6 opposite 1, 4 opposite 3, and so on.
for this exercise, the 10 sided die starts at 1 and ends on 10.
Note: topNum will never be greater than numOfSides
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 2 5\\n1 2 3\\n2 3 3\\n2\\n3 2\\n1 3\\n\", \"4 0 1\\n1\\n2 1\\n\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\\n\", \"4 0 0\\n1\\n2 1\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"3 2 5\\n1 2 3\\n2 2 3\\n2\\n3 2\\n1 3\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 5\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n5 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"3 2 5\\n2 2 3\\n2 3 3\\n2\\n3 2\\n1 3\", \"5 4 4\\n1 2 2\\n3 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 2\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n3 5 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 3\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 0\\n1 2 2\\n3 5 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"3 2 5\\n1 2 3\\n1 3 3\\n2\\n3 2\\n1 3\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n5 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 3\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n3 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 2 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 3\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"3 2 5\\n1 2 3\\n1 3 3\\n2\\n1 2\\n1 3\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n5 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 3\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n0 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 5 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n5 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 3\\n2 4\\n3 4\\n5 4\\n1 5\\n2 4\\n3 5\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n0 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 6\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n4 5 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n5 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 3\\n2 4\\n3 4\\n5 4\\n1 5\\n2 4\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n5 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n4 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n1 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n5 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n2 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 2\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n3 5 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 1\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 3\\n3 2\\n4 2\\n5 2\\n1 4\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 0\\n3 1\\n3 1\\n5 1\\n1 2\\n0 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n4 5 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n3 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 0\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n4 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n1 2\\n5 3\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n3 5 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 1\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n6 5\", \"5 4 4\\n1 4 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 3\\n3 2\\n4 2\\n5 2\\n1 4\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 1\\n20\\n3 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n1 2\\n5 3\\n1 3\\n1 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 4 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 3\\n3 2\\n4 2\\n5 2\\n1 4\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n2 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 1\\n20\\n3 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n1 4\\n4 3\\n5 3\\n1 4\\n2 4\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n0 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 2\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n3 5\", \"5 4 1\\n1 2 2\\n3 2 2\\n3 4 1\\n4 5 3\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 1\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n1 2\\n5 3\\n1 3\\n1 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n2 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 4 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 3\\n3 2\\n4 2\\n5 2\\n1 4\\n1 4\\n4 3\\n5 3\\n1 4\\n2 4\\n2 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 2 2\\n20\\n0 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 2\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n3 5\", \"5 4 4\\n2 2 2\\n1 3 0\\n3 4 3\\n4 2 2\\n20\\n0 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 2\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n3 5\", \"5 4 4\\n2 2 2\\n1 2 0\\n3 4 3\\n4 2 2\\n20\\n0 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n3 2\\n1 2\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n3 5\", \"5 4 4\\n2 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 5\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 4 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 1 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 5\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 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2\\n1 3\\n2 3\\n4 3\\n5 1\\n1 3\\n2 4\\n3 4\\n5 4\\n1 5\\n2 4\\n3 5\\n4 5\", \"5 4 4\\n1 2 2\\n2 3 2\\n5 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n2 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n1 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n1 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n2 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 2\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"3 2 2\\n1 2 3\\n1 3 0\\n2\\n3 2\\n1 3\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 0\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"5 4 4\\n2 2 2\\n2 3 0\\n3 1 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n0 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 5\\n4 3\\n5 3\\n1 4\\n3 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5\", \"6 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 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\"1\\n1\\n0\\n-1\\n1\\n0\\n0\\n-1\\n1\\n-1\\n0\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"0\\n1\\n2\\n3\\n2\\n0\\n1\\n2\\n1\\n1\\n0\\n1\\n2\\n0\\n3\\n0\\n3\\n2\\n1\\n0\\n\", \"0\\n1\\n2\\n3\\n1\\n0\\n1\\n2\\n1\\n1\\n0\\n1\\n2\\n2\\n0\\n0\\n3\\n2\\n1\\n0\\n\", \"0\\n0\\n0\\n2\\n0\\n-1\\n-1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n1\\n0\\n1\\n1\\n1\\n0\\n1\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n1\\n0\\n\", \"0\\n0\\n0\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n-1\\n1\\n1\\n0\\n1\\n2\\n2\\n1\\n0\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n1\\n0\\n\", \"0\\n0\\n2\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n2\\n0\\n1\\n0\\n0\\n2\\n1\\n1\\n0\\n\", \"0\\n0\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n\", \"0\\n1\\n2\\n3\\n0\\n0\\n0\\n2\\n1\\n1\\n0\\n1\\n2\\n1\\n2\\n0\\n3\\n2\\n1\\n0\\n\", \"0\\n1\\n2\\n0\\n2\\n0\\n1\\n0\\n1\\n1\\n0\\n0\\n2\\n1\\n1\\n1\\n1\\n0\\n0\\n1\\n\", \"-1\\n0\\n\", \"0\\n-1\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n\", \"0\\n0\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n0\\n\", \"0\\n0\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n-1\\n1\\n0\\n0\\n2\\n2\\n1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n0\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n0\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"2\\n1\\n0\\n1\\n1\\n0\\n1\\n2\\n1\\n0\\n0\\n1\\n0\\n1\\n1\\n0\\n1\\n2\\n1\\n0\\n\", \"-1\\n1\\n0\\n1\\n0\\n1\\n0\\n1\\n0\\n1\\n0\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"0\\n0\\n1\\n2\\n0\\n0\\n0\\n2\\n0\\n1\\n0\\n1\\n1\\n1\\n1\\n0\\n2\\n2\\n1\\n0\\n\", \"0\\n1\\n2\\n3\\n1\\n0\\n1\\n2\\n1\\n1\\n0\\n1\\n2\\n0\\n3\\n0\\n3\\n2\\n1\\n0\\n\", \"-1\\n1\\n-1\\n-1\\n-1\\n1\\n0\\n1\\n1\\n1\\n0\\n1\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n1\\n0\\n\", \"1\\n0\\n0\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n-1\\n1\\n1\\n0\\n1\\n2\\n2\\n1\\n0\\n\", \"0\\n1\\n1\\n3\\n0\\n0\\n0\\n2\\n1\\n1\\n0\\n1\\n2\\n1\\n2\\n0\\n3\\n2\\n1\\n0\\n\", \"0\\n-1\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n2\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n1\\n1\\n\", \"0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n0\\n0\\n0\\n1\\n-1\\n0\\n0\\n0\\n2\\n1\\n1\\n-1\\n\", \"-1\\n0\\n0\\n1\\n0\\n-1\\n-1\\n-1\\n1\\n0\\n0\\n1\\n0\\n-1\\n-1\\n0\\n1\\n-1\\n1\\n0\\n\", \"-1\\n1\\n0\\n1\\n0\\n1\\n0\\n1\\n0\\n1\\n0\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n0\\n0\\n-1\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"0\\n1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n0\\n-1\\n-1\\n-1\\n0\\n\", \"1\\n0\\n0\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n-1\\n1\\n1\\n-1\\n1\\n2\\n2\\n1\\n0\\n\", \"0\\n-1\\n0\\n1\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n0\\n0\\n0\\n0\\n1\\n0\\n0\\n0\\n\", \"0\\n0\\n1\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n1\\n-1\\n1\\n0\\n0\\n2\\n2\\n1\\n-1\\n\", \"-1\\n0\\n0\\n1\\n0\\n-1\\n-1\\n-1\\n1\\n0\\n0\\n0\\n0\\n-1\\n-1\\n0\\n1\\n-1\\n0\\n0\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n0\\n0\\n0\\n-1\\n0\\n0\\n1\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n0\\n0\\n\", \"1\\n0\\n0\\n1\\n0\\n-1\\n1\\n1\\n0\\n0\\n0\\n-1\\n1\\n1\\n-1\\n1\\n1\\n1\\n0\\n0\\n\", \"0\\n1\\n1\\n3\\n0\\n0\\n0\\n2\\n1\\n1\\n0\\n1\\n2\\n1\\n2\\n0\\n3\\n2\\n1\\n2\\n\", \"0\\n0\\n1\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n0\\n-1\\n1\\n0\\n0\\n2\\n2\\n1\\n-1\\n\", \"-1\", \"0\\n0\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\", \"0\\n1\"]}", "source": "taco"}
|
There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.
Takahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.
Process the following Q queries:
- The tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.
-----Constraints-----
- All values in input are integers.
- 2 \leq N \leq 300
- 0 \leq M \leq \frac{N(N-1)}{2}
- 1 \leq L \leq 10^9
- 1 \leq A_i, B_i \leq N
- A_i \neq B_i
- \left(A_i, B_i\right) \neq \left(A_j, B_j\right) (if i \neq j)
- \left(A_i, B_i\right) \neq \left(B_j, A_j\right) (if i \neq j)
- 1 \leq C_i \leq 10^9
- 1 \leq Q \leq N\left(N-1\right)
- 1 \leq s_i, t_i \leq N
- s_i \neq t_i
- \left(s_i, t_i\right) \neq \left(s_j, t_j\right) (if i \neq j)
-----Input-----
Input is given from Standard Input in the following format:
N M L
A_1 B_1 C_1
:
A_M B_M C_M
Q
s_1 t_1
:
s_Q t_Q
-----Output-----
Print Q lines.
The i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.
-----Sample Input-----
3 2 5
1 2 3
2 3 3
2
3 2
1 3
-----Sample Output-----
0
1
To travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.
To travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [[\"\"], [\"a\"], [\"street\"], [\"STREET\"], [\" a\"], [\"st re et\"], [\"f\"], [\"quirky\"], [\"MULTIBILLIONAIRE\"], [\"alacrity\"]], \"outputs\": [[0], [1], [6], [6], [1], [6], [4], [22], [20], [13]]}", "source": "taco"}
|
Write a program that, given a word, computes the scrabble score for that word.
## Letter Values
You'll need these:
```
Letter Value
A, E, I, O, U, L, N, R, S, T 1
D, G 2
B, C, M, P 3
F, H, V, W, Y 4
K 5
J, X 8
Q, Z 10
```
```if:ruby,javascript,cfml
There will be a preloaded hashtable `$dict` with all these values: `$dict["E"] == 1`.
```
```if:haskell
There will be a preloaded list of `(Char, Int)` tuples called `dict` with all these values.
```
```if:python
There will be a preloaded dictionary `dict_scores` with all these values: `dict_scores["E"] == 1`
```
## Examples
```
"cabbage" --> 14
```
"cabbage" should be scored as worth 14 points:
- 3 points for C
- 1 point for A, twice
- 3 points for B, twice
- 2 points for G
- 1 point for E
And to total:
`3 + 2*1 + 2*3 + 2 + 1` = `3 + 2 + 6 + 3` = `14`
Empty string should return `0`. The string can contain spaces and letters (upper and lower case), you should calculate the scrabble score only of the letters in that string.
```
"" --> 0
"STREET" --> 6
"st re et" --> 6
"ca bba g e" --> 14
```
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n4 4\\n1 1 1 1\\n3 1\\n1 2 3\\n3 3\\n1 2 3\\n\", \"10\\n2 2\\n4 3\\n2 2\\n13 13\\n2 2\\n9 11\\n2 1\\n14 5\\n2 1\\n13 2\\n2 2\\n4 5\\n2 1\\n11 14\\n2 2\\n15 3\\n2 2\\n12 10\\n2 2\\n13 12\\n\", \"10\\n3 2\\n3 6 1\\n3 3\\n9 0 2\\n3 3\\n8 8 2\\n4 2\\n9 0 0 1\\n4 4\\n5 3 0 2\\n4 4\\n2 8 6 0\\n5 3\\n7 3 8 9 8\\n5 5\\n6 3 9 6 7\\n5 5\\n1 0 5 9 8\\n5 5\\n1 5 4 6 1\\n\", \"10\\n10 10\\n8 9 2 10 3 8 10 9 1 10\\n10 10\\n3 10 3 13 12 14 3 3 4 4\\n10 5\\n7 13 10 14 5 12 5 5 7 11\\n10 10\\n12 13 3 6 12 9 6 6 5 7\\n10 10\\n4 10 15 13 13 15 9 8 8 14\\n10 10\\n2 3 8 5 9 7 11 12 7 9\\n10 10\\n12 15 11 10 1 8 10 3 4 2\\n10 5\\n8 11 7 14 7 9 5 2 8 9\\n10 10\\n4 9 9 9 10 4 1 12 13 15\\n10 10\\n12 2 7 5 15 8 2 3 10 12\\n\", \"3\\n4 4\\n1 1 1 1\\n3 1\\n1 2 3\\n3 3\\n1 2 3\\n\", \"10\\n3 2\\n3 6 1\\n3 3\\n9 0 2\\n3 3\\n8 8 2\\n4 2\\n9 0 0 1\\n4 4\\n5 3 0 2\\n4 4\\n2 8 6 0\\n5 3\\n7 3 8 9 8\\n5 5\\n6 3 9 6 7\\n5 5\\n1 0 5 9 8\\n5 5\\n1 5 4 6 1\\n\", \"10\\n2 2\\n4 3\\n2 2\\n13 13\\n2 2\\n9 11\\n2 1\\n14 5\\n2 1\\n13 2\\n2 2\\n4 5\\n2 1\\n11 14\\n2 2\\n15 3\\n2 2\\n12 10\\n2 2\\n13 12\\n\", \"10\\n10 10\\n8 9 2 10 3 8 10 9 1 10\\n10 10\\n3 10 3 13 12 14 3 3 4 4\\n10 5\\n7 13 10 14 5 12 5 5 7 11\\n10 10\\n12 13 3 6 12 9 6 6 5 7\\n10 10\\n4 10 15 13 13 15 9 8 8 14\\n10 10\\n2 3 8 5 9 7 11 12 7 9\\n10 10\\n12 15 11 10 1 8 10 3 4 2\\n10 5\\n8 11 7 14 7 9 5 2 8 9\\n10 10\\n4 9 9 9 10 4 1 12 13 15\\n10 10\\n12 2 7 5 15 8 2 3 10 12\\n\", \"10\\n3 2\\n3 6 1\\n3 3\\n9 0 2\\n3 3\\n8 8 2\\n4 2\\n9 0 0 1\\n4 4\\n5 3 0 2\\n4 4\\n2 8 6 0\\n5 3\\n7 3 8 9 8\\n5 5\\n6 3 9 5 7\\n5 5\\n1 0 5 9 8\\n5 5\\n1 5 4 6 1\\n\", \"10\\n2 2\\n4 3\\n2 2\\n13 13\\n2 2\\n9 11\\n2 1\\n14 5\\n2 0\\n13 2\\n2 2\\n4 5\\n2 1\\n11 14\\n2 2\\n15 3\\n2 2\\n12 10\\n2 2\\n13 12\\n\", \"10\\n10 10\\n8 9 2 10 3 8 10 9 1 10\\n10 10\\n3 10 3 13 12 14 5 3 4 4\\n10 5\\n7 13 10 14 5 12 5 5 7 11\\n10 10\\n12 13 3 6 12 9 6 6 5 7\\n10 10\\n4 10 15 13 13 15 9 8 8 14\\n10 10\\n2 3 8 5 9 7 11 12 7 9\\n10 10\\n12 15 11 10 1 8 10 3 4 2\\n10 5\\n8 11 7 14 7 9 5 2 8 9\\n10 10\\n4 9 9 9 10 4 1 12 13 15\\n10 10\\n12 2 7 5 15 8 2 3 10 12\\n\", \"3\\n4 4\\n1 1 0 1\\n3 1\\n1 2 3\\n3 3\\n1 2 3\\n\", \"3\\n4 4\\n1 1 0 1\\n3 1\\n1 2 3\\n3 2\\n1 2 3\\n\", \"10\\n10 10\\n8 9 2 10 3 8 10 9 1 10\\n10 10\\n3 10 3 13 12 14 5 3 4 3\\n10 5\\n7 13 10 14 5 17 5 5 7 11\\n10 10\\n12 13 3 6 12 9 6 6 5 7\\n10 10\\n4 10 15 13 13 15 9 8 8 14\\n10 10\\n2 3 8 5 9 7 11 12 7 9\\n10 10\\n12 15 11 10 1 8 10 3 4 2\\n10 5\\n8 11 7 14 7 9 5 2 8 9\\n10 10\\n4 9 9 9 10 4 1 12 13 15\\n10 10\\n12 2 7 5 15 8 2 3 10 12\\n\", \"3\\n4 4\\n2 1 0 1\\n3 1\\n1 2 3\\n3 2\\n1 2 3\\n\", \"3\\n4 4\\n2 1 1 1\\n3 1\\n1 2 3\\n3 3\\n1 2 3\\n\", \"10\\n3 2\\n3 6 1\\n3 3\\n9 0 3\\n3 3\\n8 8 2\\n4 2\\n9 0 0 1\\n4 4\\n5 3 0 2\\n4 4\\n2 8 6 0\\n5 3\\n7 3 8 9 8\\n5 5\\n6 3 9 6 7\\n5 5\\n1 0 5 9 8\\n5 5\\n1 5 4 6 1\\n\", \"10\\n10 10\\n8 9 2 10 3 8 10 9 1 10\\n10 10\\n3 10 3 13 12 14 3 3 4 4\\n10 5\\n7 13 10 14 5 12 5 5 7 11\\n10 10\\n12 13 3 6 12 9 6 6 5 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2\\n2 3\\n3 4\\n4 1\\n-1\\n12\\n1 2\\n2 3\\n3 1\\n\"]}", "source": "taco"}
|
Hanh lives in a shared apartment. There are $n$ people (including Hanh) living there, each has a private fridge.
$n$ fridges are secured by several steel chains. Each steel chain connects two different fridges and is protected by a digital lock. The owner of a fridge knows passcodes of all chains connected to it. A fridge can be open only if all chains connected to it are unlocked. For example, if a fridge has no chains connected to it at all, then any of $n$ people can open it.
[Image] For exampe, in the picture there are $n=4$ people and $5$ chains. The first person knows passcodes of two chains: $1-4$ and $1-2$. The fridge $1$ can be open by its owner (the person $1$), also two people $2$ and $4$ (acting together) can open it.
The weights of these fridges are $a_1, a_2, \ldots, a_n$. To make a steel chain connecting fridges $u$ and $v$, you have to pay $a_u + a_v$ dollars. Note that the landlord allows you to create multiple chains connecting the same pair of fridges.
Hanh's apartment landlord asks you to create exactly $m$ steel chains so that all fridges are private. A fridge is private if and only if, among $n$ people living in the apartment, only the owner can open it (i.e. no other person acting alone can do it). In other words, the fridge $i$ is not private if there exists the person $j$ ($i \ne j$) that the person $j$ can open the fridge $i$.
For example, in the picture all the fridges are private. On the other hand, if there are $n=2$ fridges and only one chain (which connects them) then both fridges are not private (both fridges can be open not only by its owner but also by another person).
Of course, the landlord wants to minimize the total cost of all steel chains to fulfill his request. Determine whether there exists any way to make exactly $m$ chains, and if yes, output any solution that minimizes the total cost.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $T$ ($1 \le T \le 10$). Then the descriptions of the test cases follow.
The first line of each test case contains two integers $n$, $m$ ($2 \le n \le 1000$, $1 \le m \le n$) — the number of people living in Hanh's apartment and the number of steel chains that the landlord requires, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^4$) — weights of all fridges.
-----Output-----
For each test case:
If there is no solution, print a single integer $-1$. Otherwise, print a single integer $c$ — the minimum total cost. The $i$-th of the next $m$ lines contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$), meaning that the $i$-th steel chain connects fridges $u_i$ and $v_i$. An arbitrary number of chains can be between a pair of fridges.
If there are multiple answers, print any.
-----Example-----
Input
3
4 4
1 1 1 1
3 1
1 2 3
3 3
1 2 3
Output
8
1 2
4 3
3 2
4 1
-1
12
3 2
1 2
3 1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"1\\n0\\n1\\n\", \"15\\n101010101010101\\n010101010101010\\n\", \"8\\n10001001\\n01101110\\n\", \"6\\n110110\\n000000\\n\", \"7\\n1110001\\n0000001\\n\", \"10\\n1010101010\\n1010101010\\n\", \"91\\n0010010000110001001011011011111001000110001000100111110010010001100110010111100111011111100\\n1101110110000100110000100011010110111101100000011011100111111000110000001101101111100100100\\n\", \"19\\n1111010011111010100\\n1000000110100110110\\n\", \"7\\n1110011\\n0000000\\n\", \"4\\n1001\\n0001\\n\", \"15\\n101010101010101\\n010101010001010\\n\", \"8\\n00001001\\n01101110\\n\", \"7\\n1010001\\n0000001\\n\", \"91\\n0010010000110001001011011011111001000110001000100111110010010011100110010111100111011111100\\n1101110110000100110000100011010110111101100000011011100111111000110000001101101111100100100\\n\", \"4\\n1001\\n1001\\n\", \"15\\n101010101010101\\n011101010001010\\n\", \"8\\n01001001\\n01101110\\n\", \"15\\n001010101010101\\n011101010001011\\n\", \"91\\n0010010000110001011011011011111001000110001000100111110010010011100110010111100111011111100\\n1101110110000100100000100011010110111101100100011011100111111000110000011101101111100100100\\n\", \"19\\n1111100011111110100\\n1010000110100100111\\n\", \"91\\n0010010000110001011011011011111001000110001000101111110010010011100110010111100111011111100\\n1101110110000100100000100011010110111101100100011011100111111000110000011101101111100100110\\n\", \"6\\n110111\\n000000\\n\", \"10\\n1010101010\\n1110101010\\n\", \"4\\n0101\\n0010\\n\", \"3\\n100\\n101\\n\", \"19\\n1111000011111010100\\n1000000110100110110\\n\", \"7\\n1110011\\n0000010\\n\", \"6\\n110011\\n000000\\n\", \"7\\n1010001\\n1000001\\n\", \"10\\n1010101010\\n1110111010\\n\", \"4\\n0001\\n0010\\n\", \"3\\n100\\n100\\n\", \"91\\n0010010000110001001011011011111001000110001000100111110010010011100110010111100111011111100\\n1101110110000100110000100011010110111101100000011011100111111000110000011101101111100100100\\n\", \"19\\n1111000011111010100\\n1010000110100110110\\n\", \"7\\n1110011\\n0000110\\n\", \"4\\n1101\\n1001\\n\", \"15\\n001010101010101\\n011101010001010\\n\", \"8\\n01011001\\n01101110\\n\", \"6\\n110011\\n100000\\n\", \"7\\n0010001\\n1000001\\n\", \"10\\n1010101110\\n1110111010\\n\", \"4\\n0001\\n0011\\n\", \"3\\n101\\n101\\n\", \"91\\n0010010000110001011011011011111001000110001000100111110010010011100110010111100111011111100\\n1101110110000100110000100011010110111101100000011011100111111000110000011101101111100100100\\n\", \"19\\n1111000011111010100\\n1010000110100110111\\n\", \"7\\n1110011\\n0000100\\n\", \"4\\n1001\\n1011\\n\", \"8\\n00011001\\n01101110\\n\", \"6\\n010011\\n100000\\n\", \"7\\n0011001\\n1000001\\n\", \"10\\n1010101110\\n1010111010\\n\", \"4\\n0000\\n0010\\n\", \"3\\n001\\n101\\n\", \"91\\n0010010000110001011011011011111001000110001000100111110010010011100110010111100111011111100\\n1101110110000100110000100011010110111101100100011011100111111000110000011101101111100100100\\n\", \"19\\n1111000011111110100\\n1010000110100110111\\n\", \"7\\n1110011\\n0010100\\n\", \"4\\n1000\\n1011\\n\", \"15\\n001000101010101\\n011101010001011\\n\", \"8\\n00011001\\n01100110\\n\", \"6\\n010111\\n100000\\n\", \"7\\n0011101\\n1000001\\n\", \"10\\n1010101111\\n1010111010\\n\", \"4\\n0000\\n0110\\n\", \"3\\n001\\n100\\n\", \"19\\n1111000011111110100\\n1010000110100100111\\n\", \"7\\n1110111\\n0010100\\n\", \"4\\n1000\\n1010\\n\", \"15\\n001000101010111\\n011101010001011\\n\", \"8\\n00011001\\n11100110\\n\", \"6\\n010111\\n100001\\n\", \"7\\n0011101\\n1010001\\n\", \"10\\n1010101101\\n1010111010\\n\", \"4\\n0000\\n1110\\n\", \"3\\n001\\n110\\n\", \"91\\n0010010000110001011011011011111001000110001000101111110010010011100110010111100111011111100\\n1101110110000100100000100011010110111101100100011011100111111000110000011101101111100100100\\n\", \"7\\n1110011\\n0011100\\n\", \"4\\n1100\\n1010\\n\", \"15\\n001000101000111\\n011101010001011\\n\", \"8\\n00011001\\n11100111\\n\", \"6\\n010011\\n100001\\n\", \"7\\n0001101\\n1000001\\n\", \"10\\n1010111101\\n1010111010\\n\", \"4\\n0000\\n1111\\n\", \"3\\n001\\n111\\n\", \"19\\n1111101011111110100\\n1010000110100100111\\n\", \"7\\n1110011\\n0011000\\n\", \"4\\n1100\\n1011\\n\", \"15\\n001000101000111\\n011101010011011\\n\", \"8\\n00011001\\n11110111\\n\", \"6\\n010011\\n000001\\n\", \"7\\n0001001\\n1000001\\n\", \"10\\n1010111101\\n1000111010\\n\", \"4\\n0000\\n1101\\n\", \"3\\n011\\n111\\n\", \"91\\n0010010000110001011011011011111001000110001000101111110010010001100110010111100111011111100\\n1101110110000100100000100011010110111101100100011011100111111000110000011101101111100100110\\n\", \"19\\n1110101011111110100\\n1010000110100100111\\n\", \"7\\n1100011\\n0011000\\n\", \"4\\n1100\\n1111\\n\", \"15\\n001000101100111\\n011101010011011\\n\", \"8\\n00011001\\n11111111\\n\", \"6\\n110011\\n000001\\n\", \"7\\n0001001\\n1010001\\n\", \"10\\n1110111101\\n1000111010\\n\", \"4\\n0000\\n1001\\n\", \"3\\n011\\n110\\n\", \"91\\n0010010000110001011011011011111001000110001000101111110010010001100010010111100111011111100\\n1101110110000100100000100011010110111101100100011011100111111000110000011101101111100100110\\n\", \"4\\n0101\\n0011\\n\", \"3\\n100\\n001\\n\"], \"outputs\": [\"2\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"4\\n\", \"8\\n\", \"4\\n\", \"3\\n\", \"43\\n\", \"8\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"43\\n\", \"8\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"8\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"0\\n\", \"42\", \"9\", \"5\", \"1\", \"8\", \"4\", \"2\", \"43\", \"0\", \"7\", \"3\", \"6\", \"44\", \"10\", \"45\", \"5\", \"1\", \"2\", \"1\", \"8\", \"4\", \"4\", \"1\", \"2\", \"1\", \"0\", \"43\", \"7\", \"5\", \"1\", \"7\", \"3\", \"3\", \"2\", \"3\", \"1\", \"0\", \"43\", \"8\", \"5\", \"1\", \"4\", \"3\", \"3\", \"2\", \"1\", \"1\", \"43\", \"8\", \"4\", \"2\", \"6\", \"4\", \"4\", \"4\", \"3\", \"2\", \"2\", \"9\", \"4\", \"1\", \"6\", \"5\", \"3\", \"3\", \"3\", \"3\", \"2\", \"44\", \"5\", \"1\", \"5\", \"5\", \"2\", \"3\", \"2\", \"4\", \"2\", \"10\", \"5\", \"2\", \"6\", \"5\", \"2\", \"2\", \"3\", \"3\", \"1\", \"44\", \"9\", \"5\", \"2\", \"6\", \"5\", \"3\", \"2\", \"4\", \"2\", \"2\", \"43\", \"1\\n\", \"2\\n\"]}", "source": "taco"}
|
You are given two binary strings $a$ and $b$ of the same length. You can perform the following two operations on the string $a$:
Swap any two bits at indices $i$ and $j$ respectively ($1 \le i, j \le n$), the cost of this operation is $|i - j|$, that is, the absolute difference between $i$ and $j$. Select any arbitrary index $i$ ($1 \le i \le n$) and flip (change $0$ to $1$ or $1$ to $0$) the bit at this index. The cost of this operation is $1$.
Find the minimum cost to make the string $a$ equal to $b$. It is not allowed to modify string $b$.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 10^6$) — the length of the strings $a$ and $b$.
The second and third lines contain strings $a$ and $b$ respectively.
Both strings $a$ and $b$ have length $n$ and contain only '0' and '1'.
-----Output-----
Output the minimum cost to make the string $a$ equal to $b$.
-----Examples-----
Input
3
100
001
Output
2
Input
4
0101
0011
Output
1
-----Note-----
In the first example, one of the optimal solutions is to flip index $1$ and index $3$, the string $a$ changes in the following way: "100" $\to$ "000" $\to$ "001". The cost is $1 + 1 = 2$.
The other optimal solution is to swap bits and indices $1$ and $3$, the string $a$ changes then "100" $\to$ "001", the cost is also $|1 - 3| = 2$.
In the second example, the optimal solution is to swap bits at indices $2$ and $3$, the string $a$ changes as "0101" $\to$ "0011". The cost is $|2 - 3| = 1$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n5\\n2 1 aa\\n1 2 a\\n2 3 a\\n1 2 b\\n2 3 abca\\n2\\n1 5 mihai\\n2 2 buiucani\\n3\\n1 5 b\\n2 3 a\\n2 4 paiu\\n\", \"1\\n5\\n2 1 bb\\n1 2 b\\n2 3 b\\n1 2 c\\n2 3 bcdbweakpretests\\n\", \"1\\n2\\n1 1 ab\\n2 1 ab\\n\", \"1\\n2\\n1 3 c\\n2 3 b\\n\", \"1\\n3\\n2 1 z\\n2 1 a\\n1 1 z\\n\", \"1\\n2\\n1 1 b\\n2 1 b\\n\", \"1\\n2\\n2 1 b\\n1 1 b\\n\", \"1\\n2\\n1 2 zz\\n2 2 zz\\n\", \"1\\n2\\n1 1 c\\n2 1 b\\n\", \"1\\n2\\n1 1 z\\n2 1 z\\n\", \"1\\n4\\n1 1 b\\n1 1 c\\n2 1 b\\n2 1 c\\n\", \"1\\n2\\n2 1 b\\n1 2 bb\\n\", \"1\\n2\\n2 1 bb\\n1 2 b\\n\", \"1\\n2\\n1 1 c\\n2 1 c\\n\", \"1\\n2\\n1 3 c\\n2 3 c\\n\", \"1\\n2\\n2 1 a\\n1 1 z\\n\", \"1\\n8\\n2 7 z\\n1 2 xpt\\n2 5 aosu\\n2 3 veel\\n1 3 dnx\\n1 8 tgly\\n2 5 rqlmvchcir\\n1 10 qklu\\n\"], \"outputs\": [\"YES\\nNO\\nYES\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nYES\\n\", \"NO\\nYES\\n\", \"YES\\nYES\\nYES\\n\", \"NO\\nYES\\n\", \"YES\\nYES\\n\", \"NO\\nYES\\n\", \"NO\\nYES\\n\", \"NO\\nYES\\n\", \"NO\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\n\", \"YES\\nYES\\n\", \"NO\\nYES\\n\", \"NO\\nYES\\n\", \"YES\\nNO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\"]}", "source": "taco"}
|
Alperen has two strings, $s$ and $t$ which are both initially equal to "a".
He will perform $q$ operations of two types on the given strings:
$1 \;\; k \;\; x$ — Append the string $x$ exactly $k$ times at the end of string $s$. In other words, $s := s + \underbrace{x + \dots + x}_{k \text{ times}}$.
$2 \;\; k \;\; x$ — Append the string $x$ exactly $k$ times at the end of string $t$. In other words, $t := t + \underbrace{x + \dots + x}_{k \text{ times}}$.
After each operation, determine if it is possible to rearrange the characters of $s$ and $t$ such that $s$ is lexicographically smaller$^{\dagger}$ than $t$.
Note that the strings change after performing each operation and don't go back to their initial states.
$^{\dagger}$ Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. A formal definition is as follows: string $p$ is lexicographically smaller than string $q$ if there exists a position $i$ such that $p_i < q_i$, and for all $j < i$, $p_j = q_j$. If no such $i$ exists, then $p$ is lexicographically smaller than $q$ if the length of $p$ is less than the length of $q$. For example, ${abdc} < {abe}$ and ${abc} < {abcd}$, where we write $p < q$ if $p$ is lexicographically smaller than $q$.
-----Input-----
The first line of the input contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains an integer $q$ $(1 \leq q \leq 10^5)$ — the number of operations Alperen will perform.
Then $q$ lines follow, each containing two positive integers $d$ and $k$ ($1 \leq d \leq 2$; $1 \leq k \leq 10^5$) and a non-empty string $x$ consisting of lowercase English letters — the type of the operation, the number of times we will append string $x$ and the string we need to append respectively.
It is guaranteed that the sum of $q$ over all test cases doesn't exceed $10^5$ and that the sum of lengths of all strings $x$ in the input doesn't exceed $5 \cdot 10^5$.
-----Output-----
For each operation, output "YES", if it is possible to arrange the elements in both strings in such a way that $s$ is lexicographically smaller than $t$ and "NO" otherwise.
-----Examples-----
Input
3
5
2 1 aa
1 2 a
2 3 a
1 2 b
2 3 abca
2
1 5 mihai
2 2 buiucani
3
1 5 b
2 3 a
2 4 paiu
Output
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
-----Note-----
In the first test case, the strings are initially $s = $ "a" and $t = $ "a".
After the first operation the string $t$ becomes "aaa". Since "a" is already lexicographically smaller than "aaa", the answer for this operation should be "YES".
After the second operation string $s$ becomes "aaa", and since $t$ is also equal to "aaa", we can't arrange $s$ in any way such that it is lexicographically smaller than $t$, so the answer is "NO".
After the third operation string $t$ becomes "aaaaaa" and $s$ is already lexicographically smaller than it so the answer is "YES".
After the fourth operation $s$ becomes "aaabb" and there is no way to make it lexicographically smaller than "aaaaaa" so the answer is "NO".
After the fifth operation the string $t$ becomes "aaaaaaabcaabcaabca", and we can rearrange the strings to: "bbaaa" and "caaaaaabcaabcaabaa" so that $s$ is lexicographically smaller than $t$, so we should answer "YES".
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 30\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 21\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 6 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 11 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 11 40\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 1\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 6 10\\ninsert 5 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 2 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 105\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 4\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 27\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 8 1\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 2 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 52 47\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 62\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 14\\ndelete 35\\ndelete 127\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 14\\ndelete 32\\ndelete 57\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 67\\ninsert 42 3\\ninsert 86 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 48 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 4 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 32 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 46\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 11 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 26\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 66 99\\ninsert 3 80\\ninsert 1 29\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 1 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 57\\ninsert 4 80\\ninsert 1 53\\ninsert 14 25\\ninsert 11 40\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 46 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 26 6\\ninsert 12 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 105\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 4\\ninsert 1 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 41 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 7 1\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 5\\ninsert 86 47\\ninsert 26 12\\ninsert 3 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 2 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 89\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 8 1\\ninsert 1 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 2 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 6\\ninsert 52 47\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 105\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 4\\ninsert 11 10\\ninsert 6 139\\nprint\\nfind 51\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 26 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 83\\ninsert 3 105\\ninsert 1 12\\ninsert 14 25\\ninsert 118 76\\ninsert 42 3\\ninsert 141 58\\ninsert 21 4\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 51\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 2 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 127\\nprint\", \"16\\ninsert 35 20\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 33\\nfind 22\\ndelete 62\\ndelete 73\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 39 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 14\\ndelete 35\\ndelete 57\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 3 90\\nprint\\nfind 21\\nfind 14\\ndelete 32\\ndelete 57\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 67\\ninsert 42 3\\ninsert 86 47\\ninsert 21 12\\ninsert 7 10\\ninsert 9 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 102 47\\ninsert 1 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 48 12\\ninsert 7 10\\ninsert 0 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 172\\nprint\\nfind 21\\nfind 22\\ndelete 46\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 48\\ninsert 80 26\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 66 99\\ninsert 3 80\\ninsert 1 29\\ninsert 14 25\\ninsert 62 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 81\\ninsert 14 25\\ninsert 1 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 3 44\\ninsert 1 53\\ninsert 46 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 31\\ninsert 42 5\\ninsert 86 47\\ninsert 26 12\\ninsert 3 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 189\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 78 47\\ninsert 26 12\\ninsert 6 10\\ninsert 5 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 24 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 9\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 80 150\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 83\\ninsert 3 105\\ninsert 1 12\\ninsert 14 48\\ninsert 80 76\\ninsert 0 3\\ninsert 141 47\\ninsert 21 4\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 51\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 2 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 107\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 127\\nprint\", \"16\\ninsert 35 99\\ninsert 3 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 13\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 3 90\\nprint\\nfind 21\\nfind 14\\ndelete 32\\ndelete 57\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 81\\ninsert 14 25\\ninsert 1 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 8 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 1 44\\ninsert 1 53\\ninsert 46 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 31\\ninsert 42 5\\ninsert 154 47\\ninsert 26 12\\ninsert 3 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 4 80\\ninsert 1 53\\ninsert 24 25\\ninsert 44 150\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 105\\ninsert 2 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 4\\ninsert 11 10\\ninsert 6 139\\nprint\\nfind 54\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 83\\ninsert 3 105\\ninsert 1 12\\ninsert 14 48\\ninsert 75 76\\ninsert 0 3\\ninsert 141 47\\ninsert 21 4\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 51\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 26 99\\ninsert 6 77\\ninsert 1 53\\ninsert 14 25\\ninsert 94 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 14 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 73\\nprint\", \"16\\ninsert 35 99\\ninsert 1 44\\ninsert 1 53\\ninsert 46 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 0 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 24 25\\ninsert 44 150\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 31\\ninsert 42 5\\ninsert 154 65\\ninsert 26 12\\ninsert 3 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 2 53\\ninsert 24 25\\ninsert 44 150\\ninsert 42 3\\ninsert 86 47\\ninsert 34 12\\ninsert 5 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 2 44\\ninsert 1 53\\ninsert 46 37\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 0 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 13\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 255 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 2 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 2 80\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 8 25\\ninsert 87 76\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 25 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 6 80\\ninsert 1 53\\ninsert 21 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 148\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 11 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 14\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 57\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 11 40\\ninsert 42 3\\ninsert 86 1\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 95\\nprint\", \"16\\ninsert 35 25\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 55\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 87 150\\ninsert 42 3\\ninsert 102 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 26\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 33 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 58 47\\ninsert 26 12\\ninsert 7 1\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 11\\ninsert 23 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 6\\ninsert 7 10\\ninsert 6 245\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 4 101\\ninsert 1 53\\ninsert 24 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 26 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 3 80\\ninsert 2 12\\ninsert 14 3\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 26 6\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 21 99\\ninsert 6 105\\ninsert 1 12\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 141 47\\ninsert 21 4\\ninsert 7 10\\ninsert 6 139\\nprint\\nfind 27\\nfind 22\\ndelete 35\\ndelete 99\\nprint\", \"16\\ninsert 35 99\\ninsert 3 80\\ninsert 1 53\\ninsert 14 25\\ninsert 80 76\\ninsert 42 3\\ninsert 86 47\\ninsert 21 12\\ninsert 7 10\\ninsert 6 90\\nprint\\nfind 21\\nfind 22\\ndelete 35\\ndelete 99\\nprint\"], \"outputs\": [\" 1 3 6 7 14 21 35 42 80 102\\n 35 6 3 1 14 7 21 80 42 102\\nyes\\nno\\n 1 3 6 7 14 21 42 80 102\\n 6 3 1 80 14 7 21 42 102\\n\", \" 1 3 6 7 14 26 35 42 80 86\\n 35 6 3 1 14 7 26 80 42 86\\nno\\nno\\n 1 3 6 7 14 26 42 80 86\\n 6 3 1 80 14 7 26 42 86\\n\", \" 1 3 6 7 14 26 35 42 80 86\\n 6 3 1 80 35 14 7 26 42 86\\nno\\nno\\n 1 3 6 7 14 26 42 80 86\\n 6 3 1 80 14 7 26 42 86\\n\", \" 1 3 6 7 14 21 35 42 80 86\\n 6 3 1 35 14 7 21 80 42 86\\nyes\\nno\\n 1 3 6 7 14 21 42 80 86\\n 6 3 1 80 14 7 21 42 86\\n\", \" 1 3 6 7 14 21 35 42 80 102\\n 35 6 3 1 14 7 21 80 42 102\\nno\\nno\\n 1 3 6 7 14 21 42 80 102\\n 6 3 1 80 14 7 21 42 102\\n\", \" 1 3 6 7 14 21 35 42 80 141\\n 6 3 1 35 14 7 21 80 42 141\\nyes\\nno\\n 1 3 6 7 14 21 42 80 141\\n 6 3 1 80 14 7 21 42 141\\n\", \" 1 3 6 7 14 21 42 80 141\\n 6 3 1 21 14 7 80 42 141\\nyes\\nno\\n 1 3 6 7 14 21 42 80 141\\n 6 3 1 21 14 7 80 42 141\\n\", \" 1 3 6 7 14 21 35 42 80 86\\n 35 6 3 1 14 7 21 80 42 86\\nyes\\nno\\n 1 3 6 7 14 42 80 86\\n 6 3 1 80 14 7 42 86\\n\", \" 1 3 6 7 14 21 35 42 87 102\\n 35 6 3 1 14 7 21 87 42 102\\nyes\\nno\\n 1 3 6 7 14 21 42 87 102\\n 6 3 1 87 14 7 21 42 102\\n\", \" 1 3 6 7 14 26 35 42 58 80\\n 35 6 3 1 14 7 26 80 58 42\\nno\\nno\\n 1 3 6 7 14 26 42 58 80\\n 6 3 1 80 58 14 7 26 42\\n\", \" 1 6 7 14 26 35 42 80 86\\n 35 6 1 14 7 26 80 42 86\\nno\\nno\\n 1 6 7 14 26 42 80 86\\n 6 1 80 14 7 26 42 86\\n\", \" 1 3 6 14 26 35 42 58 80\\n 35 3 1 14 6 26 80 58 42\\nno\\nno\\n 1 3 6 14 26 42 58 80\\n 3 1 80 58 14 6 26 42\\n\", \" 1 3 6 7 11 14 26 35 42 86\\n 6 3 1 11 7 35 14 26 86 42\\nno\\nno\\n 1 3 6 7 11 14 26 42 86\\n 6 3 1 11 7 86 14 26 42\\n\", \" 1 3 6 7 11 14 26 35 42 86\\n 6 3 1 35 11 7 14 26 86 42\\nno\\nno\\n 1 3 6 7 11 14 26 42 86\\n 6 3 1 86 11 7 14 26 42\\n\", \" 1 3 6 7 24 26 35 42 80 86\\n 35 6 3 1 24 7 26 80 42 86\\nno\\nno\\n 1 3 6 7 24 26 42 80 86\\n 6 3 1 80 24 7 26 42 86\\n\", \" 1 3 6 7 14 21 35 42 80 141\\n 6 3 1 35 14 7 21 80 42 141\\nyes\\nno\\n 1 3 6 7 14 21 42 80 141\\n 6 3 1 80 14 7 42 21 141\\n\", \" 1 3 6 7 14 21 26 42 80 141\\n 6 3 1 21 14 7 80 26 42 141\\nyes\\nno\\n 1 3 6 7 14 21 26 42 80 141\\n 6 3 1 21 14 7 80 26 42 141\\n\", \" 1 3 5 6 14 26 35 42 58 80\\n 35 5 3 1 14 6 26 80 58 42\\nno\\nno\\n 1 3 5 6 14 26 42 58 80\\n 5 3 1 80 58 14 6 26 42\\n\", \" 1 4 6 7 24 26 35 42 80 86\\n 35 6 4 1 24 7 26 80 42 86\\nno\\nno\\n 1 4 6 7 24 26 42 80 86\\n 6 4 1 80 24 7 26 42 86\\n\", \" 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 14 7 80 26 42 141\\nyes\\nno\\n 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 14 7 80 26 42 141\\n\", \" 1 3 6 7 14 21 42 80 141\\n 6 3 1 21 14 7 80 42 141\\nno\\nno\\n 1 3 6 7 14 21 42 80 141\\n 6 3 1 21 14 7 80 42 141\\n\", \" 1 3 6 14 21 35 42 87 102\\n 35 6 3 1 14 21 87 42 102\\nyes\\nno\\n 1 3 6 14 21 42 87 102\\n 6 3 1 87 14 21 42 102\\n\", \" 1 3 6 8 14 26 35 42 58 80\\n 35 6 3 1 14 8 26 80 58 42\\nno\\nno\\n 1 3 6 8 14 26 42 58 80\\n 6 3 1 80 58 14 8 26 42\\n\", \" 1 4 5 6 24 26 35 42 80 86\\n 35 6 4 1 5 24 26 80 42 86\\nno\\nno\\n 1 4 5 6 24 26 42 80 86\\n 6 4 1 5 80 24 26 42 86\\n\", \" 2 3 6 7 14 21 26 42 52 80\\n 6 3 2 21 14 7 80 52 26 42\\nyes\\nno\\n 2 3 6 7 14 21 26 42 52 80\\n 6 3 2 21 14 7 80 52 26 42\\n\", \" 1 4 5 6 24 26 35 42 80 86\\n 35 6 4 1 5 24 26 80 42 86\\nno\\nno\\n 1 4 5 6 24 26 35 42 80 86\\n 35 6 4 1 5 24 26 80 42 86\\n\", \" 1 3 6 14 21 35 42 94 102\\n 35 6 3 1 14 21 94 42 102\\nyes\\nno\\n 1 3 6 14 21 42 94 102\\n 6 3 1 94 14 21 42 102\\n\", \" 1 3 6 14 21 35 42 94 102\\n 35 6 3 1 14 21 94 42 102\\nyes\\nyes\\n 1 3 6 14 21 42 94 102\\n 6 3 1 94 14 21 42 102\\n\", \" 1 3 6 14 21 35 42 94 102\\n 35 6 3 1 14 21 94 42 102\\nyes\\nyes\\n 1 3 6 14 21 35 42 94 102\\n 35 6 3 1 14 21 94 42 102\\n\", \" 1 3 6 7 14 21 35 42 80 86\\n 35 6 3 1 14 7 21 80 42 86\\nyes\\nno\\n 1 3 6 7 14 21 42 80 86\\n 6 3 1 80 14 7 21 42 86\\n\", \" 1 6 7 14 21 35 42 80 102\\n 35 6 1 14 7 21 80 42 102\\nyes\\nno\\n 1 6 7 14 21 42 80 102\\n 6 1 80 14 7 21 42 102\\n\", \" 1 3 6 7 14 35 42 48 80 86\\n 35 6 3 1 14 7 80 48 42 86\\nno\\nno\\n 1 3 6 7 14 42 48 80 86\\n 6 3 1 80 14 7 48 42 86\\n\", \" 1 3 6 7 14 34 35 42 80 86\\n 6 3 1 80 35 14 7 34 42 86\\nno\\nno\\n 1 3 6 7 14 34 42 80 86\\n 6 3 1 80 14 7 34 42 86\\n\", \" 1 3 4 7 14 21 35 42 80 141\\n 4 3 1 35 14 7 21 80 42 141\\nyes\\nno\\n 1 3 4 7 14 21 42 80 141\\n 4 3 1 80 14 7 21 42 141\\n\", \" 1 3 6 7 14 21 32 42 80 141\\n 6 3 1 32 14 7 21 80 42 141\\nyes\\nno\\n 1 3 6 7 14 21 32 42 80 141\\n 6 3 1 32 14 7 21 80 42 141\\n\", \" 1 3 6 7 14 21 35 42 87 102\\n 35 6 3 1 14 7 21 87 42 102\\nyes\\nno\\n 1 3 6 7 14 21 35 42 87 102\\n 35 6 3 1 14 7 21 87 42 102\\n\", \" 1 6 7 11 26 35 42 80 86\\n 35 6 1 11 7 26 80 42 86\\nno\\nno\\n 1 6 7 11 26 42 80 86\\n 6 1 80 11 7 26 42 86\\n\", \" 1 3 6 7 14 26 35 42 80 86\\n 6 3 1 35 14 7 26 86 80 42\\nno\\nno\\n 1 3 6 7 14 26 42 80 86\\n 6 3 1 86 80 14 7 26 42\\n\", \" 1 3 6 7 14 21 42 66 87 102\\n 66 6 3 1 14 7 21 42 87 102\\nyes\\nno\\n 1 3 6 7 14 21 42 66 87 102\\n 66 6 3 1 14 7 21 42 87 102\\n\", \" 1 3 6 7 14 26 35 42 86\\n 6 3 1 35 14 7 26 86 42\\nno\\nno\\n 1 3 6 7 14 26 42 86\\n 6 3 1 86 14 7 26 42\\n\", \" 1 4 6 7 11 14 26 35 42 86\\n 6 4 1 35 11 7 14 26 86 42\\nno\\nno\\n 1 4 6 7 11 14 26 42 86\\n 6 4 1 86 11 7 14 26 42\\n\", \" 1 3 6 7 26 35 42 46 80 86\\n 35 6 3 1 26 7 80 46 42 86\\nno\\nno\\n 1 3 6 7 26 42 46 80 86\\n 6 3 1 80 46 26 7 42 86\\n\", \" 1 3 6 12 14 21 26 42 80 141\\n 6 3 1 21 14 12 80 26 42 141\\nyes\\nno\\n 1 3 6 12 14 21 26 42 80 141\\n 6 3 1 21 14 12 80 26 42 141\\n\", \" 1 3 6 14 21 42 80 141\\n 6 3 1 21 14 80 42 141\\nyes\\nno\\n 1 3 6 14 21 42 80 141\\n 6 3 1 21 14 80 42 141\\n\", \" 1 3 6 7 14 26 35 41 42 58\\n 35 6 3 1 14 7 26 41 58 42\\nno\\nno\\n 1 3 6 7 14 26 41 42 58\\n 6 3 1 41 14 7 26 58 42\\n\", \" 1 3 6 14 26 35 42 80 86\\n 6 3 1 80 35 14 26 42 86\\nno\\nno\\n 1 3 6 14 26 42 80 86\\n 6 3 1 80 14 26 42 86\\n\", \" 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 14 7 141 80 26 42\\nyes\\nno\\n 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 14 7 141 80 26 42\\n\", \" 1 3 8 14 26 35 42 58 80\\n 35 3 1 14 8 26 80 58 42\\nno\\nno\\n 1 3 8 14 26 42 58 80\\n 3 1 80 58 14 8 26 42\\n\", \" 1 4 5 6 24 34 35 42 80 86\\n 35 6 4 1 5 24 34 80 42 86\\nno\\nno\\n 1 4 5 6 24 34 42 80 86\\n 6 4 1 5 80 24 34 42 86\\n\", \" 2 3 6 7 14 21 26 42 52 80\\n 6 3 2 21 14 7 80 52 42 26\\nyes\\nno\\n 2 3 6 7 14 21 26 42 52 80\\n 6 3 2 21 14 7 80 52 42 26\\n\", \" 1 3 6 11 14 21 42 80 141\\n 6 3 1 21 14 11 80 42 141\\nno\\nno\\n 1 3 6 11 14 21 42 80 141\\n 6 3 1 21 14 11 80 42 141\\n\", \" 1 3 6 14 21 26 42 94 102\\n 26 6 3 1 14 21 94 42 102\\nyes\\nyes\\n 1 3 6 14 21 26 42 94 102\\n 26 6 3 1 14 21 94 42 102\\n\", \" 1 3 6 7 14 21 42 118 141\\n 6 3 1 21 14 7 118 42 141\\nno\\nno\\n 1 3 6 7 14 21 42 118 141\\n 6 3 1 21 14 7 118 42 141\\n\", \" 2 3 6 14 21 35 42 94 102\\n 35 6 3 2 14 21 94 42 102\\nyes\\nno\\n 2 3 6 14 21 42 94 102\\n 6 3 2 94 14 21 42 102\\n\", \" 1 4 5 6 24 26 35 42 80 86\\n 6 4 1 5 80 24 35 26 42 86\\nno\\nno\\n 1 4 5 6 24 26 35 42 80 86\\n 6 4 1 5 80 24 35 26 42 86\\n\", \" 1 3 6 14 21 35 39 42 102\\n 35 6 3 1 14 21 39 102 42\\nyes\\nyes\\n 1 3 6 14 21 39 42 102\\n 6 3 1 39 14 21 102 42\\n\", \" 1 3 14 21 35 42 94 102\\n 35 3 1 14 21 94 42 102\\nyes\\nyes\\n 1 3 14 21 35 42 94 102\\n 35 3 1 14 21 94 42 102\\n\", \" 1 3 7 9 14 21 35 42 80 86\\n 35 9 3 1 7 14 21 80 42 86\\nyes\\nno\\n 1 3 7 9 14 21 42 80 86\\n 9 3 1 7 80 14 21 42 86\\n\", \" 1 6 7 14 35 42 80 102\\n 35 6 1 14 7 80 42 102\\nno\\nno\\n 1 6 7 14 42 80 102\\n 6 1 80 14 7 42 102\\n\", \" 0 1 3 7 14 35 42 48 80 86\\n 35 0 3 1 14 7 80 48 42 86\\nno\\nno\\n 0 1 3 7 14 42 48 80 86\\n 0 3 1 80 14 7 48 42 86\\n\", \" 1 3 6 7 14 21 35 42 87 102\\n 6 3 1 35 14 7 21 87 42 102\\nyes\\nno\\n 1 3 6 7 14 21 35 42 87 102\\n 6 3 1 35 14 7 21 87 42 102\\n\", \" 1 3 6 7 14 26 35 42 80 86\\n 6 3 1 35 14 7 26 86 80 42\\nno\\nno\\n 1 3 6 7 14 26 42 80 86\\n 6 3 1 14 7 86 80 26 42\\n\", \" 1 3 6 7 14 21 42 62 66 102\\n 66 6 3 1 62 14 7 21 42 102\\nyes\\nno\\n 1 3 6 7 14 21 42 62 66 102\\n 66 6 3 1 62 14 7 21 42 102\\n\", \" 1 3 6 7 14 26 35 42 86\\n 6 1 3 35 14 7 26 86 42\\nno\\nno\\n 1 3 6 7 14 26 42 86\\n 6 1 3 86 14 7 26 42\\n\", \" 1 3 6 7 26 35 42 46 80 86\\n 35 6 1 3 26 7 80 46 42 86\\nno\\nno\\n 1 3 6 7 26 42 46 80 86\\n 6 1 3 80 46 26 7 42 86\\n\", \" 1 3 6 14 26 35 42 80 86\\n 6 3 1 35 14 26 86 80 42\\nno\\nno\\n 1 3 6 14 26 42 80 86\\n 6 3 1 86 80 14 26 42\\n\", \" 1 3 5 6 14 26 35 42 78 80\\n 35 5 3 1 14 6 26 80 78 42\\nno\\nno\\n 1 3 5 6 14 26 42 78 80\\n 5 3 1 80 78 14 6 26 42\\n\", \" 1 3 6 14 21 24 35 42 87 102\\n 35 6 3 1 14 21 24 87 42 102\\nyes\\nno\\n 1 3 6 14 21 24 42 87 102\\n 6 3 1 87 14 21 24 42 102\\n\", \" 1 4 5 6 24 34 35 42 80 86\\n 80 35 6 4 1 5 24 34 42 86\\nno\\nno\\n 1 4 5 6 24 34 42 80 86\\n 80 6 4 1 5 24 34 42 86\\n\", \" 0 1 3 6 7 14 21 80 141\\n 6 3 1 0 21 14 7 80 141\\nno\\nno\\n 0 1 3 6 7 14 21 80 141\\n 6 3 1 0 21 14 7 80 141\\n\", \" 2 3 6 14 21 35 42 94 102\\n 6 3 2 35 14 21 94 42 102\\nyes\\nno\\n 2 3 6 14 21 42 94 102\\n 6 3 2 94 14 21 42 102\\n\", \" 1 3 14 21 35 42 94 102\\n 35 3 1 14 21 102 94 42\\nyes\\nyes\\n 1 3 14 21 35 42 94 102\\n 35 3 1 14 21 102 94 42\\n\", \" 1 3 7 8 14 26 35 42 86\\n 8 1 3 7 35 14 26 86 42\\nno\\nno\\n 1 3 7 8 14 26 42 86\\n 8 1 3 7 86 14 26 42\\n\", \" 1 6 7 26 35 42 46 80 86\\n 35 6 1 26 7 80 46 42 86\\nno\\nno\\n 1 6 7 26 42 46 80 86\\n 6 1 80 46 26 7 42 86\\n\", \" 1 3 6 14 26 35 42 80 154\\n 6 3 1 35 14 26 154 80 42\\nno\\nno\\n 1 3 6 14 26 42 80 154\\n 6 3 1 154 80 14 26 42\\n\", \" 1 4 5 6 24 34 35 42 44 86\\n 44 35 6 4 1 5 24 34 42 86\\nno\\nno\\n 1 4 5 6 24 34 42 44 86\\n 44 6 4 1 5 24 34 42 86\\n\", \" 2 3 6 11 14 21 42 80 141\\n 6 3 2 21 14 11 80 42 141\\nno\\nno\\n 2 3 6 11 14 21 42 80 141\\n 6 3 2 21 14 11 80 42 141\\n\", \" 0 1 3 6 7 14 21 75 141\\n 6 3 1 0 21 14 7 75 141\\nno\\nno\\n 0 1 3 6 7 14 21 75 141\\n 6 3 1 0 21 14 7 75 141\\n\", \" 1 6 14 21 26 42 94 102\\n 26 6 1 14 21 94 42 102\\nyes\\nyes\\n 1 6 14 21 26 42 94 102\\n 26 6 1 14 21 94 42 102\\n\", \" 0 1 6 7 35 42 46 80 86\\n 35 6 1 0 7 80 46 42 86\\nno\\nno\\n 0 1 6 7 42 46 80 86\\n 6 1 0 80 46 7 42 86\\n\", \" 1 5 6 24 34 35 42 44 86\\n 44 35 6 1 5 24 34 42 86\\nno\\nno\\n 1 5 6 24 34 42 44 86\\n 44 6 1 5 24 34 42 86\\n\", \" 1 3 6 14 26 35 42 80 154\\n 6 3 1 154 35 14 26 80 42\\nno\\nno\\n 1 3 6 14 26 42 80 154\\n 6 3 1 154 80 14 26 42\\n\", \" 2 5 6 24 34 35 42 44 86\\n 44 35 6 2 5 24 34 42 86\\nno\\nno\\n 2 5 6 24 34 42 44 86\\n 44 6 2 5 24 34 42 86\\n\", \" 0 1 2 6 7 35 42 46 80 86\\n 35 6 1 0 2 7 80 46 42 86\\nno\\nno\\n 0 1 2 6 7 42 46 80 86\\n 6 1 0 2 80 46 7 42 86\\n\", \" 1 3 6 7 14 26 35 42 80 86\\n 6 3 1 80 14 7 35 26 42 86\\nno\\nno\\n 1 3 6 7 14 26 42 80 86\\n 6 3 1 80 14 7 26 42 86\\n\", \" 1 3 6 7 14 21 35 42 80 255\\n 6 3 1 35 14 7 21 80 42 255\\nyes\\nno\\n 1 3 6 7 14 21 42 80 255\\n 6 3 1 80 14 7 21 42 255\\n\", \" 1 2 3 6 7 21 35 42 80 141\\n 6 3 1 2 35 7 21 80 42 141\\nyes\\nno\\n 1 2 3 6 7 21 42 80 141\\n 6 3 1 2 80 7 21 42 141\\n\", \" 1 2 6 7 14 21 35 42 80 141\\n 6 2 1 35 14 7 21 80 42 141\\nyes\\nno\\n 1 2 6 7 14 21 42 80 141\\n 6 2 1 80 14 7 21 42 141\\n\", \" 1 3 6 7 8 21 35 42 87 102\\n 35 6 3 1 8 7 21 87 42 102\\nyes\\nno\\n 1 3 6 7 8 21 42 87 102\\n 6 3 1 87 8 7 21 42 102\\n\", \" 1 3 6 7 25 26 35 42 58 80\\n 35 6 3 1 25 7 26 80 58 42\\nno\\nno\\n 1 3 6 7 25 26 42 58 80\\n 6 3 1 80 58 25 7 26 42\\n\", \" 1 6 7 21 26 35 42 80 86\\n 35 6 1 21 7 26 80 42 86\\nyes\\nno\\n 1 6 7 21 26 42 80 86\\n 6 1 80 21 7 26 42 86\\n\", \" 1 3 6 7 11 14 26 35 42 86\\n 6 3 1 11 7 35 14 26 86 42\\nyes\\nno\\n 1 3 6 7 11 14 26 42 86\\n 6 3 1 11 7 86 14 26 42\\n\", \" 1 3 6 7 11 14 26 35 42 86\\n 6 3 1 35 11 7 14 26 42 86\\nno\\nno\\n 1 3 6 7 11 14 26 42 86\\n 6 3 1 11 7 14 26 42 86\\n\", \" 1 3 6 7 14 21 35 42 80 141\\n 6 3 1 80 35 14 7 21 42 141\\nyes\\nno\\n 1 3 6 7 14 21 42 80 141\\n 6 3 1 80 14 7 21 42 141\\n\", \" 1 3 6 7 14 21 35 42 87 102\\n 87 35 6 3 1 14 7 21 42 102\\nyes\\nno\\n 1 3 6 7 14 21 42 87 102\\n 87 6 3 1 14 7 21 42 102\\n\", \" 1 3 6 7 14 26 33 42 58 80\\n 33 6 3 1 14 7 26 80 58 42\\nno\\nno\\n 1 3 6 7 14 26 33 42 58 80\\n 33 6 3 1 14 7 26 80 58 42\\n\", \" 1 3 6 7 21 23 35 42 80 141\\n 6 3 1 35 23 7 21 80 42 141\\nyes\\nno\\n 1 3 6 7 21 23 42 80 141\\n 6 3 1 80 23 7 21 42 141\\n\", \" 1 4 6 7 24 26 35 42 80 86\\n 4 1 35 6 24 7 26 80 42 86\\nno\\nno\\n 1 4 6 7 24 26 42 80 86\\n 4 1 6 80 24 7 26 42 86\\n\", \" 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 7 14 80 26 42 141\\nyes\\nno\\n 2 3 6 7 14 21 26 42 80 141\\n 6 3 2 21 7 14 80 26 42 141\\n\", \" 1 6 7 14 21 42 80 141\\n 6 1 21 14 7 80 42 141\\nno\\nno\\n 1 6 7 14 21 42 80 141\\n 6 1 21 14 7 80 42 141\\n\", \"1 3 6 7 14 21 35 42 80 86\\n 35 6 3 1 14 7 21 80 42 86\\nyes\\nno\\n 1 3 6 7 14 21 42 80 86\\n 6 3 1 80 14 7 21 42 86\"]}", "source": "taco"}
|
A binary search tree can be unbalanced depending on features of data. For example, if we insert $n$ elements into a binary search tree in ascending order, the tree become a list, leading to long search times. One of strategies is to randomly shuffle the elements to be inserted. However, we should consider to maintain the balanced binary tree where different operations can be performed one by one depending on requirement.
We can maintain the balanced binary search tree by assigning a priority randomly selected to each node and by ordering nodes based on the following properties. Here, we assume that all priorities are distinct and also that all keys are distinct.
* binary-search-tree property. If $v$ is a left child of $u$, then $v.key < u.key$ and if $v$ is a right child of $u$, then $u.key < v.key$
* heap property. If $v$ is a child of $u$, then $v.priority < u.priority$
This combination of properties is why the tree is called Treap (tree + heap).
An example of Treap is shown in the following figure.
<image>
Insert
To insert a new element into a Treap, first of all, insert a node which a randomly selected priority value is assigned in the same way for ordinal binary search tree. For example, the following figure shows the Treap after a node with key = 6 and priority = 90 is inserted.
<image>
It is clear that this Treap violates the heap property, so we need to modify the structure of the tree by rotate operations. The rotate operation is to change parent-child relation while maintaing the binary-search-tree property.
<image>
The rotate operations can be implemented as follows.
rightRotate(Node t)
Node s = t.left
t.left = s.right
s.right = t
return s // the new root of subtree
|
leftRotate(Node t)
Node s = t.right
t.right = s.left
s.left = t
return s // the new root of subtree
---|---
The following figure shows processes of the rotate operations after the insert operation to maintain the properties.
<image>
The insert operation with rotate operations can be implemented as follows.
insert(Node t, int key, int priority) // search the corresponding place recursively
if t == NIL
return Node(key, priority) // create a new node when you reach a leaf
if key == t.key
return t // ignore duplicated keys
if key < t.key // move to the left child
t.left = insert(t.left, key, priority) // update the pointer to the left child
if t.priority < t.left.priority // rotate right if the left child has higher priority
t = rightRotate(t)
else // move to the right child
t.right = insert(t.right, key, priority) // update the pointer to the right child
if t.priority < t.right.priority // rotate left if the right child has higher priority
t = leftRotate(t)
return t
Delete
To delete a node from the Treap, first of all, the target node should be moved until it becomes a leaf by rotate operations. Then, you can remove the node (the leaf). These processes can be implemented as follows.
delete(Node t, int key) // seach the target recursively
if t == NIL
return NIL
if key < t.key // search the target recursively
t.left = delete(t.left, key)
else if key > t.key
t.right = delete(t.right, key)
else
return _delete(t, key)
return t
_delete(Node t, int key) // if t is the target node
if t.left == NIL && t.right == NIL // if t is a leaf
return NIL
else if t.left == NIL // if t has only the right child, then perform left rotate
t = leftRotate(t)
else if t.right == NIL // if t has only the left child, then perform right rotate
t = rightRotate(t)
else // if t has both the left and right child
if t.left.priority > t.right.priority // pull up the child with higher priority
t = rightRotate(t)
else
t = leftRotate(t)
return delete(t, key)
Write a program which performs the following operations to a Treap $T$ based on the above described algorithm.
* insert ($k$, $p$): Insert a node containing $k$ as key and $p$ as priority to $T$.
* find ($k$): Report whether $T$ has a node containing $k$.
* delete ($k$): Delete a node containing $k$.
* print(): Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.
Constraints
* The number of operations $ \leq 200,000$
* $0 \leq k, p \leq 2,000,000,000$
* The height of the binary tree does not exceed 50 if you employ the above algorithm
* The keys in the binary search tree are all different.
* The priorities in the binary search tree are all different.
* The size of output $\leq 10$ MB
Input
In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k \; p$, find $k$, delete $k$ or print are given.
Output
For each find($k$) operation, print "yes" if $T$ has a node containing $k$, "no" if not.
In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.
Example
Input
16
insert 35 99
insert 3 80
insert 1 53
insert 14 25
insert 80 76
insert 42 3
insert 86 47
insert 21 12
insert 7 10
insert 6 90
print
find 21
find 22
delete 35
delete 99
print
Output
1 3 6 7 14 21 35 42 80 86
35 6 3 1 14 7 21 80 42 86
yes
no
1 3 6 7 14 21 42 80 86
6 3 1 80 14 7 21 42 86
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"1 1\\n-16\", \"5 3\\n-10 10 -18 10 -10\", \"4 2\\n7 -10 -10 10\", \"4 2\\n7 -6 -10 12\", \"4 2\\n7 -6 -10 20\", \"4 2\\n9 -1 -10 20\", \"4 2\\n13 -1 -10 20\", \"4 2\\n3 -1 -10 20\", \"4 3\\n3 -1 -10 20\", \"4 3\\n3 -1 -1 20\", \"10 5\\n5 -4 -5 -8 -4 0 2 -4 0 7\", \"4 4\\n9 -1 -10 20\", \"4 3\\n3 -1 -1 27\", \"4 2\\n1 -10 -10 10\", \"4 2\\n7 -6 -5 15\", \"4 1\\n7 -6 -10 8\", \"4 2\\n7 -2 -10 38\", \"4 4\\n1 -1 -16 20\", \"4 2\\n7 0 -6 5\", \"10 5\\n5 -4 -5 -8 -4 7 2 -4 0 14\", \"4 2\\n3 -2 -10 38\", \"10 5\\n5 -4 -5 -16 -4 0 1 -4 -1 3\", \"5 3\\n-3 0 -2 2 -10\", \"1 1\\n1\", \"4 2\\n3 -1 -10 22\", \"4 2\\n14 -6 -6 12\", \"4 2\\n7 0 -2 27\", \"4 1\\n3 -1 -2 27\", \"5 3\\n-6 0 -18 8 -1\", \"4 2\\n1 -12 -6 12\", \"4 3\\n7 -15 -10 2\", \"4 2\\n3 -1 -10 36\", \"4 2\\n7 1 -2 27\", \"5 3\\n-25 6 -10 3 -4\", \"10 5\\n5 -5 -5 -8 -4 0 7 -4 1 3\", \"4 2\\n8 0 -10 28\", \"4 1\\n7 1 -2 35\", \"5 1\\n-6 10 -10 38 0\", \"4 1\\n5 -8 -13 0\", \"10 5\\n5 -1 -3 -3 0 13 2 -4 1 14\", \"10 5\\n5 -1 -3 -3 0 13 2 -4 2 14\", \"5 2\\n0 16 -3 38 0\", \"5 3\\n2 26 0 13 1\", \"5 2\\n2 26 0 17 1\", \"4 3\\n3 -1 -2 51\", \"4 2\\n3 -2 -12 44\", \"4 3\\n0 -15 -10 3\", \"4 2\\n2 0 -10 55\", \"4 2\\n2 0 -24 36\", \"5 2\\n0 10 -10 38 1\", \"4 3\\n3 0 -2 52\", \"4 2\\n3 -1 0 41\", \"4 2\\n7 -2 -3 52\", \"1 1\\n-2\", \"5 3\\n-10 10 -18 10 -13\", \"4 2\\n7 -6 -10 10\", \"4 2\\n7 -1 -10 20\", \"1 1\\n-20\", \"5 3\\n-10 8 -10 10 -10\", \"4 2\\n0 -10 -10 10\", \"1 1\\n-25\", \"5 3\\n-6 10 -18 10 -10\", \"4 2\\n7 -6 -5 10\", \"1 1\\n-3\", \"4 2\\n7 -6 -6 12\", \"4 1\\n7 -6 -10 20\", \"4 2\\n7 -2 -10 20\", \"4 2\\n3 -1 -16 20\", \"4 3\\n3 -1 -8 20\", \"10 5\\n5 -4 -5 -8 -4 0 2 -4 0 3\", \"5 3\\n-10 8 -10 10 -18\", \"1 1\\n-11\", \"5 3\\n-6 0 -18 10 -10\", \"4 2\\n2 -6 -6 12\", \"4 2\\n1 -1 -16 20\", \"4 3\\n3 -2 -8 20\", \"10 5\\n5 -4 -5 -16 -4 0 2 -4 0 3\", \"5 3\\n-10 8 -10 10 -4\", \"5 3\\n-6 0 -18 14 -10\", \"4 1\\n7 -3 -10 8\", \"4 4\\n7 -2 -10 38\", \"10 5\\n5 -4 -5 -16 -4 0 2 -4 -1 3\", \"5 3\\n-10 6 -10 10 -4\", \"5 3\\n-3 0 -18 14 -10\", \"4 1\\n7 -3 -6 8\", \"4 4\\n7 -2 -10 2\", \"4 4\\n1 -1 -16 13\", \"10 5\\n6 -4 -5 -16 -4 0 2 -4 -1 3\", \"5 3\\n-11 6 -10 10 -4\", \"5 3\\n-3 0 -21 14 -10\", \"4 2\\n7 -3 -6 8\", \"10 5\\n6 -4 -5 -16 -4 0 2 -4 -2 3\", \"5 3\\n-3 0 -2 14 -10\", \"4 2\\n7 0 -6 8\", \"1 1\\n-9\", \"5 3\\n-10 10 -10 8 -10\", \"4 3\\n10 -10 -10 10\", \"5 3\\n-10 10 -21 10 -10\", \"4 2\\n7 -15 -10 10\", \"1 1\\n0\", \"10 5\\n5 -4 -5 -8 -4 7 2 -4 0 7\", \"1 1\\n-10\", \"5 3\\n-10 10 -10 10 -10\", \"4 2\\n10 -10 -10 10\"], \"outputs\": [\"0\\n\", \"10\\n\", \"17\\n\", \"19\\n\", \"27\\n\", \"29\\n\", \"33\\n\", \"23\\n\", \"20\\n\", \"21\\n\", \"14\\n\", \"18\\n\", \"28\\n\", \"11\\n\", \"22\\n\", \"15\\n\", \"45\\n\", \"4\\n\", \"12\\n\", \"24\\n\", \"41\\n\", \"9\\n\", \"2\\n\", \"1\\n\", \"25\\n\", \"26\\n\", \"34\\n\", \"30\\n\", \"8\\n\", \"13\\n\", \"7\\n\", \"39\\n\", \"35\\n\", \"6\\n\", \"16\\n\", \"36\\n\", \"43\\n\", \"48\\n\", \"5\\n\", \"31\\n\", \"32\\n\", \"54\\n\", \"42\\n\", \"46\\n\", \"51\\n\", \"47\\n\", \"3\\n\", \"57\\n\", \"38\\n\", \"49\\n\", \"53\\n\", \"44\\n\", \"59\\n\", \"0\\n\", \"10\\n\", \"17\\n\", \"27\\n\", \"0\\n\", \"10\\n\", \"10\\n\", \"0\\n\", \"10\\n\", \"17\\n\", \"0\\n\", \"19\\n\", \"27\\n\", \"27\\n\", \"23\\n\", \"20\\n\", \"10\\n\", \"10\\n\", \"0\\n\", \"10\\n\", \"14\\n\", \"21\\n\", \"20\\n\", \"10\\n\", \"10\\n\", \"14\\n\", \"15\\n\", \"33\\n\", \"10\\n\", \"10\\n\", \"14\\n\", \"15\\n\", \"0\\n\", \"0\\n\", \"11\\n\", \"10\\n\", \"14\\n\", \"15\\n\", \"11\\n\", \"14\\n\", \"15\\n\", \"0\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"17\\n\", \"0\\n\", \"17\", \"0\", \"10\", \"20\"]}", "source": "taco"}
|
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[1, 50], [3, 100], [3, 200], [6, 350], [6, 1000], [7, 1500], [7, 2500], [7, 3000], [9, 4000], [9, 5000], [11, 5000]], \"outputs\": [[8], [7], [18], [86], [214], [189], [309], [366], [487], [622], [567]]}", "source": "taco"}
|
The integers 14 and 15, are contiguous (1 the difference between them, obvious) and have the same number of divisors.
```python
14 ----> 1, 2, 7, 14 (4 divisors)
15 ----> 1, 3, 5, 15 (4 divisors)
```
The next pair of contiguous integers with this property is 21 and 22.
```python
21 -----> 1, 3, 7, 21 (4 divisors)
22 -----> 1, 2, 11, 22 (4 divisors)
```
We have 8 pairs of integers below 50 having this property, they are:
```python
[[2, 3], [14, 15], [21, 22], [26, 27], [33, 34], [34, 35], [38, 39], [44, 45]]
```
Let's see now the integers that have a difference of 3 between them. There are seven pairs below 100:
```python
[[2, 5], [35, 38], [55, 58], [62, 65], [74, 77], [82, 85], [91, 94]]
```
Let's name, diff, the difference between two integers, next and prev, (diff = next - prev) and nMax, an upper bound of the range.
We need a special function, count_pairsInt(), that receives two arguments, diff and nMax and outputs the amount of pairs of integers that fulfill this property, all of them being smaller (not smaller or equal) than nMax.
Let's see it more clearly with examples.
```python
count_pairsInt(1, 50) -----> 8 (See case above)
count_pairsInt(3, 100) -----> 7 (See case above)
```
Happy coding!!!
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
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|
There is a graph of $n$ rows and $10^6 + 2$ columns, where rows are numbered from $1$ to $n$ and columns from $0$ to $10^6 + 1$:
Let's denote the node in the row $i$ and column $j$ by $(i, j)$.
Initially for each $i$ the $i$-th row has exactly one obstacle — at node $(i, a_i)$. You want to move some obstacles so that you can reach node $(n, 10^6+1)$ from node $(1, 0)$ by moving through edges of this graph (you can't pass through obstacles). Moving one obstacle to an adjacent by edge free node costs $u$ or $v$ coins, as below:
If there is an obstacle in the node $(i, j)$, you can use $u$ coins to move it to $(i-1, j)$ or $(i+1, j)$, if such node exists and if there is no obstacle in that node currently.
If there is an obstacle in the node $(i, j)$, you can use $v$ coins to move it to $(i, j-1)$ or $(i, j+1)$, if such node exists and if there is no obstacle in that node currently.
Note that you can't move obstacles outside the grid. For example, you can't move an obstacle from $(1,1)$ to $(0,1)$.
Refer to the picture above for a better understanding.
Now you need to calculate the minimal number of coins you need to spend to be able to reach node $(n, 10^6+1)$ from node $(1, 0)$ by moving through edges of this graph without passing through obstacles.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first line of each test case contains three integers $n$, $u$ and $v$ ($2 \le n \le 100$, $1 \le u, v \le 10^9$) — the number of rows in the graph and the numbers of coins needed to move vertically and horizontally respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — where $a_i$ represents that the obstacle in the $i$-th row is in node $(i, a_i)$.
It's guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^4$.
-----Output-----
For each test case, output a single integer — the minimal number of coins you need to spend to be able to reach node $(n, 10^6+1)$ from node $(1, 0)$ by moving through edges of this graph without passing through obstacles.
It can be shown that under the constraints of the problem there is always a way to make such a trip possible.
-----Examples-----
Input
3
2 3 4
2 2
2 3 4
3 2
2 4 3
3 2
Output
7
3
3
-----Note-----
In the first sample, two obstacles are at $(1, 2)$ and $(2,2)$. You can move the obstacle on $(2, 2)$ to $(2, 3)$, then to $(1, 3)$. The total cost is $u+v = 7$ coins.
In the second sample, two obstacles are at $(1, 3)$ and $(2,2)$. You can move the obstacle on $(1, 3)$ to $(2, 3)$. The cost is $u = 3$ coins.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"AAA\", [1]], [\"AAA\", [2]], [\"AAA\", [-1]], [\"AAAA\", [2]], [\"AGGTGACACCGCAAGCCTTATATTAGC\"], [\"AGGTGACACCGCAAGCCTTATATTAGC\", [1, 2]], [\"AGGTGACACCGCAAGCCTTATATTAGC\", [2, 1]], [\"AGGTGACACCGCAAGCCTTATATTAGC\", []], [\"\"], [\"\", []]], \"outputs\": [[[\"K\"]], [[\"\"]], [[\"F\"]], [[\"K\"]], [[\"R*HRKPYIS\", \"GDTASLIL\", \"VTPQALY*\", \"ANIRLAVSP\", \"LI*GLRCH\", \"*YKACGVT\"]], [[\"R*HRKPYIS\", \"GDTASLIL\"]], [[\"GDTASLIL\", \"R*HRKPYIS\"]], [[]], [[\"\", \"\", \"\", \"\", \"\", \"\"]], [[]]]}", "source": "taco"}
|
In genetics a reading frame is a way to divide a sequence of nucleotides (DNA bases) into a set of consecutive non-overlapping triplets (also called codon). Each of this triplets is translated into an amino-acid during a translation process to create proteins.
In a single strand of DNA you find 3 Reading frames, for example the following sequence:
```
AGGTGACACCGCAAGCCTTATATTAGC
```
will be decompose in:
```
Frame 1: AGG·TGA·CAC·CGC·AAG·CCT·TAT·ATT·AGC
Frame 2: A·GGT·GAC·ACC·GCA·AGC·CTT·ATA·TTA·GC
Frame 3: AG·GTG·ACA·CCG·CAA·GCC·TTA·TAT·TAG·C
```
In a double strand DNA you find 3 more Reading frames base on the reverse complement-strand, given the previous DNA sequence, in the reverse complement ( A-->T, G-->C, T-->A, C-->G).
Due to the splicing of DNA strands and the fixed reading direction of a nucleotide strand, the reverse complement gets read from right to left
```
AGGTGACACCGCAAGCCTTATATTAGC
Reverse complement: TCCACTGTGGCGTTCGGAATATAATCG
reversed reverse frame: GCTAATATAAGGCTTGCGGTGTCACCT
```
You have:
```
Reverse Frame 1: GCT AAT ATA AGG CTT GCG GTG TCA CCT
reverse Frame 2: G CTA ATA TAA GGC TTG CGG TGT CAC CT
reverse Frame 3: GC TAA TAT AAG GCT TGC GGT GTC ACC T
```
You can find more information about the Open Reading frame in wikipedia just [here] (https://en.wikipedia.org/wiki/Reading_frame)
Given the [standard table of genetic code](http://www.ncbi.nlm.nih.gov/Taxonomy/Utils/wprintgc.cgi#SG1):
```
AAs = FFLLSSSSYY**CC*WLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSRRVVVVAAAADDEEGGGG
Base1 = TTTTTTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG
Base2 = TTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGG
Base3 = TCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAG
```
The tri-nucleotide TTT = F, TTC = F, TTA = L...
So our 6 frames will be translate as:
```
Frame 1: AGG·TGA·CAC·CGC·AAG·CCT·TAT·ATT·AGC
R * H R K P Y I S
Frame 2: A·GGT·GAC·ACC·GCA·AGC·CTT·ATA·TTA·GC
G D T A S L I L
Frame 3: AG·GTG·ACA·CCG·CAA·GCC·TTA·TAT·TAG·C
V T P Q A L Y *
Reverse Frame 1: GCT AAT ATA AGG CTT GCG GTG TCA CCT
A N I R L A V S P
Reverse Frame 2: G CTA ATA TAA GGC TTG CGG TGT CAC CT
L I * G L R C H
Reverse Frame 3: GC TAA TAT AAG GCT TGC GGT GTC ACC T
* Y K A C G V T
```
In this kata you should create a function that translates DNA on all 6 frames, this function takes 2 arguments.
The first one is the DNA sequence the second one is an array of frame number for example if we want to translate in Frame 1 and Reverse 1 this array will be [1,-1]. Valid frames are 1, 2, 3 and -1, -2, -3.
The translation hash is available for you under a translation hash `$codons` [Ruby] or `codon` [other languages] (for example to access value of 'TTT' you should call $codons['TTT'] => 'F').
The function should return an array with all translation asked for, by default the function do the translation on all 6 frames.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"scout\", [20, 12, 18, 30, 21]], [\"masterpiece\", [14, 10, 22, 29, 6, 27, 19, 18, 6, 12, 8]], [\"nomoretears\", [15, 17, 14, 17, 19, 7, 21, 7, 2, 20, 20]], [\"notencrypted\", [14, 15, 20, 5, 14, 3, 18, 25, 16, 20, 5, 4]], [\"tenthousand\", [21, 5, 14, 20, 8, 16, 21, 19, 1, 14, 5]], [\"oneohone\", [16, 14, 6, 16, 8, 16, 15, 5]]], \"outputs\": [[1939], [1939], [12], [0], [10000], [101]]}", "source": "taco"}
|
# Introduction
Digital Cypher assigns a unique number to each letter of the alphabet:
```
a b c d e f g h i j k l m n o p q r s t u v w x y z
1 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
```
In the encrypted word we write the corresponding numbers instead of the letters. For example, the word `scout` becomes:
```
s c o u t
19 3 15 21 20
```
Then we add to each number a digit from the key (repeated if necessary). For example if the key is `1939`:
```
s c o u t
19 3 15 21 20
+ 1 9 3 9 1
---------------
20 12 18 30 21
m a s t e r p i e c e
13 1 19 20 5 18 16 9 5 3 5
+ 1 9 3 9 1 9 3 9 1 9 3
--------------------------------
14 10 22 29 6 27 19 18 6 12 8
```
# Task
Write a function that accepts a `message` string and an array of integers `code`. As the result, return the `key` that was used to encrypt the `message`. The `key` has to be shortest of all possible keys that can be used to code the `message`: i.e. when the possible keys are `12` , `1212`, `121212`, your solution should return `12`.
#### Input / Output:
* The `message` is a string containing only lowercase letters.
* The `code` is an array of positive integers.
* The `key` output is a positive integer.
# Examples
```python
find_the_key("scout", [20, 12, 18, 30, 21]) # --> 1939
find_the_key("masterpiece", [14, 10, 22, 29, 6, 27, 19, 18, 6, 12, 8]) # --> 1939
find_the_key("nomoretears", [15, 17, 14, 17, 19, 7, 21, 7, 2, 20, 20]) # --> 12
```
# Digital cypher series
- [Digital cypher vol 1](https://www.codewars.com/kata/592e830e043b99888600002d)
- [Digital cypher vol 2](https://www.codewars.com/kata/592edfda5be407b9640000b2)
- [Digital cypher vol 3 - missing key](https://www.codewars.com/kata/5930d8a4b8c2d9e11500002a)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 5\\n1 4 4 3 4\\n1 4 1 4 2\\n1 4 4 4 3\\n\", \"1 1\\n1\\n\", \"1 1\\n2\\n\", \"3 1\\n1\\n1\\n1\\n\", \"1 1\\n1\\n\", \"1 1\\n2\\n\", \"3 1\\n1\\n1\\n1\\n\", \"3 1\\n1\\n1\\n2\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 2\\n1 4 4 4 3\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 2\\n1 3 4 4 3\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n1 3 3 4 4\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 4 4 1\\n\", \"3 5\\n1 4 4 2 4\\n1 1 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 4 1 4 4\\n2 4 4 4 3\\n\", \"1 1\\n2\\n1\\n1\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 1 4 3\\n\", \"3 5\\n1 4 2 2 4\\n1 1 2 4 2\\n1 2 2 4 4\\n\", \"3 5\\n1 3 4 2 4\\n2 1 2 4 2\\n1 2 3 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 4\\n2 4 4 4 3\\n\", \"3 5\\n1 4 2 2 4\\n1 1 2 1 2\\n1 2 2 4 4\\n\", \"3 5\\n2 3 2 4 4\\n1 4 2 3 2\\n1 3 4 2 1\\n\", \"3 5\\n1 3 2 2 2\\n1 2 2 1 2\\n1 1 2 4 4\\n\", \"3 5\\n1 3 4 3 1\\n1 1 1 4 2\\n1 2 2 2 4\\n\", \"3 1\\n3\\n2\\n4\\n\", \"3 1\\n4\\n4\\n2\\n\", \"3 5\\n1 4 4 3 4\\n1 4 1 4 2\\n2 4 4 4 3\\n\", \"3 1\\n2\\n1\\n2\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 4 4 3\\n\", \"3 1\\n2\\n1\\n3\\n\", \"3 5\\n1 4 4 3 4\\n1 2 2 4 2\\n1 3 3 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 2\\n1 4 3 4 3\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n2 4 1 4 2\\n2 4 4 4 3\\n\", \"3 5\\n2 2 4 3 4\\n1 4 2 4 2\\n1 3 4 4 3\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n1 2 3 4 4\\n\", \"3 1\\n2\\n1\\n4\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 4 2 1\\n\", \"3 5\\n2 4 4 2 4\\n1 4 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n2 4 1 4 3\\n2 4 4 4 3\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n1 2 2 4 4\\n\", \"3 5\\n2 4 4 2 1\\n1 4 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n2 4 4 2 1\\n1 4 2 4 2\\n2 3 4 4 4\\n\", \"1 1\\n1\\n1\\n1\\n\", \"3 5\\n1 4 4 1 4\\n1 4 1 4 2\\n1 4 4 4 3\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 2\\n1 1 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 4 4 2\\n1 3 3 4 4\\n\", \"3 1\\n2\\n1\\n1\\n\", \"3 5\\n2 4 4 3 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1\\n\", \"3 5\\n1 4 2 4 4\\n1 1 4 2 3\\n1 2 2 4 4\\n\", \"3 5\\n1 3 2 2 2\\n1 2 1 1 2\\n1 1 2 4 4\\n\", \"3 5\\n4 3 2 2 4\\n1 4 2 3 1\\n2 3 4 2 1\\n\", \"3 5\\n1 3 2 2 2\\n1 2 1 1 2\\n1 1 2 3 4\\n\", \"3 5\\n4 3 2 2 4\\n1 4 2 1 1\\n2 3 4 2 1\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 4 1\\n1 4 4 4 3\\n\", \"3 5\\n2 4 4 3 4\\n1 1 2 4 2\\n1 3 4 4 4\\n\", \"3 5\\n2 4 4 3 3\\n1 4 2 4 2\\n1 3 4 4 3\\n\", \"3 1\\n2\\n2\\n3\\n\", \"3 5\\n2 4 4 3 4\\n1 4 4 4 2\\n1 3 4 4 4\\n\", \"3 5\\n2 4 4 3 4\\n2 4 1 4 2\\n2 4 4 4 3\\n\", \"3 5\\n1 4 4 4 4\\n1 1 2 4 2\\n1 2 3 4 4\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 3 3 2 1\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 4\\n1 2 2 4 4\\n\", \"3 5\\n2 4 4 2 1\\n1 4 2 4 1\\n2 3 4 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 4 4 2\\n1 3 3 4 2\\n\", \"3 5\\n2 1 4 2 4\\n1 4 2 3 2\\n1 3 4 4 4\\n\", \"2 1\\n2\\n1\\n0\\n\", \"3 5\\n1 2 4 1 4\\n1 4 1 4 2\\n1 4 4 3 3\\n\", \"3 5\\n1 3 4 2 4\\n2 1 2 2 2\\n1 2 3 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n1 3 4 3 3\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 3 2\\n1 3 1 4 3\\n\", \"1 1\\n1\\n1\\n3\\n\", \"3 5\\n1 4 4 1 1\\n2 4 1 4 2\\n1 4 4 4 3\\n\", \"3 5\\n1 3 4 3 1\\n1 1 2 4 2\\n2 2 3 4 4\\n\", \"3 5\\n2 4 4 3 4\\n1 4 2 4 2\\n1 2 2 4 3\\n\", \"3 5\\n1 3 4 3 4\\n2 1 4 4 2\\n1 2 3 2 4\\n\", \"3 5\\n1 4 2 2 4\\n1 1 4 1 2\\n1 2 2 4 4\\n\", \"3 5\\n2 2 4 3 4\\n1 4 2 4 1\\n1 3 4 4 3\\n\", \"3 5\\n2 4 4 1 1\\n1 4 2 4 2\\n1 4 4 3 3\\n\", \"3 5\\n1 4 4 3 4\\n1 2 4 4 1\\n1 3 3 4 1\\n\", \"3 5\\n2 3 2 4 4\\n1 4 2 3 2\\n1 4 4 2 1\\n\", \"3 5\\n1 4 4 2 4\\n1 4 1 4 2\\n1 4 4 1 3\\n\", \"3 5\\n1 4 3 3 4\\n2 4 1 4 2\\n2 2 4 4 3\\n\", \"3 5\\n1 4 3 1 4\\n1 4 2 4 2\\n1 4 4 3 3\\n\", \"3 5\\n1 4 4 2 4\\n1 1 4 4 4\\n1 3 3 4 4\\n\", \"3 5\\n1 4 2 3 4\\n1 4 2 4 2\\n1 3 4 4 2\\n\", \"3 5\\n2 4 2 3 4\\n1 2 2 4 2\\n1 2 2 4 4\\n\", \"3 5\\n2 4 4 3 4\\n2 4 2 4 2\\n1 3 1 4 3\\n\", \"3 5\\n1 3 4 3 1\\n1 1 3 4 1\\n1 2 3 4 4\\n\", \"3 5\\n1 4 4 1 4\\n1 4 2 4 3\\n1 4 4 2 3\\n\", \"3 5\\n2 4 4 2 4\\n2 4 2 4 2\\n1 3 2 4 3\\n\", \"3 5\\n2 4 4 1 4\\n1 1 2 4 2\\n1 1 4 3 3\\n\", \"3 5\\n1 3 4 3 4\\n4 1 2 4 4\\n1 3 3 2 4\\n\", \"3 5\\n2 4 2 3 4\\n1 3 4 4 2\\n1 3 4 4 2\\n\", \"3 5\\n2 4 4 3 4\\n3 4 2 4 2\\n1 3 1 4 3\\n\", \"3 5\\n1 4 4 1 4\\n1 2 1 4 4\\n3 2 4 4 3\\n\", \"3 5\\n2 4 4 3 4\\n2 4 2 3 2\\n1 3 2 4 1\\n\", \"3 5\\n1 3 2 4 4\\n1 2 2 1 2\\n1 1 2 4 4\\n\", \"3 5\\n1 4 4 3 4\\n1 1 1 3 4\\n1 3 3 4 3\\n\", \"3 5\\n3 4 2 3 4\\n1 3 2 4 2\\n1 3 4 4 1\\n\", \"3 5\\n1 3 2 3 4\\n2 2 2 4 2\\n1 2 3 4 4\\n\", \"3 5\\n1 4 4 1 4\\n1 3 1 4 2\\n4 2 4 4 3\\n\", \"3 5\\n1 4 2 4 4\\n1 1 2 2 3\\n1 2 1 4 4\\n\", \"3 5\\n1 3 2 2 2\\n1 2 2 1 2\\n1 1 3 4 4\\n\", \"3 5\\n4 3 2 1 4\\n1 4 2 3 1\\n1 3 4 2 1\\n\", \"3 5\\n2 3 2 2 2\\n1 2 1 1 2\\n1 1 2 4 4\\n\", \"3 5\\n4 3 1 2 4\\n1 4 2 1 1\\n2 3 4 2 1\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 2 1\\n1 4 4 4 3\\n\", \"3 1\\n2\\n3\\n3\\n\", \"3 5\\n2 4 4 2 1\\n1 4 2 4 1\\n3 3 4 4 4\\n\", \"2 1\\n2\\n1\\n-1\\n\", \"3 5\\n1 4 4 3 4\\n1 1 2 4 2\\n2 3 4 3 3\\n\", \"3 5\\n1 4 4 3 4\\n1 4 2 3 2\\n2 3 1 4 3\\n\", \"1 1\\n2\\n1\\n3\\n\", \"3 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|
Monocarp is playing a game "Assimilation IV". In this game he manages a great empire: builds cities and conquers new lands.
Monocarp's empire has $n$ cities. In order to conquer new lands he plans to build one Monument in each city. The game is turn-based and, since Monocarp is still amateur, he builds exactly one Monument per turn.
Monocarp has $m$ points on the map he'd like to control using the constructed Monuments. For each point he knows the distance between it and each city. Monuments work in the following way: when built in some city, a Monument controls all points at distance at most $1$ to this city. Next turn, the Monument controls all points at distance at most $2$, the turn after — at distance at most $3$, and so on. Monocarp will build $n$ Monuments in $n$ turns and his empire will conquer all points that are controlled by at least one Monument.
Monocarp can't figure out any strategy, so during each turn he will choose a city for a Monument randomly among all remaining cities (cities without Monuments). Monocarp wants to know how many points (among $m$ of them) he will conquer at the end of turn number $n$. Help him to calculate the expected number of conquered points!
-----Input-----
The first line contains two integers $n$ and $m$ ($1 \le n \le 20$; $1 \le m \le 5 \cdot 10^4$) — the number of cities and the number of points.
Next $n$ lines contains $m$ integers each: the $j$-th integer of the $i$-th line $d_{i, j}$ ($1 \le d_{i, j} \le n + 1$) is the distance between the $i$-th city and the $j$-th point.
-----Output-----
It can be shown that the expected number of points Monocarp conquers at the end of the $n$-th turn can be represented as an irreducible fraction $\frac{x}{y}$. Print this fraction modulo $998\,244\,353$, i. e. value $x \cdot y^{-1} mod 998244353$ where $y^{-1}$ is such number that $y \cdot y^{-1} mod 998244353 = 1$.
-----Examples-----
Input
3 5
1 4 4 3 4
1 4 1 4 2
1 4 4 4 3
Output
166374062
-----Note-----
Let's look at all possible orders of cities Monuments will be build in:
$[1, 2, 3]$:
the first city controls all points at distance at most $3$, in other words, points $1$ and $4$;
the second city controls all points at distance at most $2$, or points $1$, $3$ and $5$;
the third city controls all points at distance at most $1$, or point $1$.
In total, $4$ points are controlled.
$[1, 3, 2]$: the first city controls points $1$ and $4$; the second city — points $1$ and $3$; the third city — point $1$. In total, $3$ points.
$[2, 1, 3]$: the first city controls point $1$; the second city — points $1$, $3$ and $5$; the third city — point $1$. In total, $3$ points.
$[2, 3, 1]$: the first city controls point $1$; the second city — points $1$, $3$ and $5$; the third city — point $1$. In total, $3$ points.
$[3, 1, 2]$: the first city controls point $1$; the second city — points $1$ and $3$; the third city — points $1$ and $5$. In total, $3$ points.
$[3, 2, 1]$: the first city controls point $1$; the second city — points $1$, $3$ and $5$; the third city — points $1$ and $5$. In total, $3$ points.
The expected number of controlled points is $\frac{4 + 3 + 3 + 3 + 3 + 3}{6}$ $=$ $\frac{19}{6}$ or $19 \cdot 6^{-1}$ $\equiv$ $19 \cdot 166374059$ $\equiv$ $166374062$ $\pmod{998244353}$
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
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|
The legendary Farmer John is throwing a huge party, and animals from all over the world are hanging out at his house. His guests are hungry, so he instructs his cow Bessie to bring out the snacks! Moo!
There are $n$ snacks flavors, numbered with integers $1, 2, \ldots, n$. Bessie has $n$ snacks, one snack of each flavor. Every guest has exactly two favorite flavors. The procedure for eating snacks will go as follows: First, Bessie will line up the guests in some way. Then in this order, guests will approach the snacks one by one. Each guest in their turn will eat all remaining snacks of their favorite flavor. In case no favorite flavors are present when a guest goes up, they become very sad.
Help Bessie to minimize the number of sad guests by lining the guests in an optimal way.
-----Input-----
The first line contains integers $n$ and $k$ ($2 \le n \le 10^5$, $1 \le k \le 10^5$), the number of snacks and the number of guests.
The $i$-th of the following $k$ lines contains two integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le n$, $x_i \ne y_i$), favorite snack flavors of the $i$-th guest.
-----Output-----
Output one integer, the smallest possible number of sad guests.
-----Examples-----
Input
5 4
1 2
4 3
1 4
3 4
Output
1
Input
6 5
2 3
2 1
3 4
6 5
4 5
Output
0
-----Note-----
In the first example, Bessie can order the guests like this: $3, 1, 2, 4$. Guest $3$ goes first and eats snacks $1$ and $4$. Then the guest $1$ goes and eats the snack $2$ only, because the snack $1$ has already been eaten. Similarly, the guest $2$ goes up and eats the snack $3$ only. All the snacks are gone, so the guest $4$ will be sad.
In the second example, one optimal ordering is $2, 1, 3, 5, 4$. All the guests will be satisfied.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 3\\n...\\n.#.\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n-...#.\", \"2 6\\n#.#...\\n......\\n..#0.\\n......\\n.#.-..\\n--..#-\", \"2 3\\n...\\n.#.\\n..-\", \"2 3\\n/..\\n.#.\\n..-\", \"2 3\\n/..\\n.#.\\n..,\", \"3 3\\n...\\n/#.\\n...\", \"2 3\\n...\\n.#.\\n..,\", \"3 3\\n../\\n/#.\\n...\", \"3 3\\n-..\\n.#.\\n...\", \"2 3\\n...\\n/#.\\n..-\", \"3 3\\n...\\n/#.\\n..-\", \"2 3\\n...\\n.#.\\n.-.\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n../.#.\", \"2 3\\n-..\\n.#.\\n..-\", \"2 3\\n/..\\n.#.\\n./-\", \"3 3\\n..-\\n/#.\\n...\", \"3 3\\n.-/\\n/#.\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n-..-#.\", \"2 3\\n-..\\n.#.\\n.-.\", \"6 6\\n..#..#\\n......\\n..#./\\n......\\n.#....\\n../.#.\", \"3 3\\n..-\\n.#.\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n--.-#.\", \"6 6\\n..#-.#\\n......\\n..#./\\n......\\n.#....\\n../.#.\", \"3 3\\n,..\\n.#.\\n...\", \"6 6\\n..#-.#\\n....-.\\n..#./\\n......\\n.#....\\n../.#.\", \"3 3\\n,..\\n.#.\\n..-\", \"3 3\\n,..\\n.#.\\n../\", \"3 3\\n,..\\n.#-\\n../\", \"6 6\\n..#..#\\n......\\n..#/.\\n......\\n.#....\\n....#.\", \"2 3\\n...\\n-#.\\n..-\", \"2 3\\n...\\n/#.\\n...\", \"2 3\\n...\\n.#.\\n./,\", \"3 3\\n..-\\n.#-\\n...\", \"6 6\\n..#..#\\n...-..\\n..#..\\n......\\n.#....\\n-...#.\", \"2 3\\n...\\n/#.\\n..,\", \"2 3\\n..-\\n.#.\\n..-\", \"3 3\\n-..\\n/#.\\n...\", \"3 3\\n--/\\n/#.\\n...\", \"2 3\\n-..\\n.#.\\n.,.\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n--..#-\", \"3 3\\n,..\\n/#.\\n...\", \"3 3\\n,.-\\n.#.\\n..-\", \"2 3\\n...\\n.#.\\n/.,\", \"2 3\\n...\\n/#.\\n,..\", \"2 3\\n-..\\n/#.\\n...\", \"2 3\\n-..\\n.#.\\n/,.\", \"2 3\\n...\\n.#-\\n/.,\", \"2 3\\n...\\n/#.\\n,-.\", \"2 3\\n-..\\n/#.\\n./.\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#./..\\n....#.\", \"2 3\\n..-\\n.#.\\n...\", \"2 3\\n...\\n.#.\\n.--\", \"3 3\\n...\\n.#/\\n...\", \"3 3\\n/..\\n/#.\\n...\", \"3 3\\n./-\\n/#.\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n./....\\n.#....\\n-..-#.\", \"6 6\\n..#-.#\\n......\\n..\\\"./\\n......\\n.#....\\n../.#.\", \"3 3\\n,..\\n-#.\\n...\", \"3 3\\n,./\\n.#.\\n..-\", \"3 3\\n..,\\n.#-\\n../\", \"6 6\\n..#..#\\n......\\n..#/.\\n......\\n.#...-\\n....#.\", \"3 3\\n-..\\n.#-\\n...\", \"2 3\\n...\\n/#.\\n./,\", \"2 3\\n..-\\n.#.\\n..,\", \"2 3\\n-..\\n.#.\\n.+.\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#.-..\\n--..#-\", \"2 3\\n-..\\n/#.\\n-/.\", \"2 3\\n..-\\n.#-\\n...\", \"2 3\\n...\\n.#.\\n-.-\", \"3 3\\n./.\\n.#/\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n..../.\\n.#....\\n-..-#.\", \"2 3\\n,..\\n-#.\\n...\", \"3 3\\n..,\\n.#-\\n...\", \"2 3\\n...\\n/#.\\n,/.\", \"2 3\\n..-\\n.#.\\n,..\", \"2 3\\n-..\\n/#.\\n/,.\", \"2 6\\n..#..#\\n......\\n..#..\\n......\\n.#.-..\\n--..#-\", \"2 3\\n,..\\n/#.\\n-/.\", \"2 3\\n..-\\n.#-\\n/..\", \"3 3\\n.//\\n.#/\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n..../.\\n.#....\\n.-.-#.\", \"2 3\\n...\\n/#.\\n+/.\", \"2 6\\n..#..#\\n......\\n..#/.\\n......\\n.#.-..\\n--..#-\", \"2 3\\n..-\\n.#-\\n./.\", \"2 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n....#.\", \"2 3\\n/..\\n.#.\\n/.-\", \"3 3\\n./.\\n/#.\\n...\", \"3 3\\n-..\\n.#.\\n.-.\", \"2 3\\n...\\n.#.\\n--.\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#.../\\n../.#.\", \"3 3\\n..-\\n/#.\\n-..\", \"3 3\\n.-/\\n/#.\\n-..\", \"2 3\\n..-\\n.#.\\n.-.\", \"3 3\\n..-\\n.#.\\n..-\", \"3 3\\n..,\\n.#.\\n...\", \"2 6\\n..#-.#\\n....-.\\n..#./\\n......\\n.#....\\n../.#.\", \"3 3\\n,..\\n.#-\\n...\", \"6 6\\n..#..#\\n......\\n..#/.\\n.-....\\n.#....\\n....#.\", \"2 3\\n-..\\n-#.\\n..-\", \"3 3\\n...\\n.#.\\n...\", \"6 6\\n..#..#\\n......\\n..#..\\n......\\n.#....\\n....#.\"], \"outputs\": [\"2\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\", \"3\"]}", "source": "taco"}
|
You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
We will repeatedly perform the following operation until all the squares are black:
* Every white square that shares a side with a black square, becomes black.
Find the number of operations that will be performed. The initial grid has at least one black square.
Constraints
* 1 \leq H,W \leq 1000
* A_{ij} is `#` or `.`.
* The given grid has at least one black square.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the number of operations that will be performed.
Examples
Input
3 3
...
.#.
...
Output
2
Input
6 6
..#..#
......
..#..
......
.#....
....#.
Output
3
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Ivan has got an array of n non-negative integers a_1, a_2, ..., a_{n}. Ivan knows that the array is sorted in the non-decreasing order.
Ivan wrote out integers 2^{a}_1, 2^{a}_2, ..., 2^{a}_{n} on a piece of paper. Now he wonders, what minimum number of integers of form 2^{b} (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2^{v} - 1 for some integer v (v ≥ 0).
Help Ivan, find the required quantity of numbers.
-----Input-----
The first line contains integer n (1 ≤ n ≤ 10^5). The second input line contains n space-separated integers a_1, a_2, ..., a_{n} (0 ≤ a_{i} ≤ 2·10^9). It is guaranteed that a_1 ≤ a_2 ≤ ... ≤ a_{n}.
-----Output-----
Print a single integer — the answer to the problem.
-----Examples-----
Input
4
0 1 1 1
Output
0
Input
1
3
Output
3
-----Note-----
In the first sample you do not need to add anything, the sum of numbers already equals 2^3 - 1 = 7.
In the second sample you need to add numbers 2^0, 2^1, 2^2.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
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|
Luckily, Serval got onto the right bus, and he came to the kindergarten on time. After coming to kindergarten, he found the toy bricks very funny.
He has a special interest to create difficult problems for others to solve. This time, with many $1 \times 1 \times 1$ toy bricks, he builds up a 3-dimensional object. We can describe this object with a $n \times m$ matrix, such that in each cell $(i,j)$, there are $h_{i,j}$ bricks standing on the top of each other.
However, Serval doesn't give you any $h_{i,j}$, and just give you the front view, left view, and the top view of this object, and he is now asking you to restore the object. Note that in the front view, there are $m$ columns, and in the $i$-th of them, the height is the maximum of $h_{1,i},h_{2,i},\dots,h_{n,i}$. It is similar for the left view, where there are $n$ columns. And in the top view, there is an $n \times m$ matrix $t_{i,j}$, where $t_{i,j}$ is $0$ or $1$. If $t_{i,j}$ equals $1$, that means $h_{i,j}>0$, otherwise, $h_{i,j}=0$.
However, Serval is very lonely because others are bored about his unsolvable problems before, and refused to solve this one, although this time he promises there will be at least one object satisfying all the views. As his best friend, can you have a try?
-----Input-----
The first line contains three positive space-separated integers $n, m, h$ ($1\leq n, m, h \leq 100$) — the length, width and height.
The second line contains $m$ non-negative space-separated integers $a_1,a_2,\dots,a_m$, where $a_i$ is the height in the $i$-th column from left to right of the front view ($0\leq a_i \leq h$).
The third line contains $n$ non-negative space-separated integers $b_1,b_2,\dots,b_n$ ($0\leq b_j \leq h$), where $b_j$ is the height in the $j$-th column from left to right of the left view.
Each of the following $n$ lines contains $m$ numbers, each is $0$ or $1$, representing the top view, where $j$-th number of $i$-th row is $1$ if $h_{i, j}>0$, and $0$ otherwise.
It is guaranteed that there is at least one structure satisfying the input.
-----Output-----
Output $n$ lines, each of them contains $m$ integers, the $j$-th number in the $i$-th line should be equal to the height in the corresponding position of the top view. If there are several objects satisfying the views, output any one of them.
-----Examples-----
Input
3 7 3
2 3 0 0 2 0 1
2 1 3
1 0 0 0 1 0 0
0 0 0 0 0 0 1
1 1 0 0 0 0 0
Output
1 0 0 0 2 0 0
0 0 0 0 0 0 1
2 3 0 0 0 0 0
Input
4 5 5
3 5 2 0 4
4 2 5 4
0 0 0 0 1
1 0 1 0 0
0 1 0 0 0
1 1 1 0 0
Output
0 0 0 0 4
1 0 2 0 0
0 5 0 0 0
3 4 1 0 0
-----Note-----
[Image]
The graph above illustrates the object in the first example.
[Image]
[Image]
The first graph illustrates the object in the example output for the second example, and the second graph shows the three-view drawing of it.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"z\\na\\n\", \"abc\\naaac\\n\", \"bcbcdddbbd\\nbcbcdbdbbd\\n\", \"aaabccadac\\nacabbbabaa\\n\", \"a\\nb\\n\", \"acaccaaadz\\ncaadccaaaa\\n\", \"aa\\nab\\n\", \"abacaba\\naba\\n\", \"aabbaa\\naaaaaaaaaaaaaaaaaaaa\\n\", \"ac\\na\\n\", \"a\\na\\n\", \"aabbaa\\ncaaaaaaaaa\\n\", \"aaaaaaaaa\\na\\n\", \"ccc\\ncc\\n\", \"acbdcbacbb\\ncbcddabcbdaccdd\\n\", \"zaaa\\naaaw\\n\", \"bbbaabbaab\\nbbbaabbaab\\n\", \"z\\nww\\n\", \"acaccaaadd\\nacaccaaadd\\n\", \"aabbaa\\na\\n\", \"ccabcaabcc\\nbcca\\n\", \"adbddbccdacbaab\\nadaddcbddb\\n\", \"abc\\ncaa\\n\", \"ab\\nb\\n\", \"aa\\naa\\n\", \"zzzzzzzzzzzz\\na\\n\", \"aa\\na\\n\", \"abc\\ncac\\n\", \"aaaaaaaaz\\nwwwwwwwwwwwwwwwwwwww\\n\", \"ab\\naa\\n\", \"aaa\\naa\\n\", \"aab\\naa\\n\", \"zzzzzzzzzz\\naaaaaaaaa\\n\", \"bbbaabbaaz\\nabaabbbbaa\\n\", \"bbbaabbaab\\nababbaaabb\\n\", \"bcbcdddbbd\\nabbbcbdcdc\\n\", \"abbabaaabaaabbbbabbbbbababababaaaabbabbbbabbbbbabbbbababbaaaaabbbabbbbabbbbbbabaabababaabbbabababbaz\\nabaaabaabbbbaabbbbaabababbaabaabababbbaabbbaaabbabbabbbbbbbbaabbbbbabababbbbaaabaaaabbbbbbbbabababba\\n\", \"abab\\naaba\\n\", \"abcabc\\naaccba\\n\", \"bcbcdddbbz\\ndbbccbddba\\n\", \"bbbbaacacb\\ncbacbaabb\\n\", \"adbddbccdacbaab\\nadcddbdcda\\n\", \"abc\\nbbb\\n\", \"z\\nanana\\n\", \"adbddbccdacbaaz\\ndacdcaddbb\\n\", \"abc\\naca\\n\", \"babbaccbab\\nb\\n\", \"abc\\nabbc\\n\", \"aaaaaaaaaaaaaaa\\naaaaaaaaaaaaaa\\n\", \"acaccaaadd\\nbabcacbadd\\n\", \"abacaba\\nabababa\\n\", \"abbabaaabaaabbbbabbbbbababababaaaabbabbbbabbbbbabbbbababbaaaaabbbabbbbabbbbbbabaabababaabbbabababbaa\\nabbabaaabaaabbbbabbbabababababaaaabbabbbbabbbbbabbbbababbaaaaabbaabbbbabbbbbbabaabababaabbbabababbaa\\n\", \"abbabaaabaaabbbbabbbbbababababaaaabbabbbbabbbbbabbbbababbaaaaabbbabbbbabbbbbbabaabababaabbbabababbaa\\nbbaabaabaaaabbabaaaababababaabaabaaaabbaabbbbabbbaabaabaababbaababaaaabababbaabbaaabbbaaaaaaabaabbbb\\n\", \"aaabccadac\\naabbccbdac\\n\", \"bbbcaabcaa\\ncacbababab\\n\", \"aaabccadaz\\nacabcaadaa\\n\", \"qwertyz\\nqwertyuiop\\n\", \"ab\\na\\n\", \"abc\\naabb\\n\", \"abcabc\\nabccaa\\n\", \"z\\nzz\\n\", \"cba\\naaac\\n\", \"bcbcdddbbd\\ndbbdbdcbcb\\n\", \"cadaccbaaa\\nacabbbabaa\\n\", \"b\\nb\\n\", \"acaccaaadz\\naaaaccdaac\\n\", \"abadaba\\naba\\n\", \"abbbaa\\naaaaaaaaaaaaaaaaaaaa\\n\", \"bc\\na\\n\", \"b\\na\\n\", \"cbc\\ncc\\n\", \"zaaa\\nwaaa\\n\", \"bbbaabbaab\\nabbaabbaab\\n\", \"y\\nww\\n\", \"acaccaaadd\\nacaccaaadc\\n\", \"aabbaa\\nb\\n\", \"ccabcaaccc\\nbcca\\n\", \"adbddaccdacbaab\\nadaddcbddb\\n\", \"zzzzzzzzzzzz\\nb\\n\", \"cba\\ncac\\n\", \"bb\\naa\\n\", \"aab\\nab\\n\", \"zzzzzzzzzz\\naaaaa`aaa\\n\", \"bbbaabbaaz\\naabbbbaaba\\n\", \"bbbaabbaab\\nbbaaabbaba\\n\", \"bcbcdddbcd\\nabbbcbdcdc\\n\", \"abbabaaabaaabbbbabbbbbababababaaaabbabbbbabbbbbabbbbababbaaaaabbbabbbbabbbbbbabaabababaabbbabababbaz\\nabbabababbbbbbbbaaaabaaabbbbabababbbbbaabbbbbbbbabbabbaaabbbaabbbababaabaabbababaabbbbaabbbbaabaaaba\\n\", \"bcbcdddbbz\\ndbbcdbdcba\\n\", \"bbbbaaaccb\\ncbacbaabb\\n\", \"adbddbccdacbaab\\nadcdbddcda\\n\", \"acc\\nbbb\\n\", \"z\\nanan`\\n\", \"adbddbccdacbaaz\\ndacdcbddbb\\n\", \"babbaccabb\\nb\\n\", \"abc\\nbbac\\n\", \"acaccaaadd\\nddabcacbab\\n\", \"aaacaba\\nabababa\\n\", \"abbabaaabaaabbbbabbbbbababababaaaabbabbbbabbbbbabbbbababbaaaaabbbabbbbabbbbbbabaabababaabbbabababbaa\\nabbbbaaabaaabbbbabbbabababababaaaabbabbbbabbbbbabbbbababbaaaaabbaabbbbabbbbbbabaabababaaabbabababbaa\\n\", \"aabbabababbbaabababaababbbbbbabbbbabbbaaaaabbababbbbabbbbbabbbbabbaaaabababababbbbbabbbbaaabaaababba\\nbbaabaabaaaabbabaaaababababaabaabaaaabbaabbbbabbbaabaabaababbaababaaaabababbaabbaaabbbaaaaaaabaabbbb\\n\", \"aaabccadac\\nbabaccbdac\\n\", \"bbbcaabcaa\\ncacbabbbaa\\n\", \"aaabcbadaz\\nacabcaadaa\\n\", \"qwertyz\\npoiuytrewq\\n\", \"aac\\naabb\\n\", \"czaaab\\ndbcaef\\n\", \"aad\\ncaa\\n\", \"adab\\nbob\\n\", \"aaaaaaaaa\\nb\\n\", \"abc\\ndaa\\n\", \"ab\\nc\\n\", \"aa\\nb\\n\", \"z\\nzy\\n\", \"cba\\ndefg\\n\", \"abc\\ndefg\\n\", \"czaaab\\nabcdef\\n\", \"aad\\naac\\n\", \"abad\\nbob\\n\"], \"outputs\": [\"z\\n\", \"abc\\n\", \"bcbcdbdbdd\\n\", \"acabcaaacd\\n\", \"-1\\n\", \"caadccaaaz\\n\", \"-1\\n\", \"abaaabc\\n\", \"aaaabb\\n\", \"ac\\n\", \"-1\\n\", \"-1\\n\", \"aaaaaaaaa\\n\", \"ccc\\n\", \"cbdaabbbcc\\n\", \"aaaz\\n\", \"bbbaabbaba\\n\", \"z\\n\", \"acaccaadad\\n\", \"aaaabb\\n\", \"bccaaabccc\\n\", \"adaddccaabbbbcd\\n\", \"cab\\n\", \"ba\\n\", \"-1\\n\", \"zzzzzzzzzzzz\\n\", \"aa\\n\", \"cba\\n\", \"zaaaaaaaa\\n\", \"ab\\n\", \"aaa\\n\", \"aab\\n\", \"zzzzzzzzzz\\n\", \"abaabbbbaz\\n\", \"ababbaabbb\\n\", \"bbbbccdddd\\n\", \"abaaabaabbbbaabbbbaabababbaabaabababbbaabbbaaabbabbabbbbbbbbaabbbbbabababbbbaaabaaaabbbbbbbbabababbz\\n\", \"aabb\\n\", \"aaccbb\\n\", \"dbbccbddbz\\n\", \"cbacbaabbb\\n\", \"adcddcaaabbbbcd\\n\", \"bca\\n\", \"z\\n\", \"dacdcaddbbaabcz\\n\", \"acb\\n\", \"baaabbbbcc\\n\", \"abc\\n\", \"aaaaaaaaaaaaaaa\\n\", \"caaaaaccdd\\n\", \"ababaca\\n\", \"abbabaaabaaabbbbabbbabababababaaaabbabbbbabbbbbabbbbababbaaaaabbaabbbbabbbbbbabaabababaabbbabababbbb\\n\", \"bbaabaabaaaabbabaaaababababaabaabaaaabbaabbbbabbbaabaabaababbaababaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n\", \"aabcaaaccd\\n\", \"cacbababba\\n\", \"acabcaadaz\\n\", \"qwertyz\\n\", \"ab\\n\", \"abc\\n\", \"abccab\\n\", \"-1\\n\", \"abc\", \"dbbdbdcbcd\", \"acabcaaacd\", \"-1\", \"aaaaccdacz\", \"abaaabd\", \"aaabbb\", \"bc\", \"b\", \"ccb\", \"zaaa\", \"abbaabbabb\", \"y\", \"acaccaaadd\", \"baaaab\", \"bccaaacccc\", \"adaddccaaabbbcd\", \"zzzzzzzzzzzz\", \"cba\", \"bb\", \"aba\", \"zzzzzzzzzz\", \"aabbbbaabz\", \"bbaaabbabb\", \"bbbcccdddd\", \"abbabababbbbbbbbaaaabaaabbbbabababbbbbaabbbbbbbbabbabbaaabbbaabbbababaabaabbababaabbbbaabbbbaabaaabz\", \"dbbcdbdcbz\", \"cbacbaabbb\", \"adcdcaaabbbbcdd\", \"cac\", \"z\", \"dacdcbddbbaaacz\", \"baaabbbbcc\", \"bca\", \"ddacaaaacc\", \"abacaaa\", \"abbbbaaabaaabbbbabbbabababababaaaabbabbbbabbbbbabbbbababbaaaaabbaabbbbabbbbbbabaabababaaabbabababbbb\", \"bbaabaabaaaabbabaaaababababaabaabaaaabbaabbbbabbbaabaabaababbaababaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\", \"bacaaaaccd\", \"cacbbaaabb\", \"acabdaaabz\", \"qertwyz\", \"aac\", \"zaaabc\", \"daa\", \"daab\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\\n\", \"abczaa\\n\", \"aad\\n\", \"daab\\n\"]}", "source": "taco"}
|
Everything got unclear to us in a far away constellation Tau Ceti. Specifically, the Taucetians choose names to their children in a very peculiar manner.
Two young parents abac and bbad think what name to give to their first-born child. They decided that the name will be the permutation of letters of string s. To keep up with the neighbours, they decided to call the baby so that the name was lexicographically strictly larger than the neighbour's son's name t.
On the other hand, they suspect that a name tax will be introduced shortly. According to it, the Taucetians with lexicographically larger names will pay larger taxes. That's the reason abac and bbad want to call the newborn so that the name was lexicographically strictly larger than name t and lexicographically minimum at that.
The lexicographical order of strings is the order we are all used to, the "dictionary" order. Such comparison is used in all modern programming languages to compare strings. Formally, a string p of length n is lexicographically less than string q of length m, if one of the two statements is correct:
* n < m, and p is the beginning (prefix) of string q (for example, "aba" is less than string "abaa"),
* p1 = q1, p2 = q2, ..., pk - 1 = qk - 1, pk < qk for some k (1 ≤ k ≤ min(n, m)), here characters in strings are numbered starting from 1.
Write a program that, given string s and the heighbours' child's name t determines the string that is the result of permutation of letters in s. The string should be lexicographically strictly more than t and also, lexicographically minimum.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000), where |s| is its length. The second line contains a non-empty string t (1 ≤ |t| ≤ 5000), where |t| is its length. Both strings consist of lowercase Latin letters.
Output
Print the sought name or -1 if it doesn't exist.
Examples
Input
aad
aac
Output
aad
Input
abad
bob
Output
daab
Input
abc
defg
Output
-1
Input
czaaab
abcdef
Output
abczaa
Note
In the first sample the given string s is the sought one, consequently, we do not need to change the letter order there.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 1000000000\\n2 1\\n\", \"2 1\\n2 1\\n\", \"4 1\\n4 1\\n2 4\\n3 1\\n\", \"3 1000000000\\n3 2\\n2 1\\n\", \"4 1\\n1 3\\n1 4\\n2 1\\n\", \"4 1\\n2 3\\n1 4\\n2 1\\n\", \"6 1\\n2 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"6 1\\n2 1\\n2 3\\n2 5\\n2 4\\n5 6\\n\", \"4 5\\n1 2\\n1 3\\n1 4\\n\", \"6 2\\n2 1\\n4 3\\n4 5\\n1 4\\n5 6\\n\", \"6 0\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"6 2\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"4 5\\n1 2\\n1 3\\n2 4\\n\", \"2 3\\n2 1\\n\", \"4 6\\n4 2\\n2 1\\n3 1\\n\", \"5 8\\n1 2\\n2 3\\n3 4\\n3 5\\n\", \"6 1\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"6 1\\n2 1\\n4 3\\n4 5\\n1 4\\n5 6\\n\", \"4 1\\n4 3\\n1 4\\n2 1\\n\", \"6 1\\n2 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n4 1\\n2 4\\n3 1\\n\", \"4 0\\n1 3\\n1 4\\n2 1\\n\", \"6 1\\n3 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"5 5\\n1 2\\n2 3\\n3 4\\n2 5\\n\", \"4 0\\n4 2\\n2 4\\n3 1\\n\", \"2 2\\n2 1\\n\", \"4 2\\n4 1\\n2 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n1 4\\n5 6\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n1 2\\n1 4\\n2 1\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"4 5\\n1 2\\n2 3\\n2 4\\n\", \"4 2\\n4 1\\n2 1\\n3 1\\n\", \"6 1\\n6 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"6 1\\n2 1\\n4 3\\n4 6\\n1 4\\n5 6\\n\", \"4 2\\n4 3\\n1 4\\n2 1\\n\", \"6 0\\n2 1\\n4 1\\n2 5\\n1 4\\n5 6\\n\", \"4 0\\n1 3\\n1 3\\n2 1\\n\", \"5 3\\n1 2\\n2 3\\n3 4\\n2 5\\n\", \"6 3\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"4 0\\n4 4\\n2 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n1 6\\n1 4\\n5 6\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 1\\n5 6\\n\", \"4 2\\n4 2\\n2 1\\n3 1\\n\", \"6 0\\n2 1\\n4 1\\n2 3\\n1 4\\n5 6\\n\", \"4 3\\n4 2\\n2 1\\n3 1\\n\", \"6 0\\n2 1\\n4 1\\n2 6\\n1 4\\n5 6\\n\", \"2 0\\n2 1\\n\", \"4 3\\n1 2\\n1 3\\n2 4\\n\", \"6 1\\n2 1\\n6 3\\n2 5\\n1 4\\n5 6\\n\", \"4 5\\n1 2\\n2 3\\n1 4\\n\", \"6 2\\n3 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"4 5\\n1 4\\n1 3\\n2 4\\n\", \"4 0\\n4 2\\n2 1\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n1 4\\n5 1\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n4 6\\n\", \"4 0\\n1 2\\n1 3\\n2 1\\n\", \"4 5\\n4 2\\n2 1\\n3 1\\n\", \"6 2\\n3 1\\n2 3\\n2 5\\n2 4\\n5 6\\n\", \"6 2\\n2 1\\n4 3\\n2 6\\n1 4\\n5 1\\n\", \"6 0\\n4 1\\n4 3\\n4 5\\n2 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n3 6\\n\", \"6 0\\n4 1\\n4 3\\n4 5\\n4 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 3\\n1 6\\n\", \"6 0\\n2 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n4 1\\n1 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n2 4\\n5 6\\n\", \"6 1\\n2 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"4 3\\n1 2\\n1 3\\n1 4\\n\", \"5 5\\n1 2\\n2 3\\n3 4\\n3 5\\n\"], \"outputs\": [\"1000000000.0000000000\\n\", \"1.0000000000\\n\", \"1.0000000000\\n\", \"1000000000.0000000000\\n\", \"0.6666666667\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.5000000000\\n\", \"3.3333333333\\n\", \"1.3333333333\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"5.0000000000\\n\", \"3.0000000000\\n\", \"6.0000000000\\n\", \"5.3333333333\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"3.3333333333\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"2.0000000000\\n\", \"1.3333333333\\n\", \"0.5000000000\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"3.3333333333\\n\", \"1.3333333333\\n\", \"0.6666666667\\n\", \"0.6666666667\\n\", \"2.0000000000\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"3.0000000000\\n\", \"0.0000000000\\n\", \"1.3333333333\\n\", \"0.6666666667\\n\", \"2.0000000000\\n\", \"0.0000000000\\n\", \"3.0000000000\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"3.0000000000\\n\", \"1.0000000000\\n\", \"5.0000000000\\n\", \"1.3333333333\\n\", \"5.0000000000\\n\", \"0.0000000000\\n\", \"1.0000000000\\n\", \"0.5000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"5.0000000000\\n\", \"1.3333333333\\n\", \"1.3333333333\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"1.3333333333\\n\", \"0.5000000000\\n\", \"2.0000000000\\n\", \"3.3333333333\\n\"]}", "source": "taco"}
|
You are given a tree (an undirected connected graph without cycles) and an integer s.
Vanya wants to put weights on all edges of the tree so that all weights are non-negative real numbers and their sum is s. At the same time, he wants to make the diameter of the tree as small as possible.
Let's define the diameter of a weighed tree as the maximum sum of the weights of the edges lying on the path between two some vertices of the tree. In other words, the diameter of a weighed tree is the length of the longest simple path in the tree, where length of a path is equal to the sum of weights over all edges in the path.
Find the minimum possible diameter that Vanya can get.
Input
The first line contains two integer numbers n and s (2 ≤ n ≤ 10^5, 1 ≤ s ≤ 10^9) — the number of vertices in the tree and the sum of edge weights.
Each of the following n−1 lines contains two space-separated integer numbers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) — the indexes of vertices connected by an edge. The edges are undirected.
It is guaranteed that the given edges form a tree.
Output
Print the minimum diameter of the tree that Vanya can get by placing some non-negative real weights on its edges with the sum equal to s.
Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6}.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if \frac {|a-b|} {max(1, b)} ≤ 10^{-6}.
Examples
Input
4 3
1 2
1 3
1 4
Output
2.000000000000000000
Input
6 1
2 1
2 3
2 5
5 4
5 6
Output
0.500000000000000000
Input
5 5
1 2
2 3
3 4
3 5
Output
3.333333333333333333
Note
In the first example it is necessary to put weights like this:
<image>
It is easy to see that the diameter of this tree is 2. It can be proved that it is the minimum possible diameter.
In the second example it is necessary to put weights like this:
<image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [[5], [12], [13], [16], [17], [20], [9001], [9004], [9005], [9008], [90001], [90002], [90004], [90005], [90009], [900001], [900004], [900005], [9000001], [9000004], [90000001], [90000004], [900000012], [9000000041]], \"outputs\": [[[[3, 1]]], [[[4, 1]]], [[[7, 3]]], [[[4, 0]]], [[[9, 4]]], [[[6, 2]]], [[[4501, 2250]]], [[[2252, 1125]]], [[[4503, 2251], [903, 449]]], [[[1128, 562]]], [[[45001, 22500]]], [[]], [[[22502, 11250]]], [[[45003, 22501], [9003, 4499], [981, 467], [309, 37]]], [[[45005, 22502], [15003, 7500], [5005, 2498], [653, 290], [397, 130], [315, 48]]], [[[450001, 225000]]], [[[225002, 112500], [32150, 16068]]], [[[450003, 225001], [90003, 44999]]], [[[4500001, 2250000], [73801, 36870]]], [[[2250002, 1125000], [173090, 86532], [132370, 66168], [10402, 4980]]], [[[45000001, 22500000], [6428575, 3214284], [3461545, 1730766], [494551, 247230]]], [[[22500002, 11250000], [252898, 126360], [93602, 46560], [22498, 10200]]], [[[225000004, 112500001], [75000004, 37499999], [3358276, 1679071], [1119604, 559601]]], [[[4500000021, 2250000010], [155172429, 77586200]]]]}", "source": "taco"}
|
In mathematics, a [Diophantine equation](https://en.wikipedia.org/wiki/Diophantine_equation) is a polynomial equation, usually with two or more unknowns, such that only the integer solutions are sought or studied.
In this kata we want to find all integers `x, y` (`x >= 0, y >= 0`) solutions of a diophantine equation of the form:
#### x^(2) - 4 \* y^(2) = n
(where the unknowns are `x` and `y`, and `n` is a given positive number)
in decreasing order of the positive xi.
If there is no solution return `[]` or `"[]" or ""`. (See "RUN SAMPLE TESTS" for examples of returns).
## Examples:
```
solEquaStr(90005) --> "[[45003, 22501], [9003, 4499], [981, 467], [309, 37]]"
solEquaStr(90002) --> "[]"
```
## Hint:
x^(2) - 4 \* y^(2) = (x - 2\*y) \* (x + 2\*y)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n5 2\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n3 5\\n7 1\\n1\", \"2\\n5 2\\n3 3\\n7 1\\n1\", \"2\\n6 2\\n1 3\\n7 1\\n2\", \"2\\n6 0\\n1 3\\n7 0\\n1\", \"2\\n5 2\\n3 3\\n7 0\\n1\", \"2\\n5 2\\n1 3\\n7 0\\n1\", \"2\\n6 2\\n1 3\\n7 0\\n1\", \"2\\n6 2\\n1 3\\n7 1\\n1\", \"2\\n6 2\\n1 0\\n7 1\\n2\", \"2\\n6 2\\n1 0\\n8 1\\n2\", \"2\\n4 2\\n1 0\\n8 1\\n2\", \"2\\n7 2\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n3 7\\n7 1\\n1\", \"2\\n5 2\\n3 3\\n6 0\\n1\", \"2\\n5 2\\n1 3\\n7 1\\n1\", \"2\\n3 2\\n1 3\\n7 1\\n1\", \"2\\n6 0\\n1 3\\n7 1\\n2\", \"2\\n4 0\\n1 0\\n8 2\\n2\", \"2\\n7 1\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n4 7\\n7 1\\n1\", \"2\\n5 2\\n1 3\\n8 1\\n1\", \"2\\n10 0\\n1 3\\n7 0\\n1\", \"2\\n3 2\\n1 4\\n7 1\\n1\", \"2\\n6 0\\n1 5\\n7 1\\n2\", \"2\\n4 0\\n1 0\\n8 0\\n2\", \"2\\n2 1\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n4 10\\n7 1\\n1\", \"2\\n10 0\\n1 3\\n7 0\\n2\", \"2\\n3 2\\n1 4\\n13 1\\n1\", \"2\\n5 0\\n1 5\\n7 1\\n2\", \"2\\n8 0\\n1 0\\n8 0\\n2\", \"2\\n4 1\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n4 0\\n7 1\\n1\", \"2\\n4 0\\n1 3\\n7 0\\n2\", \"2\\n3 2\\n1 4\\n25 1\\n1\", \"2\\n5 0\\n1 2\\n7 1\\n2\", \"2\\n8 0\\n2 0\\n8 0\\n2\", \"2\\n8 1\\n3 5\\n5 1\\n1\", \"2\\n5 2\\n4 0\\n7 0\\n1\", \"2\\n4 0\\n1 3\\n14 0\\n2\", \"2\\n2 2\\n1 4\\n25 1\\n1\", \"2\\n5 0\\n1 2\\n0 1\\n2\", \"2\\n8 0\\n2 0\\n16 0\\n2\", \"2\\n8 1\\n3 5\\n1 1\\n1\", \"2\\n5 2\\n4 0\\n11 0\\n1\", \"2\\n4 1\\n1 3\\n14 0\\n2\", \"2\\n6 0\\n2 0\\n16 0\\n2\", \"2\\n8 1\\n3 3\\n1 1\\n1\", \"2\\n5 2\\n2 0\\n11 0\\n1\", \"2\\n0 1\\n1 3\\n14 0\\n2\", \"2\\n8 1\\n3 4\\n1 1\\n1\", \"2\\n5 1\\n2 0\\n11 0\\n1\", \"2\\n0 2\\n1 3\\n14 0\\n2\", \"2\\n4 1\\n3 4\\n1 1\\n1\", \"2\\n5 1\\n2 0\\n22 0\\n1\", \"2\\n0 2\\n1 3\\n11 0\\n2\", \"2\\n7 1\\n3 4\\n1 1\\n1\", \"2\\n0 2\\n1 3\\n11 -1\\n2\", \"2\\n1 1\\n3 4\\n1 1\\n1\", \"2\\n0 2\\n0 3\\n11 -1\\n2\", \"2\\n0 1\\n3 4\\n1 1\\n1\", \"2\\n0 2\\n0 3\\n11 -2\\n2\", \"2\\n0 1\\n3 4\\n2 1\\n1\", \"2\\n1 1\\n3 4\\n2 1\\n1\", \"2\\n5 2\\n3 4\\n5 1\\n1\", \"2\\n6 2\\n3 5\\n7 1\\n1\", \"2\\n5 2\\n3 3\\n7 0\\n0\", \"2\\n5 2\\n0 3\\n7 0\\n1\", \"2\\n6 2\\n1 3\\n1 0\\n1\", \"2\\n6 2\\n1 6\\n7 1\\n1\", \"2\\n6 2\\n1 3\\n7 1\\n0\", \"2\\n11 2\\n1 0\\n7 1\\n2\", \"2\\n3 2\\n1 0\\n8 1\\n2\", \"2\\n4 2\\n2 0\\n8 1\\n2\", \"2\\n7 2\\n6 5\\n5 1\\n1\", \"2\\n8 1\\n3 3\\n6 0\\n1\", \"2\\n5 2\\n1 3\\n13 1\\n1\", \"2\\n6 0\\n1 1\\n7 0\\n1\", \"2\\n3 2\\n1 3\\n7 1\\n2\", \"2\\n4 0\\n1 0\\n8 2\\n3\", \"2\\n7 1\\n3 5\\n9 1\\n1\", \"2\\n5 2\\n8 7\\n7 1\\n1\", \"2\\n5 2\\n0 3\\n8 1\\n1\", \"2\\n10 0\\n0 3\\n7 0\\n2\", \"2\\n3 2\\n1 4\\n7 1\\n2\", \"2\\n3 0\\n1 5\\n7 1\\n2\", \"2\\n1 0\\n1 0\\n8 0\\n2\", \"2\\n2 1\\n3 5\\n5 1\\n2\", \"2\\n5 2\\n3 10\\n7 1\\n1\", \"2\\n10 0\\n1 3\\n7 0\\n4\", \"2\\n3 2\\n1 4\\n23 1\\n1\", \"2\\n5 0\\n1 1\\n7 1\\n2\", \"2\\n8 0\\n1 0\\n8 1\\n2\", \"2\\n4 0\\n3 5\\n5 1\\n1\", \"2\\n4 1\\n1 3\\n7 0\\n2\", \"2\\n5 0\\n1 2\\n7 1\\n4\", \"2\\n8 0\\n2 0\\n8 0\\n4\", \"2\\n8 1\\n2 5\\n5 1\\n1\", \"2\\n5 2\\n4 -1\\n7 0\\n1\", \"2\\n2 0\\n1 3\\n14 0\\n2\", \"2\\n5 2\\n3 5\\n5 1\\n1\"], \"outputs\": [\"Mom\\nChef\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nMom\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nMom\\n\", \"Mom\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nMom\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nMom\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nMom\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Chef\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nChef\\n\", \"Chef\\nMom\\n\", \"Mom\\nChef\\n\", \"Chef\\nChef\\n\", \"Mom\\nMom\\n\", \"Mom\\nChef\"]}", "source": "taco"}
|
Read problems statements in Mandarin Chinese and Russian.
Today is Chef's birthday. His mom gifted him a truly lovable gift, a permutation of first N positive integers.
She placed the permutation on a very long table in front of Chef and left it for him to play with it. But as there was a lot of people coming and wishing him. It was interfering with his game which made him very angry and he banged the table very hard due to which K numbers from the permutation fell down and went missing.
Seeing her son's gift being spoilt, his mom became very sad. Chef didn't want his mom to be sad as he loves her the most. So to make her happy, he decided to play a game with her with the remaining N - K numbers on the table. Chef wants his mom to win all the games.
Chef and his mom play alternatively and optimally. In Xth move, a player can choose some numbers out of all the numbers available on the table such that chosen numbers sum up to X. After the move, Chosen numbers are placed back on the table.The player who is not able to make a move loses.
Now, Chef has to decide who should move first so that his Mom wins the game.
As Chef is a small child, he needs your help to decide who should move first. Please help him, he has promised to share his birthday cake with you :)
------ Input ------
First Line of input contains a single integer T denoting the number of test cases.
First line of each test case contains two space separated integers N and K denoting the size of
permutation and number of numbers fall down from the table.
Next line of each test case contains K space separated integers denoting the values of missing numbers.
------ Output ------
For each test case, print "Chef" if chef should move first otherwise print "Mom" (without quotes).
------ Constraints ------
1 ≤ T ≤ 10^{5}, 1 ≤ N ≤ 10^{9}
0 ≤ K ≤ min(10^{5}, N)
All K numbers are distinct.
Value of each of K number belongs to [1,N].
Sum of K over all the test cases does not exceed 5*10^{5}.
------ Scoring ------
Subtask 1 (13 pts): 1 ≤ T ≤ 100, 1 ≤ N ≤ 10^{2}, 1 ≤ K < N.
Subtask 2 (17 pts): 1 ≤ T ≤ 100, 1 ≤ N ≤ 10^{5}, K = 0.
Subtask 3 (70 pts): Original Constraints.
----- Sample Input 1 ------
2
5 2
3 5
5 1
1
----- Sample Output 1 ------
Mom
Chef
----- explanation 1 ------
For test case 1.
Mom can choose {1} to make 1.
Chef can choose {2} to make 2.
Mom can choose {1,2} to make 3.
Chef can choose {4} to make 4.
Mom can choose {1,4} to make 5.
Chef can choose {2,4} to make 6.
Mom can choose {1,2,4} to make 7.
Chef cannot make 8 out of the numbers on the table.
So,Chef loses and Mom wins.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"1\\naabaababb`bbbbbbbbabbbab`bb`babccbbbab`bba\\n\", \"1\\nabb`babcbdbbababbababbbabbbbbbbb`bbabaabaa\\n\", \"1\\nabbabcbbbbcbababbabaabbabbbbaabbabbabaabba\\n\", \"1\\naabaababb`bbabcbbbabbbababb`babcbbbbababaa\\n\", \"1\\nabbaabaababbbabbbaabbbababbabacabbabacabba\\n\", \"1\\naababbbabbbbababbababbaabbbbaabbabbabaabba\\n\", \"1\\naabaababb`baabbbbbababacabbababcbbabababba\\n\", \"1\\naabaababb`bbbbbbbbabbbab`bbacbbbcbbbab`aba\\n\", \"1\\naabaababb`bbabbbababbaabbbbababccb`babbbba\\n\", \"1\\nabb`b`bbbccbababbababbbabbbbbbbb`bbaaaaaaa\\n\", \"1\\nabbbbbbbbbcb`babbababbaabbbbaabbaabacaabba\\n\", \"1\\naabaababb`bbbbbbbbababacabbacabbdbbbbb`bba\\n\", \"4\\nd\\naaabbacaa\\nabbb\\naababb\\n\", \"1\\nabbabbcccbcb`babbababbaabbbbaabbabbabaabba\\n\", \"1\\naabaabaab_baabbbbbabababaabababcbbbbababba\\n\", \"1\\nabbaababaabbaabbbbabbbababbacabbbbbbababba\\n\", \"1\\nabbbbaabbbbaababbababbbabbbbaabbabbbbabbba\\n\", \"1\\nabbacabbbbcbababbbbababababbaabbabbabaabba\\n\", \"1\\nabb`b`bbbccbababbabaabbabbbcbabb`bbabaabba\\n\", \"1\\naabaababb`bbbbbbbbabbbab`bb`babccbabbb`bba\\n\", \"1\\nabb`babcbdbbabababbabbbabbbbbbbb`bbabaabaa\\n\", \"1\\naabababbbbcbab`bbababbbabbbcbabb`bbabaabaa\\n\", \"1\\nabbaabaababbb`bbbaabbbababbabacabbabacabba\\n\", \"1\\naababbbabbbbababbababbaabcbbaabbabbabaabba\\n\", \"1\\nabbabababbcbababbacabababbbbbaab`bbabaabaa\\n\", \"1\\naabaababb`bbbbbbbb`bbbab`bbacbbbcbbbab`aba\\n\", \"1\\naabaababb`bbabbbababbaabbcbababccb`babbbba\\n\", \"1\\nabbbbbbbbbcb`babb`babbaabbbbaabbaabacaabba\\n\", \"1\\naabaababb`bbbbbbbbababacabbacabbdbbbab`bba\\n\", \"4\\nc\\naaabbacaa\\nabbb\\naababb\\n\", \"1\\nabbaababbabbaabbbbaabbababbab`bcbcccbbabba\\n\", \"1\\naabaabaab`baabbbbbabababaabababcbbbbababba\\n\", \"1\\nabbbbaabbbbaababbababbbabbbbaabbabbbbababa\\n\", \"1\\nabb`b`bbbccbababbabaabbbbbbcbabb`bbabaabba\\n\", \"1\\naababbbabbbbababbababbaabcbbaabb`bbabaabba\\n\", \"1\\nabbabababbcbababbacacababbbbbaab`bbabaabaa\\n\", \"1\\naabaababb`bbabbbababbaaabcbababccb`babbbba\\n\", \"1\\nabbbbbbbbbcb`babb`babbaabcbbaabbaabacaabba\\n\", \"1\\naabaababb`bbbabbbbababacabbacabbdbbbab`bba\\n\", \"1\\nabababbbbabbaabbbbabbbababbabaabbbbaabbbba\\n\", \"1\\naababbbabbbbababbababbaabcbbaaab`bbabaabba\\n\", \"1\\naabaababb`baabbbbbabacacabbababcbbabababba\\n\", \"1\\nabbbbbbbbbcb`babb`b`bbaabcbbaabbaabacaabba\\n\", \"1\\naa`aababb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"1\\nabbbbaabbbbaababbababbbabbbbaabbaabbbababa\\n\", \"1\\naababbbabbbbababbababbaabcbbaabb`bbabbabba\\n\", \"1\\nabbbbbbbbbcb`babb`b`bbaabcbbaabbaaaacaabba\\n\", \"1\\nabbbbabbbdbbacabbacabababbbbabbb`bbabaa`aa\\n\", \"1\\nabababbbaabbaabbbbabbbababbabaabbbbaabbbba\\n\", \"1\\nabbbbbbbbbcb`babb`b`bbbabcbbaabbaaaacaabba\\n\", \"1\\nabbbbabbbdbbacabbacabababbbbabbb`bbabaaaaa\\n\", \"1\\nabababbbaabbaabbbbabbbab`bbabaabbbbaabbbba\\n\", \"1\\nabbaacaaaabbaabbcbabbb`b`bbab`bcbbbbbbbbba\\n\", \"1\\naaaaababb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"1\\nabbbbabbbdbbacabbacabababbbbabbb`bb`baaaaa\\n\", \"1\\naaaaab`bb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"1\\naaaaab`bb`bbbabbbbababacabbacabbebbbabbbba\\n\", \"1\\naaaaab`bb`bbbabbbbababacabbacabbebbaabbbba\\n\", \"1\\naabaab`bb`bbbabbbbababacabbacabbebbaabbbba\\n\", \"1\\nabbabababbabab`bbababbbabbbbabbbabaabaabba\\n\", \"1\\naaaaaaaaaaaaaaaaaaaabbbbbbcbbbbbbbbbbbbbab\\n\", \"4\\nb\\naabbaabaa\\nabbb\\nabbaab\\n\", \"1\\nabbaabaababbbabbbbabbbababbababbbbabababba\\n\", \"1\\nabbabababbbbababbababbbaabbbaabbabbbbaabba\\n\", \"1\\nabbaababbabbaabbbbabbbababbaaabbbbabababba\\n\", \"1\\nabbaabbbbabaaabbbbabbbababbababbbbbbababba\\n\", \"1\\nabbaababbabbaabbbbabbbababbabaabbbbbababba\\n\", \"1\\nabbababbbbabababbababbbabbbbaabbabbabaabba\\n\", \"1\\nabbaababbabbaabbbbabbbababaababcbbbbababba\\n\", \"1\\nabbababbbbcbababbababbbabbbbaabbabb`baabba\\n\", \"1\\nabbababbbbcbababbababbbabbbbbabbabbacaabba\\n\", \"1\\nabb`babbbccbababbababbbabbbbbabb`bbabaabba\\n\", \"1\\naabaababb`bbbbbbbbabbbabaabababccbbbab`bba\\n\", \"1\\nabb`babbbccbababbbbabbbabbbbbbbb`baabaabaa\\n\", \"1\\nabb`babbbcbbab`bbababbbabbbbbbbb`bbabaabaa\\n\", \"1\\nabbabababbabababbababbbabbbbabbbababbaabba\\n\", \"4\\nb\\naabbaabaa\\nabbb\\nabbabb\\n\", \"1\\naababababbbbababbababbbabbbbaabbabbacaabba\\n\", \"1\\nabbababbbbbaababbababbbabbbbaabbabbabbabba\\n\", \"1\\nabbaababbabbabbbbbabbbababbacabcbbbbababba\\n\", \"4\\nb\\naabbbabaa\\nabbb\\nabbaab\\n\"], \"outputs\": [\"b\\naabbbabaa\\nbbbb\\nbbbaab\\n\", \"baaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbab\\n\", \"abbabababbabababbababbbabbbbabbbabaabaabba\\n\", \"abbabababbabababbababbbabbbbabbbabaabaabba\\n\", \"b\\naabbbabaa\\nbbbb\\nbbbaab\\n\", \"baaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbab\\n\", \"abbabababbbbababbababbbabbbbabbbabaabaabba\\n\", \"abbabababbbbababbababbbabbbbaabbabbabaabba\\n\", \"abbaababbabbaabbbbabbbababbababbbbabababba\\n\", \"abbaababbabaaabbbbabbbababbababbbbbbababba\\n\", \"abbaababbabbaabbbbabbbababbababbbbbbababba\\n\", \"abbababbbbbbababbababbbabbbbaabbabbabaabba\\n\", \"abbaababbabbaabbbbabbbababbababcbbbbababba\\n\", \"abbababbbbcbababbababbbabbbbaabbabbabaabba\\n\", \"abbababbbbcbababbababbbabbbbbabbabbabaabba\\n\", \"abbababbbbcbababbababbbabbbbbabb`bbabaabba\\n\", \"abbaababb`bbabbbbbabbbababbababcbbbbababba\\n\", \"abbaababb`bbabbbbbabbbababbababcbbbbab`bba\\n\", \"abbaababb`bbabbbbbabbbababbababccbbbab`bba\\n\", \"aabaababb`bbbbbbbbabbbababbababccbbbab`bba\\n\", \"abb`babbbccbababbababbbabbbbbbbb`bbabaabaa\\n\", \"aabaababb`bbbbbbbbabbbababbababbcbbbab`bba\\n\", \"abbaabaababbbabbbbabbbababbabababbabababba\\n\", \"a\\naabbbabaa\\nbbbb\\nbbbaab\\n\", \"b\\naabbbabaa\\nbbbb\\nbbbabb\\n\", \"aababababbbbababbababbbabbbbaabbabbabaabba\\n\", \"abbababbbbbbababbababbbabbbbaaababbabaabba\\n\", \"abbabbabbabbaabbbbabbbababbabaabbbbbababba\\n\", \"abbaababbabbaabbbbabbbababbababcbbbbbbabba\\n\", \"abbaababbabbabbbbbabbbababbababcbbbbababba\\n\", \"abbababbbbcbababbacabbbabbbbbabb`bbabaabba\\n\", \"aabaababb`bbabbbbbabbbababbababcbbbbababba\\n\", \"aabaababb`bbbbbbbbabbbababbacabbcbbbab`bba\\n\", \"aabaababb`bbbbbbbbabbaabbbbababccbbbab`bba\\n\", \"abb`babbbcbbababbababbbabbbbbbbb`bbabaabaa\\n\", \"abbacababbabababbababbbabbbbabbbabaabaabba\\n\", \"a\\naabababaa\\nbbbb\\nbbbaab\\n\", \"b\\naabbbacaa\\nbbbb\\nbbbabb\\n\", \"abbaababbabbaabbbbabbbababbababbbbabababaa\\n\", \"abbabbabbabbaabbbbabbbababbbbaabbbbbababba\\n\", \"abbaababbabbaabbbbaabbababbababcbbbbbbabba\\n\", \"bbbababbbbcbababbababbbabbbbbabbabbabaabbb\\n\", \"abbababbbbcbababbacabbbabbbbbabb`bbababbba\\n\", \"aabaababb`bbabbbbbababababbababcbbbbababba\\n\", \"abb`babbbcbbacabbababbbabbbbbbbb`bbabaabaa\\n\", \"aabaababb`bbbbbbbbabbaabbbbababccb`babbbba\\n\", \"aaaaababb`bbbbbbbbabbbababbababccbbbab`bba\\n\", \"c\\naabbbacaa\\nbbbb\\nbbbabb\\n\", \"abbaababbabbaabbbbaabbababbab`bcbbbbbbabba\\n\", \"bbbababbbbcb`babbababbbabbbbbabbabbabaabbb\\n\", \"abbbababb`bbabbbbbabbbacabbababcbbbbababba\\n\", \"aabaababb`bbabbbbbababababbacabcbbbbababba\\n\", \"abb`babbbdbbacabbababbbabbbbbbbb`bbabaabaa\\n\", \"babaababb`bbbbbbbbabbaabbbbababccb`babbbbb\\n\", \"aaaaababb`bbcbbbbbabbbababbababccbbbab`bba\\n\", \"c\\naacabbbaa\\nbbbb\\nbbbabb\\n\", \"abbabbbbbbcb`babbababbaabbbbaabbabbabaabba\\n\", \"aabaabaab`bbabbbbbababababbacabcbbbbababba\\n\", \"abb`babbbdbbaaabbabcbbbabbbbbbbb`bbabaabaa\\n\", \"babaababb`bbbbbbcbabbaabbbbababccb`babbbbb\\n\", \"aaaaababb`bbcbbbbbaabbababbababccbbbbb`bba\\n\", \"abbaababbabbaabcbbaabbababbab`bcbbbbbbabba\\n\", \"aabaabaab_bbabbbbbababababbacabcbbbbababba\\n\", \"aabaababb`bbbbbbbbabbbcbabbaaabbdbbbab`bba\\n\", \"baaaaaaaaaaa`aaaaaaabbbbbbbbbbbbbbbbbbbbab\\n\", \"c\\naabbbabaa\\nbbbb\\nbbbaab\\n\", \"abbabababbbbacabbababbbabbbbabbbabaabaabba\\n\", \"abbaababbbbbaabbababbbababbababbbbabababba\\n\", \"abbaababbabbaabbbbabbaababbababbbbbbababba\\n\", \"abbbababbabbaabbbbabbbababbabaabbbbbababba\\n\", \"bbbababbbbbbababbabaabbabbbbaabbabbabaabbb\\n\", \"abbababbbbcbababbbbabbbababbaabbabbabaabba\\n\", \"abbababbbbcbababbababbbabcbbbabb`bbabaabba\\n\", \"abbaababb`bbabbbbbabbbababbababccbbb`b`bba\\n\", \"abb`babbbccbab`bbababbbabbbbbbbb`bbabaabaa\\n\", \"aabaababb`bbbbbbbbabbbababbababbdbbbab`bba\\n\", \"abbababbbbbbababbbbabbbabbbbaaababbabaabba\\n\", \"abbaababbabbaabbbbabbbababbababcbbbbcbabba\\n\", \"bbbaaabbbbcbababbacabbbabbbbbabb`bbabaabbb\\n\", \"aabaababb`bbabcbbbabbbababbababcbbbbababba\\n\", \"aabaababb`bbbbbbbbabbaabbbbababccbcbab`bba\\n\", \"abbaabaababbbabbbbabbbababbabababbabacabba\\n\", \"abbaababbabbaabbbbaabbababbababbbbabababaa\\n\", \"bbbababbbbcbababbababbbaabbbbabbabbabaabbb\\n\", \"aabaababb`baabbbbbababababbababcbbbbababba\\n\", \"abb`babbbcbbacabb`babbbabbbbbbbb`bbabaabaa\\n\", \"aabaababb`bbbbbbababbaabbbbababccb`babbbba\\n\", \"aaaaababb`bbbbbbbbabbbababbababccbbb`b`bba\\n\", \"d\\naabbbacaa\\nbbbb\\nbbbabb\\n\", \"abbaababaabbaabbbbaabbababbab`bcbbbbbbbbba\\n\", \"abbababbbbcbacabbababababbbbbabb`bbabaabaa\\n\", \"abb`babbbdbbacabbacabbbabbbbbbbb`bbabaabaa\\n\", \"c\\naabbbacaa\\nbbbb\\nbababb\\n\", \"abbabbbcbbcb`babbababbaabbbbaabbabbabaabba\\n\", \"abb`babbbdbbaaabbabcbbaabbbbbbbb`bbabbabaa\\n\", \"abbaababbaabaabcbbaabbababbab`bcbbbbbbabba\\n\", \"aabaabaab_bbabbbbbabababaabacabcbbbbababba\\n\", \"abbaab`bbbbbaabbababbbababbababbbbabababba\\n\", \"abbaababaabbaabbbbabbaababbababbbbbbababba\\n\", \"abbababbbbbaababbababbbabbbbaabbabbababbba\\n\", \"bbbababbbbbbab`bbabaabbabbbbaabbabbabaabbb\\n\", \"abbaababbabbaabbababbbabbbbababcbbbbababba\\n\", \"abbababbbbcbbbabbababbbabcbbbabb`bbabaabba\\n\", \"abb`b`bbbccbababbababbbabbbbbabb`bbabaabba\\n\", \"abb`babbbccbab`bb`babbbabbbbbbbb`bbabaabaa\\n\", \"aabaababb`bbbbbbbbabbbababbababbdbcbab`bba\\n\", \"abbabcbbbbcbababbababbbabbbbaabbabbabaabba\\n\", \"aabaababb`bbabcbbbabbbababbababcbbbbababaa\\n\", \"abbaabaababbbabbbbabbbababbabacabbabacabba\\n\", \"aababababbbbababbababbaabbbbaabbabbabaabba\\n\", \"aabaababb`baabbbbbababababbababcbbabababba\\n\", \"aba`babbbcbbbcabb`babbbabbbbbbbb`bbabaabaa\\n\", \"abbbbab`bccbababbbbaabbababbbbbb`bbabaabaa\\n\", \"aaaaaaabb`bbbbbbbbabbbababbababccbbb`b`bba\\n\", \"e\\naabbbacaa\\nbbbb\\nbbbabb\\n\", \"abbaacabaabbaabbbbaabbababbab`bcbbbbbbbbba\\n\", \"aabaababb`bbbbbbbbabbbacabbacabbdbbbab`bba\\n\", \"d\\naabbbacaa\\nbbbb\\nbababb\\n\", \"abbabbccbbcb`babbababbaabbbbaabbabbabaabba\\n\", \"abbaababbaacaabcbbaabbababbab`bcbbbbbbabba\\n\", \"aabaabaab_bbabbbbbabababaabababcbbbbababba\\n\", \"abbaab`bbbbbaabbababbbacabbababbbbabababba\\n\", \"abbaababaabbaabbbbabbaababbacabbbbbbababba\\n\", \"abbbbabbbbbaababbababbbabbbbaabbabbababbba\\n\", \"abbababbbbcbababbbbababababbaabbabbabaabba\\n\", \"abb`b`bbbccbababbabaabbabbbbbabb`bbabaabba\\n\", \"aabaababb`bbbbbbbbabbbab`bb`babccbbbab`bba\\n\", \"abb`babcbdbbababbababbbabbbbbbbb`bbabaabaa\\n\", \"abbabcbbbbcbababbabaabbabbbbaabbabbabaabba\\n\", \"aabaababb`bbabcbbbabbbababb`babcbbbbababaa\\n\", \"abbaabaababbbabbbaabbbababbabacabbabacabba\\n\", \"aababbbabbbbababbababbaabbbbaabbabbabaabba\\n\", \"aabaababb`baabbbbbababacabbababcbbabababba\\n\", \"aabaababb`bbbbbbbbabbbab`bbacbbbcbbbab`aba\\n\", \"aabaababb`bbabbbababbaabbbbababccb`babbbba\\n\", \"abb`b`bbbccbababbababbbabbbbbbbb`bbaaaaaaa\\n\", \"abbbbbbbbbcb`babbababbaabbbbaabbaabacaabba\\n\", \"aabaababb`bbbbbbbbababacabbacabbdbbbbb`bba\\n\", \"d\\naaabbacaa\\nbbbb\\nbababb\\n\", \"abbabbcccbcb`babbababbaabbbbaabbabbabaabba\\n\", \"aabaabaab_baabbbbbabababaabababcbbbbababba\\n\", \"abbaababaabbaabbbbabbbababbacabbbbbbababba\\n\", \"abbbbaabbbbaababbababbbabbbbaabbabbbbabbba\\n\", \"abbacabbbbcbababbbbababababbaabbabbabaabba\\n\", \"abb`b`bbbccbababbabaabbabbbcbabb`bbabaabba\\n\", \"aabaababb`bbbbbbbbabbbab`bb`babccbabbb`bba\\n\", \"abb`babcbdbbabababbabbbabbbbbbbb`bbabaabaa\\n\", \"aabababbbbcbab`bbababbbabbbcbabb`bbabaabaa\\n\", \"abbaabaababbb`bbbaabbbababbabacabbabacabba\\n\", \"aababbbabbbbababbababbaabcbbaabbabbabaabba\\n\", \"abbabababbcbababbacabababbbbbaab`bbabaabaa\\n\", \"aabaababb`bbbbbbbb`bbbab`bbacbbbcbbbab`aba\\n\", \"aabaababb`bbabbbababbaabbcbababccb`babbbba\\n\", \"abbbbbbbbbcb`babb`babbaabbbbaabbaabacaabba\\n\", \"aabaababb`bbbbbbbbababacabbacabbdbbbab`bba\\n\", \"c\\naaabbacaa\\nbbbb\\nbababb\\n\", \"abbaababbabbaabbbbaabbababbab`bcbcccbbabba\\n\", \"aabaabaab`baabbbbbabababaabababcbbbbababba\\n\", \"abbbbaabbbbaababbababbbabbbbaabbabbbbababa\\n\", \"abb`b`bbbccbababbabaabbbbbbcbabb`bbabaabba\\n\", \"aababbbabbbbababbababbaabcbbaabb`bbabaabba\\n\", \"abbabababbcbababbacacababbbbbaab`bbabaabaa\\n\", \"aabaababb`bbabbbababbaaabcbababccb`babbbba\\n\", \"abbbbbbbbbcb`babb`babbaabcbbaabbaabacaabba\\n\", \"aabaababb`bbbabbbbababacabbacabbdbbbab`bba\\n\", \"abababbbbabbaabbbbabbbababbabaabbbbaabbbba\\n\", \"aababbbabbbbababbababbaabcbbaaab`bbabaabba\\n\", \"aabaababb`baabbbbbabacacabbababcbbabababba\\n\", \"abbbbbbbbbcb`babb`b`bbaabcbbaabbaabacaabba\\n\", \"aa`aababb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"abbbbaabbbbaababbababbbabbbbaabbaabbbababa\\n\", \"aababbbabbbbababbababbaabcbbaabb`bbabbabba\\n\", \"abbbbbbbbbcb`babb`b`bbaabcbbaabbaaaacaabba\\n\", \"abbbbabbbdbbacabbacabababbbbabbb`bbabaa`aa\\n\", \"abababbbaabbaabbbbabbbababbabaabbbbaabbbba\\n\", \"abbbbbbbbbcb`babb`b`bbbabcbbaabbaaaacaabba\\n\", \"abbbbabbbdbbacabbacabababbbbabbb`bbabaaaaa\\n\", \"abababbbaabbaabbbbabbbab`bbabaabbbbaabbbba\\n\", \"abbaacaaaabbaabbcbabbb`b`bbab`bcbbbbbbbbba\\n\", \"aaaaababb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"abbbbabbbdbbacabbacabababbbbabbb`bb`baaaaa\\n\", \"aaaaab`bb`bbbabbbbababacabbacabbdbbbabbbba\\n\", \"aaaaab`bb`bbbabbbbababacabbacabbebbbabbbba\\n\", \"aaaaab`bb`bbbabbbbababacabbacabbebbaabbbba\\n\", \"aabaab`bb`bbbabbbbababacabbacabbebbaabbbba\\n\", \"abbabababbabab`bbababbbabbbbabbbabaabaabba\\n\", \"baaaaaaaaaaaaaaaaaaabbbbbbcbbbbbbbbbbbbbab\\n\", \"b\\naabbaabaa\\nbbbb\\nbbbaab\\n\", \"abbaabaababbbabbbbabbbababbababbbbabababba\\n\", \"abbabababbbbababbababbbaabbbaabbabbbbaabba\\n\", \"abbaababbabbaabbbbabbbababbaaabbbbabababba\\n\", \"abbaabbbbabaaabbbbabbbababbababbbbbbababba\\n\", \"abbaababbabbaabbbbabbbababbabaabbbbbababba\\n\", \"abbababbbbabababbababbbabbbbaabbabbabaabba\\n\", \"abbaababbabbaabbbbabbbababaababcbbbbababba\\n\", \"abbababbbbcbababbababbbabbbbaabbabb`baabba\\n\", \"abbababbbbcbababbababbbabbbbbabbabbacaabba\\n\", \"abb`babbbccbababbababbbabbbbbabb`bbabaabba\\n\", \"aabaababb`bbbbbbbbabbbabaabababccbbbab`bba\\n\", \"abb`babbbccbababbbbabbbabbbbbbbb`baabaabaa\\n\", \"abb`babbbcbbab`bbababbbabbbbbbbb`bbabaabaa\\n\", \"abbabababbabababbababbbabbbbabbbababbaabba\\n\", \"b\\naabbaabaa\\nbbbb\\nbbbabb\\n\", \"aababababbbbababbababbbabbbbaabbabbacaabba\\n\", \"abbababbbbbaababbababbbabbbbaabbabbabbabba\\n\", \"abbaababbabbabbbbbabbbababbacabcbbbbababba\\n\", \"b\\naabbbabaa\\nbbbb\\nbbbaab\\n\"]}", "source": "taco"}
|
You are given a string $s$ of length $n$ consisting of characters a and/or b.
Let $\operatorname{AB}(s)$ be the number of occurrences of string ab in $s$ as a substring. Analogically, $\operatorname{BA}(s)$ is the number of occurrences of ba in $s$ as a substring.
In one step, you can choose any index $i$ and replace $s_i$ with character a or b.
What is the minimum number of steps you need to make to achieve $\operatorname{AB}(s) = \operatorname{BA}(s)$?
Reminder:
The number of occurrences of string $d$ in $s$ as substring is the number of indices $i$ ($1 \le i \le |s| - |d| + 1$) such that substring $s_i s_{i + 1} \dots s_{i + |d| - 1}$ is equal to $d$. For example, $\operatorname{AB}($aabbbabaa$) = 2$ since there are two indices $i$: $i = 2$ where aabbbabaa and $i = 6$ where aabbbabaa.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). Description of the test cases follows.
The first and only line of each test case contains a single string $s$ ($1 \le |s| \le 100$, where $|s|$ is the length of the string $s$), consisting only of characters a and/or b.
-----Output-----
For each test case, print the resulting string $s$ with $\operatorname{AB}(s) = \operatorname{BA}(s)$ you'll get making the minimum number of steps.
If there are multiple answers, print any of them.
-----Examples-----
Input
4
b
aabbbabaa
abbb
abbaab
Output
b
aabbbabaa
bbbb
abbaaa
-----Note-----
In the first test case, both $\operatorname{AB}(s) = 0$ and $\operatorname{BA}(s) = 0$ (there are no occurrences of ab (ba) in b), so can leave $s$ untouched.
In the second test case, $\operatorname{AB}(s) = 2$ and $\operatorname{BA}(s) = 2$, so you can leave $s$ untouched.
In the third test case, $\operatorname{AB}(s) = 1$ and $\operatorname{BA}(s) = 0$. For example, we can change $s_1$ to b and make both values zero.
In the fourth test case, $\operatorname{AB}(s) = 2$ and $\operatorname{BA}(s) = 1$. For example, we can change $s_6$ to a and make both values equal to $1$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"2\\n5\\n1 2 3 4 5\\n7\\n3 2 4 5 1 6 7\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 2\\n\", \"3\\n3\\n1 2 3\\n4\\n3 1 2 4\\n7\\n6 4 1 7 3 5 2\\n\", \"3\\n6\\n6 2 5 1 4 3\\n6\\n3 5 1 4 2 6\\n2\\n1 2\\n\", \"1\\n2\\n1 2\\n\", \"1\\n7\\n3 2 4 1 7 6 5\\n\", \"1\\n4\\n2 1 3 4\\n\", \"1\\n5\\n1 3 4 2 5\\n\", \"1\\n6\\n3 2 1 6 5 4\\n\", \"1\\n2\\n1 2\\n\", \"1\\n5\\n1 3 4 2 5\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 2\\n\", \"3\\n3\\n1 2 3\\n4\\n3 1 2 4\\n7\\n6 4 1 7 3 5 2\\n\", \"1\\n7\\n3 2 4 1 7 6 5\\n\", \"1\\n4\\n2 1 3 4\\n\", \"1\\n6\\n2 1 3 5 4 6\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 2 4 1 5 7 6\\n6\\n3 2 1 6 5 4\\n\", \"1\\n6\\n3 2 1 6 5 4\\n\", \"1\\n5\\n2 1 3 5 4\\n\", \"3\\n6\\n6 2 5 1 4 3\\n6\\n3 5 1 4 2 6\\n2\\n1 2\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 2\\n\", \"1\\n6\\n2 1 3 5 4 3\\n\", \"1\\n5\\n1 3 4 2 6\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 2 4 1 5 7 6\\n6\\n3 2 1 6 5 1\\n\", \"3\\n6\\n6 2 5 1 4 3\\n6\\n3 5 1 4 3 6\\n2\\n1 2\\n\", \"2\\n5\\n1 2 3 4 5\\n7\\n3 2 4 5 1 6 12\\n\", \"1\\n6\\n2 1 3 5 4 1\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 5 6 2\\n\", \"1\\n3\\n2 1 3 4\\n\", \"4\\n6\\n1 3 3 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 2\\n\", \"1\\n6\\n2 2 3 5 4 1\\n\", \"1\\n5\\n2 3 4 2 6\\n\", \"4\\n6\\n1 4 3 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 2\\n\", \"1\\n6\\n2 3 3 5 4 1\\n\", \"1\\n6\\n2 3 3 5 3 1\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 0\\n\", \"1\\n7\\n3 2 4 1 7 6 8\\n\", \"1\\n4\\n2 1 2 4\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 1 4 1 5 7 6\\n6\\n3 2 1 6 5 4\\n\", \"1\\n6\\n3 2 1 6 10 4\\n\", \"2\\n5\\n1 2 3 4 5\\n7\\n3 2 4 5 1 5 7\\n\", \"1\\n6\\n2 1 3 5 6 1\\n\", \"4\\n6\\n0 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 5 6 2\\n\", \"3\\n6\\n6 2 5 1 4 3\\n6\\n3 10 1 4 3 6\\n2\\n1 2\\n\", \"1\\n6\\n2 2 3 10 4 1\\n\", \"1\\n6\\n2 3 5 5 4 1\\n\", \"1\\n6\\n2 3 5 5 3 1\\n\", \"1\\n7\\n3 2 4 1 7 5 8\\n\", \"5\\n5\\n1 3 1 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 1 4 1 5 7 6\\n6\\n3 2 1 6 5 4\\n\", \"1\\n6\\n2 1 3 5 0 1\\n\", \"3\\n6\\n6 2 5 1 4 3\\n6\\n3 17 1 4 3 6\\n2\\n1 2\\n\", \"1\\n7\\n3 2 4 1 7 5 0\\n\", \"1\\n7\\n3 2 4 1 7 5 1\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 4 4 6 2\\n\", \"1\\n7\\n3 2 4 1 8 6 5\\n\", \"1\\n6\\n2 0 3 5 4 1\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 2 4 1 5 7 6\\n6\\n3 1 1 6 5 4\\n\", \"1\\n6\\n3 2 1 6 8 4\\n\", \"1\\n5\\n2 1 3 6 4\\n\", \"2\\n5\\n1 2 3 4 5\\n7\\n3 2 4 5 1 6 2\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 7 2\\n\", \"1\\n6\\n2 1 3 5 5 3\\n\", \"1\\n6\\n0 1 3 5 4 1\\n\", \"1\\n5\\n1 2 4 2 6\\n\", \"1\\n3\\n2 0 3 4\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 3 4\\n5\\n2 1 3 5 4\\n7\\n3 2 4 1 5 7 6\\n6\\n3 2 1 6 5 2\\n\", \"1\\n6\\n0 2 3 5 4 1\\n\", \"1\\n5\\n2 3 4 2 2\\n\", \"4\\n6\\n1 4 3 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 4 4 6 2\\n\", \"1\\n6\\n2 3 3 3 4 1\\n\", \"1\\n6\\n2 2 3 5 3 1\\n\", \"4\\n6\\n1 5 3 4 2 5\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 3 4 6 0\\n\", \"1\\n7\\n2 2 4 1 7 6 8\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 4 4\\n5\\n2 1 3 5 4\\n7\\n3 1 4 1 5 7 6\\n6\\n3 2 1 6 5 4\\n\", \"1\\n6\\n2 2 3 5 6 1\\n\", \"1\\n6\\n2 4 3 10 4 1\\n\", \"1\\n6\\n1 3 5 5 3 1\\n\", \"1\\n6\\n2 1 3 5 0 2\\n\", \"1\\n7\\n2 2 4 1 7 5 0\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n2 5 3 4 6 2\\n6\\n5 1 4 4 6 2\\n\", \"1\\n7\\n0 2 4 1 8 6 5\\n\", \"1\\n6\\n3 2 1 10 8 4\\n\", \"4\\n6\\n1 4 5 4 2 6\\n6\\n5 1 3 8 2 6\\n6\\n1 5 3 4 6 2\\n6\\n5 1 4 4 6 2\\n\", \"4\\n6\\n1 5 3 4 2 5\\n6\\n5 1 3 4 2 6\\n6\\n1 5 3 3 6 2\\n6\\n5 1 3 4 6 0\\n\", \"1\\n7\\n2 1 4 1 7 6 8\\n\", \"5\\n5\\n1 3 4 2 5\\n4\\n2 1 4 4\\n5\\n2 1 3 5 4\\n7\\n3 2 4 1 5 7 6\\n6\\n3 2 1 6 5 4\\n\", \"1\\n6\\n2 3 3 5 6 1\\n\", \"1\\n6\\n2 4 3 20 4 1\\n\", \"1\\n6\\n1 3 5 6 3 1\\n\", \"1\\n7\\n2 2 4 1 6 5 0\\n\", \"4\\n6\\n1 5 3 4 2 6\\n6\\n5 1 3 4 2 6\\n6\\n2 5 3 4 6 2\\n6\\n5 1 7 4 6 2\\n\", \"2\\n5\\n1 2 3 4 5\\n7\\n3 2 4 5 1 6 7\\n\"], \"outputs\": [\"0\\n2\\n\", \"2\\n2\\n2\\n2\\n\", \"0\\n1\\n1\\n\", \"2\\n2\\n0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"2\\n2\\n2\\n2\\n\", \"0\\n1\\n1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n0\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n2\\n0\\n\", \"0\\n2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"1\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"0\\n2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n2\\n0\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n2\\n0\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"0\\n2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n\", \"1\\n1\\n2\\n2\\n2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n2\\n2\\n2\\n\", \"0\\n2\\n\"]}", "source": "taco"}
|
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across $n$ sessions follow the identity permutation (ie. in the first game he scores $1$ point, in the second game he scores $2$ points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on $[1,2,3]$ can yield $[3,1,2]$ but it cannot yield $[3,2,1]$ since the $2$ is in the same position.
Given a permutation of $n$ integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed $10^{18}$.
An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.
The first line of each test case contains integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the length of the given permutation.
The second line of each test case contains $n$ integers $a_{1},a_{2},...,a_{n}$ ($1 \leq a_{i} \leq n$) — the initial permutation.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
-----Output-----
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
-----Example-----
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
-----Note-----
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least $2$ exchanges to sort the second permutation.
$[3, 2, 4, 5, 1, 6, 7]$
Perform special exchange on range ($1, 5$)
$[4, 1, 2, 3, 5, 6, 7]$
Perform special exchange on range ($1, 4$)
$[1, 2, 3, 4, 5, 6, 7]$
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[220, 284], [220, 280], [1184, 1210], [220221, 282224], [10744, 10856], [299920, 9284], [999220, 2849], [139815, 122265], [496, 28], [8128, 8128]], \"outputs\": [[\"abundant deficient amicable\"], [\"abundant abundant not amicable\"], [\"abundant deficient amicable\"], [\"deficient abundant not amicable\"], [\"abundant deficient amicable\"], [\"abundant deficient not amicable\"], [\"abundant deficient not amicable\"], [\"deficient abundant amicable\"], [\"perfect perfect not amicable\"], [\"perfect perfect not amicable\"]]}", "source": "taco"}
|
For a given two numbers your mission is to derive a function that evaluates whether two given numbers are **abundant**, **deficient** or **perfect** and whether together they are **amicable**.
### Abundant Numbers
An abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself.
The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16 (> 12).
### Deficient Numbers
A deficient number is a number for which the sum of its proper divisors is less than the number itself.
The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9.
### Perfect Numbers
A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself.
The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6.
### Amicable Numbers
Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)
For example, the smallest pair of amicable numbers is (220, 284); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
### The Function
For a given two numbers, derive function `deficientlyAbundantAmicableNumbers(num1, num2)` which returns a string with first and second word either abundant or deficient depending on whether `num1` or `num2` are abundant, deficient or perfect. The string should finish with either amicable or not amicable depending on the relationship between `num1` and `num2`.
e.g. `deficientlyAbundantAmicableNumbers(220, 284)` returns `"abundant deficient amicable"` as 220 is an abundant number, 284 is a deficient number and amicable because 220 and 284 are an amicable number pair.
See Part 1 - [Excessively Abundant Numbers](http://www.codewars.com/kata/56a75b91688b49ad94000015)
See Part 2 - [The Most Amicable of Numbers](http://www.codewars.com/kata/56b5ebaa26fd54188b000018)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"123?45*?=?\"], [\"?*123?45=?\"], [\"??605*-63=-73???5\"], [\"123?45+?=123?45\"], [\"?8?170-1?6256=7?2?14\"], [\"?38???+595???=833444\"], [\"123?45-?=123?45\"], [\"-7715?5--484?00=-28?9?5\"], [\"50685?--1?5630=652?8?\"], [\"??+??=??\"], [\"-?56373--9216=-?47157\"]], \"outputs\": [[0], [0], [1], [0], [9], [2], [0], [6], [4], [-1], [8]]}", "source": "taco"}
|
To give credit where credit is due: This problem was taken from the ACMICPC-Northwest Regional Programming Contest. Thank you problem writers.
You are helping an archaeologist decipher some runes. He knows that this ancient society used a Base 10 system, and that they never start a number with a leading zero. He's figured out most of the digits as well as a few operators, but he needs your help to figure out the rest.
The professor will give you a simple math expression, of the form
```
[number][op][number]=[number]
```
He has converted all of the runes he knows into digits. The only operators he knows are addition (`+`),subtraction(`-`), and multiplication (`*`), so those are the only ones that will appear. Each number will be in the range from -1000000 to 1000000, and will consist of only the digits 0-9, possibly a leading -, and maybe a few ?s. If there are ?s in an expression, they represent a digit rune that the professor doesn't know (never an operator, and never a leading -). All of the ?s in an expression will represent the same digit (0-9), and it won't be one of the other given digits in the expression. No number will begin with a 0 unless the number itself is 0, therefore 00 would not be a valid number.
Given an expression, figure out the value of the rune represented by the question mark. If more than one digit works, give the lowest one. If no digit works, well, that's bad news for the professor - it means that he's got some of his runes wrong. output -1 in that case.
Complete the method to solve the expression to find the value of the unknown rune. The method takes a string as a paramater repressenting the expression and will return an int value representing the unknown rune or -1 if no such rune exists.
~~~if:php
**Most of the time, the professor will be able to figure out most of the runes himself, but sometimes, there may be exactly 1 rune present in the expression that the professor cannot figure out (resulting in all question marks where the digits are in the expression) so be careful ;)**
~~~
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 2\\n1 1\\n1 4\\n2 2\\n\", \"2 1\\n3 2\\n4 0\\n\", \"5 2\\n2 10\\n2 10\\n1 1\\n3 1\\n3 1\\n\", \"1 1\\n1 200000\\n\", \"1 2\\n1 100000\\n\", \"1 1\\n200000 0\\n\", \"9 4\\n3 10\\n4 11\\n4 2\\n1 3\\n1 7\\n2 5\\n2 6\\n3 4\\n1 7\\n\", \"3 3\\n4 154461\\n7 14431\\n3 186162\\n\", \"6 4\\n1 159371\\n1 73897\\n1 181693\\n4 187816\\n3 154227\\n1 188146\\n\", \"10 2\\n0 52\\n4 37\\n7 73\\n1 79\\n1 39\\n0 24\\n4 74\\n9 34\\n4 18\\n7 41\\n\", \"15 1\\n0 4\\n0 7\\n0 9\\n0 0\\n1 0\\n1 2\\n1 9\\n2 2\\n0 0\\n1 6\\n0 4\\n2 1\\n0 4\\n1 3\\n2 8\\n\", \"15 1\\n3 1\\n1 7\\n1 2\\n0 8\\n1 3\\n3 2\\n0 10\\n2 2\\n2 6\\n0 3\\n2 3\\n2 0\\n3 10\\n0 4\\n3 6\\n\", \"15 2\\n7 42\\n6 25\\n7 63\\n0 37\\n0 27\\n8 47\\n4 65\\n3 48\\n10 22\\n1 9\\n5 1\\n5 96\\n0 42\\n3 5\\n9 4\\n\", \"15 5\\n10 92\\n0 42\\n0 21\\n2 84\\n8 83\\n4 87\\n4 63\\n4 96\\n5 14\\n1 38\\n2 68\\n2 17\\n10 13\\n8 56\\n8 92\\n\", \"15 15\\n4 69\\n1 17\\n8 28\\n0 81\\n7 16\\n4 50\\n1 36\\n6 7\\n5 60\\n2 28\\n1 83\\n7 49\\n8 30\\n6 4\\n6 35\\n\", \"15 12\\n2 77\\n8 79\\n5 70\\n0 1\\n0 4\\n6 10\\n4 38\\n3 36\\n9 1\\n2 9\\n0 72\\n10 17\\n5 93\\n7 10\\n3 49\\n\", \"15 1\\n5 12184\\n4 79635\\n5 18692\\n5 125022\\n5 157267\\n2 15621\\n0 126533\\n0 9106\\n1 116818\\n3 65819\\n4 89314\\n5 102884\\n1 174638\\n2 191411\\n4 103238\\n\", \"15 1\\n8 79548\\n2 109344\\n1 40450\\n5 65400\\n10 93553\\n10 83467\\n4 122907\\n6 55664\\n5 111819\\n2 56263\\n10 188767\\n6 15848\\n10 110978\\n3 137786\\n10 199546\\n\", \"15 8\\n5 167779\\n4 185771\\n13 68521\\n14 9404\\n6 58046\\n0 173221\\n13 171983\\n1 54178\\n13 179027\\n0 80028\\n13 77065\\n8 181620\\n7 138547\\n11 174685\\n6 74881\\n\", \"15 7\\n5 189560\\n2 161786\\n6 30931\\n9 66796\\n3 101468\\n3 140646\\n3 30237\\n6 90950\\n10 67214\\n0 32922\\n4 98246\\n11 161468\\n9 6144\\n13 275\\n9 7847\\n\", \"15 3\\n2 39237\\n6 42209\\n8 99074\\n2 140949\\n3 33788\\n15 7090\\n13 29599\\n1 183967\\n6 20161\\n7 157097\\n10 173220\\n9 167385\\n15 123904\\n12 30799\\n5 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18692\\n5 125022\\n5 157267\\n2 15621\\n0 126533\\n0 6713\\n1 116818\\n3 65819\\n1 24049\\n5 102884\\n1 174638\\n2 191411\\n4 103238\\n\", \"40 3\\n1 62395\\n5 40319\\n4 165445\\n10 137479\\n10 47829\\n8 9741\\n5 148106\\n10 25494\\n10 162856\\n2 106581\\n0 194523\\n9 148086\\n1 100862\\n6 147600\\n6 107486\\n6 166873\\n7 16721\\n4 22192\\n0 8827\\n1 96814\\n10 8949\\n0 150443\\n9 148348\\n3 143935\\n1 139371\\n7 128821\\n10 138562\\n4 141821\\n1 35852\\n9 107522\\n10 54717\\n8 10474\\n0 97706\\n1 96515\\n1 60875\\n5 130542\\n10 63998\\n4 197179\\n7 78359\\n6 180750\\n\", \"15 2\\n7 42\\n6 41\\n7 63\\n0 37\\n0 27\\n8 47\\n7 65\\n3 48\\n10 22\\n1 9\\n5 0\\n5 96\\n0 42\\n3 5\\n9 4\\n\", \"15 1\\n15 200000\\n15 200000\\n6 200000\\n15 200000\\n15 200000\\n15 200000\\n15 200000\\n15 200000\\n15 200000\\n15 200000\\n15 200000\\n4 200000\\n15 200000\\n15 200000\\n15 200000\\n\", \"15 1\\n0 4\\n0 7\\n1 9\\n0 0\\n1 0\\n1 2\\n1 9\\n2 2\\n0 0\\n1 6\\n0 4\\n2 1\\n0 4\\n1 0\\n2 8\\n\", \"15 8\\n5 167779\\n4 185771\\n13 68521\\n1 9404\\n6 58046\\n0 173221\\n13 171983\\n1 54178\\n5 179027\\n0 80028\\n13 77065\\n8 181620\\n7 138547\\n11 174685\\n6 74881\\n\", \"40 3\\n1 62395\\n5 40319\\n4 165445\\n10 137479\\n10 47829\\n8 9741\\n5 148106\\n10 25494\\n10 162856\\n2 106581\\n0 194523\\n9 148086\\n1 100862\\n6 147600\\n6 107486\\n6 166873\\n7 16721\\n4 22192\\n0 8827\\n1 96814\\n10 8949\\n0 150443\\n9 148348\\n3 143935\\n1 139371\\n7 128821\\n10 138562\\n4 141821\\n1 35852\\n9 107522\\n10 54717\\n8 10474\\n0 97706\\n1 96515\\n1 131802\\n5 130542\\n10 63998\\n4 197179\\n7 78359\\n6 180750\\n\", \"3 3\\n5 154461\\n7 14431\\n3 186162\\n\", \"15 15\\n4 69\\n1 17\\n8 28\\n0 81\\n7 16\\n4 80\\n0 36\\n6 7\\n5 60\\n2 28\\n1 83\\n7 49\\n8 30\\n6 4\\n6 35\\n\", \"15 12\\n5 189560\\n2 161786\\n6 30931\\n9 66796\\n3 101468\\n3 140646\\n3 30237\\n6 90950\\n10 67214\\n0 32922\\n4 96123\\n11 161468\\n9 6144\\n13 275\\n9 7847\\n\", \"15 12\\n2 77\\n8 79\\n5 85\\n0 1\\n0 4\\n6 10\\n4 38\\n3 36\\n9 1\\n2 9\\n0 72\\n10 17\\n5 93\\n7 10\\n6 49\\n\", \"15 1\\n3 1\\n1 7\\n1 2\\n0 8\\n0 3\\n3 2\\n0 10\\n2 2\\n2 6\\n0 0\\n2 3\\n2 0\\n3 10\\n0 4\\n3 6\\n\", \"9 4\\n3 10\\n4 11\\n4 2\\n1 3\\n1 7\\n0 10\\n4 6\\n3 4\\n1 7\\n\", \"15 1\\n0 1\\n0 7\\n1 9\\n0 0\\n1 0\\n1 2\\n1 9\\n2 2\\n0 0\\n1 6\\n0 4\\n2 1\\n0 4\\n1 0\\n2 8\\n\", \"15 15\\n4 69\\n1 17\\n8 28\\n0 81\\n7 16\\n4 80\\n0 36\\n6 7\\n1 60\\n2 28\\n1 83\\n7 49\\n8 30\\n6 4\\n6 35\\n\", \"15 12\\n2 77\\n6 79\\n5 85\\n0 1\\n0 4\\n6 10\\n4 38\\n3 36\\n9 1\\n2 9\\n0 72\\n10 17\\n5 93\\n7 10\\n6 49\\n\", \"15 5\\n8 92\\n0 42\\n0 21\\n2 84\\n8 83\\n4 87\\n4 63\\n4 96\\n5 14\\n1 38\\n4 68\\n2 7\\n10 13\\n8 56\\n8 92\\n\", \"15 1\\n3 1\\n1 7\\n1 2\\n0 8\\n0 3\\n3 2\\n0 20\\n2 2\\n2 6\\n0 0\\n2 3\\n2 0\\n3 10\\n0 4\\n3 6\\n\", \"5 2\\n2 5\\n4 10\\n2 1\\n3 1\\n3 1\\n\", \"5 2\\n2 10\\n2 10\\n1 1\\n3 1\\n3 1\\n\", \"2 1\\n3 2\\n4 0\\n\", \"3 2\\n1 1\\n1 4\\n2 2\\n\"], \"outputs\": [\"3\\n\", \"-1\\n\", \"12\\n\", \"200000\\n\", \"0\\n\", \"-1\\n\", \"14\\n\", \"355054\\n\", \"387495\\n\", \"266\\n\", \"1\\n\", \"7\\n\", \"177\\n\", \"264\\n\", \"11\\n\", \"10\\n\", \"290371\\n\", \"909936\\n\", \"480642\\n\", \"199306\\n\", \"938616\\n\", \"3000000\\n\", \"200000\\n\", \"14\\n\", \"938616\\n\", \"3000000\\n\", \"1\\n\", \"480642\\n\", \"290371\\n\", \"387495\\n\", \"343510\\n\", \"0\\n\", \"355054\\n\", \"11\\n\", \"199306\\n\", \"909936\\n\", \"177\\n\", \"10\\n\", \"264\\n\", \"-1\\n\", \"7\\n\", \"266\\n\", \"15\\n\", \"939855\\n\", \"3000000\\n\", \"1\\n\", \"422123\\n\", \"290371\\n\", \"343510\\n\", \"355054\\n\", \"11\\n\", \"75434\\n\", \"878506\\n\", \"177\\n\", \"10\\n\", \"264\\n\", \"0\\n\", \"5\\n\", \"7\\n\", \"12\\n\", \"225106\\n\", \"1271794\\n\", \"176\\n\", \"254\\n\", \"8\\n\", \"-1\\n\", \"222713\\n\", \"341990\\n\", \"192\\n\", \"3000000\\n\", \"0\\n\", \"422123\\n\", \"343510\\n\", \"355054\\n\", \"11\\n\", \"75434\\n\", \"10\\n\", \"5\\n\", \"15\\n\", \"0\\n\", \"11\\n\", \"10\\n\", \"254\\n\", \"5\\n\", \"8\\n\", \"12\\n\", \"-1\\n\", \"3\\n\"]}", "source": "taco"}
|
This problem consists of three subproblems: for solving subproblem C1 you will receive 4 points, for solving subproblem C2 you will receive 4 points, and for solving subproblem C3 you will receive 8 points.
Manao decided to pursue a fighter's career. He decided to begin with an ongoing tournament. Before Manao joined, there were n contestants in the tournament, numbered from 1 to n. Each of them had already obtained some amount of tournament points, namely the i-th fighter had p_{i} points.
Manao is going to engage in a single fight against each contestant. Each of Manao's fights ends in either a win or a loss. A win grants Manao one point, and a loss grants Manao's opponent one point. For each i, Manao estimated the amount of effort e_{i} he needs to invest to win against the i-th contestant. Losing a fight costs no effort.
After Manao finishes all of his fights, the ranklist will be determined, with 1 being the best rank and n + 1 being the worst. The contestants will be ranked in descending order of their tournament points. The contestants with the same number of points as Manao will be ranked better than him if they won the match against him and worse otherwise. The exact mechanism of breaking ties for other fighters is not relevant here.
Manao's objective is to have rank k or better. Determine the minimum total amount of effort he needs to invest in order to fulfill this goal, if it is possible.
-----Input-----
The first line contains a pair of integers n and k (1 ≤ k ≤ n + 1). The i-th of the following n lines contains two integers separated by a single space — p_{i} and e_{i} (0 ≤ p_{i}, e_{i} ≤ 200000).
The problem consists of three subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.
In subproblem C1 (4 points), the constraint 1 ≤ n ≤ 15 will hold. In subproblem C2 (4 points), the constraint 1 ≤ n ≤ 100 will hold. In subproblem C3 (8 points), the constraint 1 ≤ n ≤ 200000 will hold.
-----Output-----
Print a single number in a single line — the minimum amount of effort Manao needs to use to rank in the top k. If no amount of effort can earn Manao such a rank, output number -1.
-----Examples-----
Input
3 2
1 1
1 4
2 2
Output
3
Input
2 1
3 2
4 0
Output
-1
Input
5 2
2 10
2 10
1 1
3 1
3 1
Output
12
-----Note-----
Consider the first test case. At the time when Manao joins the tournament, there are three fighters. The first of them has 1 tournament point and the victory against him requires 1 unit of effort. The second contestant also has 1 tournament point, but Manao needs 4 units of effort to defeat him. The third contestant has 2 points and victory against him costs Manao 2 units of effort. Manao's goal is top be in top 2. The optimal decision is to win against fighters 1 and 3, after which Manao, fighter 2, and fighter 3 will all have 2 points. Manao will rank better than fighter 3 and worse than fighter 2, thus finishing in second place.
Consider the second test case. Even if Manao wins against both opponents, he will still rank third.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 5\\n10\\n2 4 420\\n4 5 974\\n5 1 910\\n1 3 726\\n1 2 471\\n5 2 94\\n3 2 307\\n2 5 982\\n5 4 848\\n3 5 404\\n\", \"5 4\\n4\\n5 4 614\\n4 1 177\\n1 3 66\\n5 2 43\\n\", \"3 2\\n10\\n2 3 290\\n3 1 859\\n3 1 852\\n1 2 232\\n1 2 358\\n2 1 123\\n1 3 909\\n2 1 296\\n1 3 119\\n1 2 584\\n\", \"1 1\\n0\\n\", \"5 5\\n20\\n2 5 174\\n4 3 496\\n5 2 103\\n2 1 345\\n2 4 942\\n3 5 131\\n3 2 451\\n5 2 299\\n2 4 285\\n4 5 241\\n4 5 706\\n2 1 639\\n1 5 94\\n1 2 844\\n3 4 194\\n2 4 812\\n2 5 566\\n3 5 293\\n3 4 356\\n2 5 717\\n\", \"10 7\\n50\\n4 7 655\\n7 3 220\\n3 5 15\\n5 10 811\\n10 1 490\\n1 2 800\\n7 10 200\\n1 5 377\\n1 4 656\\n6 4 432\\n3 7 563\\n1 8 122\\n2 9 777\\n3 2 157\\n5 8 912\\n9 8 496\\n9 2 740\\n3 2 201\\n6 7 653\\n1 7 554\\n6 9 660\\n3 2 622\\n6 10 227\\n9 1 42\\n2 6 346\\n2 7 944\\n3 10 654\\n5 2 501\\n1 6 786\\n3 8 306\\n6 1 998\\n6 2 581\\n10 1 843\\n10 9 993\\n10 9 93\\n2 9 770\\n1 5 89\\n1 7 761\\n6 1 387\\n7 1 24\\n5 9 922\\n1 8 480\\n9 7 814\\n4 3 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\"61\\n\", \"101\\n\", \"-1\\n\", \"119\\n\", \"39\\n\", \"-1\\n\", \"-1\\n\", \"119\\n\", \"1981\\n\", \"6\\n\", \"-1\\n\", \"1403\\n\", \"119\\n\", \"-1\\n\", \"119\\n\", \"1981\\n\", \"-1\\n\", \"-1\\n\", \"1981\\n\", \"1981\\n\", \"1981\\n\", \"1981\\n\", \"-1\\n\", \"119\\n\", \"-1\\n\", \"6\\n\", \"3\\n\"]}", "source": "taco"}
|
Bankopolis is an incredible city in which all the n crossroads are located on a straight line and numbered from 1 to n along it. On each crossroad there is a bank office.
The crossroads are connected with m oriented bicycle lanes (the i-th lane goes from crossroad ui to crossroad vi), the difficulty of each of the lanes is known.
Oleg the bank client wants to gift happiness and joy to the bank employees. He wants to visit exactly k offices, in each of them he wants to gift presents to the employees.
The problem is that Oleg don't want to see the reaction on his gifts, so he can't use a bicycle lane which passes near the office in which he has already presented his gifts (formally, the i-th lane passes near the office on the x-th crossroad if and only if min(ui, vi) < x < max(ui, vi))). Of course, in each of the offices Oleg can present gifts exactly once. Oleg is going to use exactly k - 1 bicycle lane to move between offices. Oleg can start his path from any office and finish it in any office.
Oleg wants to choose such a path among possible ones that the total difficulty of the lanes he will use is minimum possible. Find this minimum possible total difficulty.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 80) — the number of crossroads (and offices) and the number of offices Oleg wants to visit.
The second line contains single integer m (0 ≤ m ≤ 2000) — the number of bicycle lanes in Bankopolis.
The next m lines contain information about the lanes.
The i-th of these lines contains three integers ui, vi and ci (1 ≤ ui, vi ≤ n, 1 ≤ ci ≤ 1000), denoting the crossroads connected by the i-th road and its difficulty.
Output
In the only line print the minimum possible total difficulty of the lanes in a valid path, or -1 if there are no valid paths.
Examples
Input
7 4
4
1 6 2
6 2 2
2 4 2
2 7 1
Output
6
Input
4 3
4
2 1 2
1 3 2
3 4 2
4 1 1
Output
3
Note
In the first example Oleg visiting banks by path 1 → 6 → 2 → 4.
Path 1 → 6 → 2 → 7 with smaller difficulity is incorrect because crossroad 2 → 7 passes near already visited office on the crossroad 6.
In the second example Oleg can visit banks by path 4 → 1 → 3.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 2 11\", \"3 0 11\", \"2 2 28\", \"3 5 28\", \"5 4 11\", \"5 3 17\", \"5 4 18\", \"6 4 12\", \"4 3 5\", \"4 8 5\", \"4 3 10\", \"11 3 9\", \"8 10 37\", \"8 6 37\", \"8 6 42\", \"8 6 39\", \"8 6 77\", \"8 9 77\", \"3 0 22\", \"3 1 22\", \"5 1 22\", \"5 0 22\", \"5 0 25\", \"3 0 25\", \"3 1 7\", \"5 2 11\", \"3 0 15\", \"5 1 6\", \"3 1 4\", \"5 1 33\", \"5 0 19\", \"3 1 25\", \"6 1 7\", \"5 2 17\", \"3 1 15\", \"7 1 6\", \"3 0 4\", \"5 1 12\", \"5 0 16\", \"5 1 7\", \"5 2 4\", \"3 1 9\", \"7 2 6\", \"3 0 7\", \"6 1 12\", \"5 0 12\", \"9 1 7\", \"5 1 4\", \"3 1 16\", \"7 1 4\", \"1 1 7\", \"11 1 12\", \"5 0 20\", \"9 1 12\", \"10 1 4\", \"3 1 28\", \"7 2 4\", \"1 1 3\", \"11 1 21\", \"7 0 20\", \"3 1 12\", \"10 2 4\", \"2 1 28\", \"4 2 4\", \"1 1 6\", \"11 0 21\", \"7 0 9\", \"3 0 12\", \"7 3 4\", \"4 2 2\", \"2 0 9\", \"3 0 23\", \"2 3 28\", \"4 2 3\", \"4 0 23\", \"2 5 28\", \"4 4 2\", \"4 4 4\", \"3 1 47\", \"3 4 4\", \"3 0 47\", \"3 4 2\", \"3 0 45\", \"1 4 2\", \"2 4 2\", \"2 0 2\", \"3 4 7\", \"1 2 11\", \"3 0 1\", \"4 0 22\", \"2 0 16\", \"5 1 25\", \"3 0 39\", \"5 0 7\", \"5 1 1\", \"2 1 33\", \"5 1 19\", \"1 1 25\", \"11 1 7\", \"1 1 15\", \"3 2 7\"], \"outputs\": [\"1\\n\", \"0\\n\", \"2\\n\", \"5\\n\", \"10\\n\", \"16\\n\", \"14\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"8\\n\", \"7\\n\", \"24\\n\", \"21\\n\", \"34\\n\", \"37\\n\", \"13\\n\", \"44\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"5\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\"]}", "source": "taco"}
|
F: Grid number
problem
Ebi-chan is trying to write exactly one integer from 1 to 2 \ times n in a grid with n columns horizontally and 2 rows vertically.
Only one integer can be written to each cell in the grid.
It's not fun just to write normally, so I set the following rules.
* The absolute value of the difference between the integers written in two adjacent cells is less than or equal to k.
* When there is a cell to the right of a cell, the integer written to the cell is truly smaller than the integer written to the cell to the right.
* When there is a cell under a cell, the integer written in the cell is truly smaller than the integer written in the cell below.
Here, two adjacent squares represent squares that share the top, bottom, left, and right sides with a certain square.
How many ways to write this? The answer can be very large, so print the remainder after dividing by the prime number m.
Supplement
The second and third rules above require you to write an integer so that it doesn't violate the inequality sign, as shown in the figure below.
<image>
Input format
You will be given three integers as input.
n k m
Constraint
* 1 \ leq n \ leq 100
* 1 \ leq k \ leq 10
* 2 \ leq m \ leq 10 ^ 9 + 7
* m is a prime number
Output format
Please output the number on one line according to how to write the number. Also, be careful not to forget the trailing line break.
Input example 1
3 2 7
Output example 1
1
<image>
* The above writing method meets the conditions, and there is no other writing method that meets the conditions.
Input example 2
5 10 11
Output example 2
9
* Output the remainder divided by m.
Example
Input
3 2 7
Output
1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"10 1 1 1 2 0 10\\n1 1\\n2 1\\n3 0\\n4 0\\n5 1\\n6 1\\n7 1\\n8 1\\n9 1\\n10 1\\n\", \"10 1 1 1 2 0 10\\n1 1\\n2 1\\n3 0\\n4 0\\n5 1\\n6 1\\n14 1\\n8 1\\n9 1\\n10 1\\n\", \"5 1 1 1 4 0 5\\n1 0\\n2 1\\n3 1\\n4 0\\n5 0\\n\", \"1 1 2 1 2 1 2\\n1 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n2 1\\n3 1\\n4 0\\n5 0\\n\", \"1 1 2 0 2 1 2\\n1 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 1\\n4 0\\n5 0\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 1\\n4 1\\n5 0\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 1\\n4 1\\n5 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 2\\n4 1\\n5 1\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 1\\n5 1\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 0\\n5 1\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 0\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n3 1\\n3 2\\n4 0\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n6 1\\n3 2\\n4 0\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n6 1\\n3 2\\n4 0\\n4 2\\n\", \"10 1 1 1 2 0 10\\n1 1\\n2 1\\n3 0\\n4 0\\n5 1\\n6 1\\n7 1\\n8 1\\n5 1\\n10 1\\n\", \"1 0 2 1 2 1 2\\n1 0\\n\", \"5 0 1 1 4 0 5\\n1 0\\n2 1\\n3 1\\n4 0\\n5 0\\n\", \"1 1 3 1 2 1 2\\n1 1\\n\", \"5 1 1 0 3 0 5\\n1 0\\n2 1\\n3 1\\n4 0\\n5 0\\n\", \"1 1 1 0 2 1 2\\n1 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 0\\n4 0\\n5 0\\n\", \"5 1 1 0 4 0 5\\n1 0\\n6 1\\n3 1\\n4 1\\n5 0\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n4 1\\n4 1\\n5 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n3 1\\n3 2\\n4 1\\n5 0\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 1\\n3 1\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 0\\n3 1\\n\", \"5 1 1 0 4 0 2\\n1 0\\n3 1\\n3 2\\n4 1\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n6 1\\n3 2\\n4 1\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n6 1\\n3 2\\n4 0\\n4 3\\n\", \"1 2 3 1 2 1 2\\n1 1\\n\", \"5 1 1 0 3 0 5\\n1 0\\n2 1\\n5 1\\n4 0\\n5 0\\n\", \"1 1 0 0 2 1 2\\n1 1\\n\", \"5 1 1 0 4 0 5\\n1 0\\n6 1\\n3 2\\n4 1\\n5 0\\n\", \"5 2 1 0 4 0 5\\n1 0\\n3 1\\n4 1\\n4 1\\n5 1\\n\", \"5 1 1 0 2 0 2\\n1 0\\n3 1\\n3 2\\n4 1\\n3 1\\n\", \"5 1 1 0 7 0 2\\n1 0\\n3 1\\n3 2\\n4 1\\n4 1\\n\", \"5 1 1 -1 4 0 2\\n1 0\\n6 1\\n3 2\\n8 1\\n4 1\\n\", \"1 2 3 1 2 1 4\\n1 1\\n\", \"5 1 1 0 3 0 5\\n1 0\\n2 1\\n5 1\\n4 1\\n5 0\\n\", \"1 1 0 0 2 1 4\\n1 1\\n\", \"5 1 1 1 4 0 5\\n1 1\\n2 1\\n3 1\\n4 0\\n5 0\\n\", \"1 1 2 1 2 1 2\\n1 0\\n\"], \"outputs\": [\"5\\n\", \"5\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"5\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"6\\n\", \"-1\\n\"]}", "source": "taco"}
|
There are two main kinds of events in the life of top-model: fashion shows and photo shoots. Participating in any of these events affects the rating of appropriate top-model. After each photo shoot model's rating increases by a and after each fashion show decreases by b (designers do too many experiments nowadays). Moreover, sometimes top-models participates in talk shows. After participating in talk show model becomes more popular and increasing of her rating after photo shoots become c and decreasing of her rating after fashion show becomes d.
Izabella wants to participate in a talk show, but she wants to do it in such a way that her rating will never become negative. Help her to find a suitable moment for participating in the talk show.
Let's assume that model's career begins in moment 0. At that moment Izabella's rating was equal to start. If talk show happens in moment t if will affect all events in model's life in interval of time [t..t + len) (including t and not including t + len), where len is duration of influence.
Izabella wants to participate in a talk show, but she wants to do it in such a way that her rating will not become become negative before talk show or during period of influence of talk show. Help her to find a suitable moment for participating in the talk show.
Input
In first line there are 7 positive integers n, a, b, c, d, start, len (1 ≤ n ≤ 3·105, 0 ≤ start ≤ 109, 1 ≤ a, b, c, d, len ≤ 109), where n is a number of fashion shows and photo shoots, a, b, c and d are rating changes described above, start is an initial rating of model and len is a duration of influence of talk show.
In next n lines descriptions of events are given. Each of those lines contains two integers ti and qi (1 ≤ ti ≤ 109, 0 ≤ q ≤ 1) — moment, in which event happens and type of this event. Type 0 corresponds to the fashion show and type 1 — to photo shoot.
Events are given in order of increasing ti, all ti are different.
Output
Print one non-negative integer t — the moment of time in which talk show should happen to make Izabella's rating non-negative before talk show and during period of influence of talk show. If there are multiple answers print smallest of them. If there are no such moments, print - 1.
Examples
Input
5 1 1 1 4 0 5
1 1
2 1
3 1
4 0
5 0
Output
6
Input
1 1 2 1 2 1 2
1 0
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
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219537305 396613042 39840356 91947418 566463810 791505982 59982983 446282153 912204581 895882687 284561729 35994526 423462628\\n\", \"10 8\\n994538714 617271264 168716105 915909382 423860021 533154890 507276501 323171960 121635370 33140162\\n\", \"48 19\\n227460648 746912227 53993110 682685526 621533699 666833118 492590399 167395932 678377837 66509685 638633256 713194370 386921921 34175133 704550052 220688092 499436761 495071386 57379330 137372655 0 720974146 209203457 946682102 237312198 943872065 957150897 357568282 367006748 0 730509325 68523190 726721460 85037180 620964626 219537306 396613043 39840357 91947419 566463811 791505983 87036027 446282154 912204582 895882688 284561730 35994527 423462629\\n\", \"15 12\\n256121252 382267043 157210108 921323934 786210452 0 962820592 824495629 642702951 556399489 660627699 454443499 406577817 234814732 387536495\\n\", \"15 8\\n256121253 531930088 157210109 921323935 786210453 1 962820593 621273612 642702951 556399489 660627699 454443499 406577818 234814733 387536496\\n\", \"10 5\\n994538715 617271265 168716106 915909383 612513762 533154890 507276501 323171960 121635371 33140163\\n\", \"10 3\\n1000100000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\\n\", \"10 5\\n3 3 3 3 4 3 3 5 3 3\\n\", \"5 4\\n3 2 3 1 3\\n\", \"5 2\\n1 554459683 978416312 784688178 722336239\\n\", \"5 2\\n3 1 0 2 7\\n\", \"3 3\\n4 3 1\\n\", \"10 8\\n994538714 617271264 168716105 915909382 423860021 593684139 507276501 323171960 121635370 33140162\\n\", \"48 19\\n227460648 746912227 53993110 682685526 621533699 666833118 492590399 167395932 678377837 66509685 638633256 713194370 386921921 34175133 704550052 220688092 499436761 495071386 57379330 137372655 0 720974146 209203457 946682102 237312198 943872065 957150897 357568282 367006748 0 730509325 68523190 726721460 85037180 620964626 219537306 396613043 39840357 91947419 566463811 791505983 87036027 710797608 912204582 895882688 284561730 35994527 423462629\\n\", \"15 12\\n256121252 382267043 157210108 921323934 786210452 1 962820592 824495629 642702951 556399489 660627699 454443499 406577817 234814732 387536495\\n\", \"15 8\\n256121253 531930088 157210109 921323935 786210453 1 962820593 621273612 642702951 1032155742 660627699 454443499 406577818 234814733 387536496\\n\", \"10 7\\n994538715 617271265 168716106 915909383 612513762 533154890 507276501 323171960 121635371 33140163\\n\", \"10 5\\n3 1 3 3 4 3 3 5 3 3\\n\", \"5 4\\n3 0 3 1 3\\n\", \"5 2\\n1 554459683 978416312 286401795 722336239\\n\", \"5 2\\n3 1 0 2 3\\n\", \"10 8\\n994538714 617271264 168716105 915909382 423860021 593684139 507276501 323171960 140088313 33140162\\n\", \"48 19\\n227460648 746912227 53993110 682685526 621533699 666833118 492590399 167395932 678377837 66509685 638633256 713194370 386921921 34175133 704550052 220688092 499436761 495071386 57379330 137372655 0 720974146 209203457 946682102 237312198 943872065 957150897 357568282 367006748 0 730509325 68523190 726721460 85037180 620964626 219537306 396613043 39840357 91947419 476206194 791505983 87036027 710797608 912204582 895882688 284561730 35994527 423462629\\n\", \"15 12\\n256121252 382267043 157210108 921323934 786210452 1 962820592 824495629 642702951 556399489 660627699 454443499 406577817 234814732 553496365\\n\", \"15 8\\n256121253 531930088 157210109 921323935 786210453 1 962820593 621273612 642702951 1032155742 660627699 626175590 406577818 234814733 387536496\\n\", \"10 5\\n3 1 3 3 4 0 3 5 3 3\\n\", \"5 4\\n3 0 4 1 3\\n\", \"5 4\\n1 554459683 978416312 286401795 722336239\\n\", \"10 8\\n994538714 617271264 168716105 915909382 423860021 593684139 4090019 323171960 140088313 33140162\\n\", \"48 19\\n227460648 746912227 53993110 682685526 621533699 666833118 492590399 167395932 678377837 66509685 638633256 713194370 386921921 34175133 704550052 220688092 499436761 495071386 57379330 137372655 0 720974146 209203457 946682102 237312198 943872065 957150897 357568282 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157210108 921323934 311804371 17 1250968917 305746706 642702950 1032155741 660627698 552190763 406577817 190264579 278534803\\n\", \"589697997 507102144 84090834 913762423 329693524 591537180 21469591 321025000 156986751 40328037\\n\", \"227460647 746912226 51958074 682685525 1080381697 666833117 492590398 167395931 678377836 125106810 638633255 713194369 386921920 34175132 704550051 192804760 499436760 469309035 57379329 137372655 0 720974146 209203457 946682102 237312198 943872065 957150897 357568282 367006748 37 730509324 68523189 699803211 85037179 620964625 219537305 396613042 39840356 91947418 476206193 791505982 53679573 710797607 912204581 545857206 284561729 26597317 423462628\\n\", \"256121252 531930087 157210108 921323934 349480252 17 1250968917 305746706 642702950 1032155741 660627698 552190763 406577817 190264579 278534803\\n\", \"2 1 4 1 6\\n\", \"1 2 3\\n\", \"3 2 5 4\\n\"]}", "source": "taco"}
|
Little Vasya had n boxes with balls in the room. The boxes stood in a row and were numbered with numbers from 1 to n from left to right.
Once Vasya chose one of the boxes, let's assume that its number is i, took all balls out from it (it is guaranteed that this box originally had at least one ball), and began putting balls (one at a time) to the boxes with numbers i + 1, i + 2, i + 3 and so on. If Vasya puts a ball into the box number n, then the next ball goes to box 1, the next one goes to box 2 and so on. He did it until he had no balls left in his hands. It is possible that Vasya puts multiple balls to the same box, and it is also possible that one or more balls will go to the box number i. If i = n, Vasya puts the first ball into the box number 1, then the next ball goes to box 2 and so on.
For example, let's suppose that initially Vasya had four boxes, and the first box had 3 balls, the second one had 2, the third one had 5 and the fourth one had 4 balls. Then, if i = 3, then Vasya will take all five balls out of the third box and put them in the boxes with numbers: 4, 1, 2, 3, 4. After all Vasya's actions the balls will lie in the boxes as follows: in the first box there are 4 balls, 3 in the second one, 1 in the third one and 6 in the fourth one.
At this point Vasya has completely forgotten the original arrangement of the balls in the boxes, but he knows how they are arranged now, and the number x — the number of the box, where he put the last of the taken out balls.
He asks you to help to find the initial arrangement of the balls in the boxes.
-----Input-----
The first line of the input contains two integers n and x (2 ≤ n ≤ 10^5, 1 ≤ x ≤ n), that represent the number of the boxes and the index of the box that got the last ball from Vasya, correspondingly. The second line contains n space-separated integers a_1, a_2, ..., a_{n}, where integer a_{i} (0 ≤ a_{i} ≤ 10^9, a_{x} ≠ 0) represents the number of balls in the box with index i after Vasya completes all the actions.
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.
-----Output-----
Print n integers, where the i-th one represents the number of balls in the box number i before Vasya starts acting. Separate the numbers in the output by spaces. If there are multiple correct solutions, you are allowed to print any of them.
-----Examples-----
Input
4 4
4 3 1 6
Output
3 2 5 4
Input
5 2
3 2 0 2 7
Output
2 1 4 1 6
Input
3 3
2 3 1
Output
1 2 3
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1\\n\", \"2\\n\", \"10\\n\", \"1000\\n\", \"2000\\n\", \"5000\\n\", \"10000\\n\", \"111199\\n\", \"101232812\\n\", \"1000000000\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"6\\n\", \"7\\n\", \"8\\n\", \"9\\n\", \"11\\n\", \"12\\n\", \"13\\n\", \"55\\n\", \"100\\n\", \"150\\n\", \"1200\\n\", \"9999999\\n\", \"100000000\\n\", \"500000000\\n\", \"600000000\\n\", \"709000900\\n\", \"999999999\\n\", \"12\\n\", \"10\\n\", \"20\\n\", \"35\\n\", \"56\\n\", \"83\\n\", \"116\\n\", \"155\\n\", \"198\\n\", \"244\\n\", \"292\\n\", \"14\\n\", \"7\\n\", \"292\\n\", \"100000000\\n\", \"2000\\n\", \"8\\n\", \"198\\n\", \"116\\n\", \"5000\\n\", \"100\\n\", \"9\\n\", \"55\\n\", \"83\\n\", \"14\\n\", \"9999999\\n\", \"500000000\\n\", \"709000900\\n\", \"111199\\n\", \"244\\n\", \"20\\n\", \"1200\\n\", \"4\\n\", \"1000000000\\n\", \"600000000\\n\", \"35\\n\", \"1000\\n\", \"999999999\\n\", \"13\\n\", \"3\\n\", \"12\\n\", \"6\\n\", \"155\\n\", \"101232812\\n\", \"56\\n\", \"10000\\n\", \"150\\n\", \"11\\n\", \"5\\n\", \"23\\n\", \"100001000\\n\", \"1529\\n\", \"173\\n\", \"87\\n\", \"5248\\n\", \"101\\n\", \"30\\n\", \"67\\n\", \"5680294\\n\", \"166677918\\n\", \"939837497\\n\", \"207305\\n\", \"53\\n\", \"37\\n\", \"419\\n\", \"1000000001\\n\", \"891702741\\n\", \"1897400395\\n\", \"22\\n\", \"17\\n\", \"92074574\\n\", \"26\\n\", \"10001\\n\", \"151\\n\", \"16\\n\", \"18\\n\", \"15\\n\", \"29\\n\", \"110001000\\n\", \"986\\n\", \"303\\n\", \"125\\n\", \"4056\\n\", \"111\\n\", \"77\\n\", \"5930601\\n\", \"257617149\\n\", \"486958104\\n\", \"171869\\n\", \"72\\n\", \"577\\n\", \"1100000001\\n\", \"678333192\\n\", \"1533257378\\n\", \"33\\n\", \"91972794\\n\", \"31\\n\", \"00001\\n\", \"165\\n\", \"21\\n\", \"51\\n\", \"100101000\\n\", \"700\\n\", \"580\\n\", \"186\\n\", \"4070\\n\", \"011\\n\", \"8171610\\n\", \"432547790\\n\", \"243841489\\n\", \"99356\\n\", \"127\\n\", \"234\\n\", \"1100000011\\n\", \"436008615\\n\", \"216438791\\n\", \"79\\n\", \"15703603\\n\", \"39\\n\", \"01001\\n\", \"32\\n\", \"84\\n\", \"2\\n\", \"10\\n\", \"1\\n\"], \"outputs\": [\"4\\n\", \"10\\n\", \"244\\n\", \"48753\\n\", \"97753\\n\", \"244753\\n\", \"489753\\n\", \"5448504\\n\", \"4960407541\\n\", \"48999999753\\n\", \"20\\n\", \"35\\n\", \"56\\n\", \"83\\n\", \"116\\n\", \"155\\n\", \"198\\n\", \"292\\n\", \"341\\n\", \"390\\n\", \"2448\\n\", \"4653\\n\", \"7103\\n\", \"58553\\n\", \"489999704\\n\", \"4899999753\\n\", \"24499999753\\n\", \"29399999753\\n\", \"34741043853\\n\", \"48999999704\\n\", \"341\\n\", \"244\\n\", \"733\\n\", \"1468\\n\", \"2497\\n\", \"3820\\n\", \"5437\\n\", \"7348\\n\", \"9455\\n\", \"11709\\n\", \"14061\\n\", \"439\\n\", \"116\", \"14061\", \"4899999753\", \"97753\", \"155\", \"9455\", \"5437\", \"244753\", \"4653\", \"198\", \"2448\", \"3820\", \"439\", \"489999704\", \"24499999753\", \"34741043853\", \"5448504\", \"11709\", \"733\", \"58553\", \"35\", \"48999999753\", \"29399999753\", \"1468\", \"48753\", \"48999999704\", \"390\", \"20\", \"341\", \"83\", \"7348\", \"4960407541\", \"2497\", \"489753\", \"7103\", \"292\", \"56\", \"880\\n\", \"4900048753\\n\", \"74674\\n\", \"8230\\n\", \"4016\\n\", \"256905\\n\", \"4702\\n\", \"1223\\n\", \"3036\\n\", \"278334159\\n\", \"8167217735\\n\", \"46052037106\\n\", \"10157698\\n\", \"2350\\n\", \"1566\\n\", \"20284\\n\", \"48999999802\\n\", \"43693434062\\n\", \"92972619108\\n\", \"831\\n\", \"586\\n\", \"4511653879\\n\", \"1027\\n\", \"489802\\n\", \"7152\\n\", \"537\\n\", \"635\\n\", \"488\\n\", \"1174\\n\", \"5390048753\\n\", \"48067\\n\", \"14600\\n\", \"5878\\n\", \"198497\\n\", \"5192\\n\", \"3526\\n\", \"290599202\\n\", \"12623240054\\n\", \"23860946849\\n\", \"8421334\\n\", \"3281\\n\", \"28026\\n\", \"53899999802\\n\", \"33238326161\\n\", \"75129611275\\n\", \"1370\\n\", \"4506666659\\n\", \"1272\\n\", \"4\\n\", \"7838\\n\", \"782\\n\", \"2252\\n\", \"4904948753\\n\", \"34053\\n\", \"28173\\n\", \"8867\\n\", \"199183\\n\", \"292\\n\", \"400408643\\n\", \"21194841463\\n\", \"11948232714\\n\", \"4868197\\n\", \"5976\\n\", \"11219\\n\", \"53900000292\\n\", \"21364421888\\n\", \"10605500512\\n\", \"3624\\n\", \"769476300\\n\", \"1664\\n\", \"48802\\n\", \"1321\\n\", \"3869\\n\", \"10\", \"244\", \"4\"]}", "source": "taco"}
|
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 $n$ ($1 \le n \le 10^9$) — 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).
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"3649596966777\\n2237884645346\\n9118992346175\\n7913620092962\\n620592935882\\n704120058101\", \"3649596966777\\n9352826644343\\n9118992346175\\n4337442177740\\n1181850814645\\n1133557799246\", \"3649596966777\\n9352826644343\\n2241662059182\\n4337442177740\\n1515065857254\\n1133557799246\", \"3649596966777\\n9352826644343\\n2241662059182\\n6439833221924\\n1515065857254\\n1440080820387\", \"3649596966777\\n9352826644343\\n2241662059182\\n6439833221924\\n284938453563\\n1440080820387\", \"3649596966777\\n9352826644343\\n2241662059182\\n6439833221924\\n284938453563\\n1878314608942\", \"3649596966777\\n9352826644343\\n2241662059182\\n11545439940720\\n284938453563\\n1878314608942\", \"3649596966777\\n6358665788577\\n9118992346175\\n9643871425498\\n4922558947109\\n1133557799246\", \"3649596966777\\n4556908617708\\n9118992346175\\n9643871425498\\n7755542764533\\n704120058101\", \"3649596966777\\n6358665788577\\n9118992346175\\n9643871425498\\n992305966219\\n115250355602\", \"3649596966777\\n2400089434482\\n9118992346175\\n9643871425498\\n7755542764533\\n1079549632139\", \"3649596966777\\n6358665788577\\n9118992346175\\n9643871425498\\n7755542764533\\n1133557799246\"], \"outputs\": [\"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 3 4 7\\n1 2 3 4 5 6 7 8 9\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n3 4\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n5 8\\n1 2 3 4 5 6 7 8 9\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n5 8\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n0\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n0\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n7\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n7\\n0\\n0\\n\", \"2 3 5 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8\\n0\\n8\\n0\\n0\\n0\\n\", \"2 3 5 8\\n3 4\\n0\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n8\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n0\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n2\\n0\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n4 7 8\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n0\\n7\\n0\\n0\\n\", \"2 3 5 8\\n3 4\\n0\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n7 8\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n1 4 7\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n0\\n1 3 6 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n0\\n0\\n0\\n8\\n0\\n\", \"2 3 5 8\\n0\\n2 5\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n7\\n0\\n0\\n0\\n\", \"2 3 5 8\\n3 4\\n0\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n8\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n4 7 8\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n0\\n0\\n6 9\\n0\\n\", \"2 3 5 8\\n0\\n8\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n4 7 8\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n0\\n6 9\\n0\\n\", \"2 3 5 8\\n0\\n0\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n0\\n5 6 9\\n0\\n\", \"2 3 5 8\\n0\\n3 6\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n8\\n0\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n0\\n0\\n8\\n0\\n0\\n\", \"2 3 5 8\\n0\\n1 2 3 4 5 6 7 8 9\\n2 9\\n0\\n0\\n\", \"2 3 5 8\\n2 5 8\\n1 2 3 4 5 6 7 8 9\\n2 9\\n0\\n0\\n\", \"2 3 5 8\\n1 3 4 7\\n1 2 3 4 5 6 7 8 9\\n7\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n3 4\\n1 2 3 4 5 6 7 8 9\\n3 6\\n0\\n0\\n\", \"2 3 5 8\\n3\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n0\\n8\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n3 4\\n4 7\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n2\\n0\\n0\\n\", \"2 3 5 8\\n7 8\\n0\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n1 3 6 9\\n0\\n5\\n0\\n\", \"2 3 5 8\\n2 5 9\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n0\\n1 7\\n0\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n1 3 6 9\\n0\\n8\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n6 9\\n0\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n0\\n3 6 9\\n0\\n\", \"2 3 5 8\\n5 8\\n0\\n2 5\\n3 6 9\\n0\\n\", \"2 3 5 8\\n6 9\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n0\\n0\\n2 9\\n0\\n0\\n\", \"2 3 5 8\\n1 3 4 7\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n5 8\\n1 2 3 4 5 6 7 8 9\\n0\\n4\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n0\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n1 2 4 5 7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n5 8\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n5 8\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n1 2 3 4 5 6 7 8 9\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n7\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n7\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n7\\n0\\n0\\n\", \"2 3 5 8\\n7\\n0\\n0\\n0\\n0\\n\", \"2 3 5 8\\n3 4\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n0\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n3 4\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n0\\n0\\n\", \"2 3 5 8\\n0\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\\n\", \"2 3 5 8\\n3 4\\n1 2 3 4 5 6 7 8 9\\n7 8 9\\n1 2 3 4 6 7 8\\n0\"]}", "source": "taco"}
|
There is a puzzle to complete by combining 14 numbers from 1 to 9. Complete by adding another number to the given 13 numbers.
The conditions for completing the puzzle are
* You must have one combination of the same numbers.
* The remaining 12 numbers are 4 combinations of 3 numbers.
The combination of three numbers is either three of the same numbers or three consecutive numbers. However, sequences such as 9 1 2 are not considered consecutive numbers.
* The same number can be used up to 4 times.
Create a program that reads a string of 13 numbers and outputs all the numbers that can complete the puzzle in ascending order. If you cannot complete the puzzle by adding any number from 1 to 9, output 0.
For example, if the given string is 3456666777999
If there is a "2", 234 567 666 77 999
If there is a "3", then 33 456 666 777 999
If there is a "5", then 345 567 666 77 999
If there is an "8", then 345 666 678 77 999
And so on, the puzzle is complete when one of the numbers 2 3 5 8 is added. Note that "6" is fine, but it will be used for the 5th time, so it cannot be used in this example.
Input
The input consists of multiple datasets. For each dataset, 13 numbers are given on one line. The number of datasets does not exceed 50.
Output
For each dataset, the numbers that can complete the puzzle are output on one line in ascending order, separated by blanks.
Example
Input
3649596966777
6358665788577
9118992346175
9643871425498
7755542764533
1133557799246
Output
2 3 5 8
3 4
1 2 3 4 5 6 7 8 9
7 8 9
1 2 3 4 6 7 8
0
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"11\\n\", \"0\\n\", \"17\\n\", \"18855321\\n\", \"34609610\\n\", \"25\\n\", \"9\\n\", \"40000000\\n\", \"17464436\\n\", \"38450759\\n\", \"395938\\n\", \"39099999\\n\", \"8\\n\", \"4\\n\", \"30426905\\n\", \"7\\n\", \"17082858\\n\", \"46341\\n\", \"46340\\n\", \"39999996\\n\", \"6\\n\", \"12823666\\n\", \"39999999\\n\", \"5\\n\", \"5626785\\n\", \"22578061\\n\", \"3766137\\n\", \"13\\n\", \"19863843\\n\", \"24562258\\n\", \"17590047\\n\", \"33146037\\n\", \"2870141\\n\", \"10\\n\", \"14\\n\", \"25329968\\n\", \"39999997\\n\", \"31975828\\n\", \"31988776\\n\", \"31416948\\n\", \"39268638\\n\", \"614109\\n\", \"24483528\\n\", \"39999998\\n\", \"15012490\\n\", \"3107977\\n\", \"2346673\\n\", \"34714265\\n\", \"12\\n\", \"15\\n\", \"16\\n\", \"1059264\\n\", \"743404\\n\", \"22\\n\", \"18712741\\n\", \"19\\n\", \"18\\n\", \"28793983\\n\", \"23224290\\n\", \"99745\\n\", \"35202758\\n\", \"29\\n\", \"12297368\\n\", \"28479\\n\", \"6339\\n\", \"14358961\\n\", \"8046391\\n\", \"21458941\\n\", \"290175\\n\", \"23635292\\n\", \"5753398\\n\", \"20\\n\", \"15059571\\n\", \"6489939\\n\", \"15765759\\n\", \"2702862\\n\", \"1116491\\n\", \"5376403\\n\", \"27801925\\n\", \"12940822\\n\", \"333126\\n\", \"32480774\\n\", \"39328213\\n\", \"14730633\\n\", \"1391775\\n\", \"867315\\n\", \"24\\n\", \"28\\n\", \"561480\\n\", \"1379091\\n\", \"31\\n\", \"4756040\\n\", \"32\\n\", \"26\\n\", \"9699318\\n\", \"11303201\\n\", \"44610\\n\", \"7174193\\n\", \"11125829\\n\", \"8284\\n\", \"2901\\n\", \"4008032\\n\", \"2043829\\n\", \"30131997\\n\", \"310519\\n\", \"13942423\\n\", \"2216663\\n\", \"33\\n\", \"28327088\\n\", \"8381907\\n\", \"28084809\\n\", \"2007849\\n\", \"1118477\\n\", \"3630257\\n\", \"12750347\\n\", \"410223\\n\", \"34348875\\n\", \"28556748\\n\", \"8702249\\n\", \"2294898\\n\", \"419940\\n\", \"42\\n\", \"34\\n\", \"796661\\n\", \"2220203\\n\", \"55\\n\", \"3850788\\n\", \"23\\n\", \"37\\n\", \"7229468\\n\", \"3005575\\n\", \"41095\\n\", \"2\\n\", \"3\\n\", \"1\\n\"], \"outputs\": [\"60\\n\", \"1\\n\", \"96\\n\", \"106661800\\n\", \"195781516\\n\", \"140\\n\", \"48\\n\", \"226274168\\n\", \"98793768\\n\", \"217510336\\n\", \"2239760\\n\", \"221182992\\n\", \"44\\n\", \"20\\n\", \"172120564\\n\", \"36\\n\", \"96635236\\n\", \"262144\\n\", \"262136\\n\", \"226274144\\n\", \"32\\n\", \"72541608\\n\", \"226274164\\n\", \"28\\n\", \"31829900\\n\", \"127720800\\n\", \"21304488\\n\", \"72\\n\", \"112366864\\n\", \"138945112\\n\", \"99504332\\n\", \"187502300\\n\", \"16235968\\n\", \"56\\n\", \"76\\n\", \"143287936\\n\", \"226274152\\n\", \"180882596\\n\", \"180955840\\n\", \"177721092\\n\", \"222136960\\n\", \"3473924\\n\", \"138499748\\n\", \"226274156\\n\", \"84923464\\n\", \"17581372\\n\", \"13274784\\n\", \"196373536\\n\", \"64\\n\", \"84\\n\", \"88\\n\", \"5992100\\n\", \"4205328\\n\", \"124\\n\", \"105855248\\n\", \"104\\n\", \"100\\n\", \"162883364\\n\", \"131376420\\n\", \"564240\\n\", \"199136868\\n\", \"164\\n\", \"69564416\\n\", \"161100\\n\", \"35856\\n\", \"81226548\\n\", \"45517260\\n\", \"121390100\\n\", \"1641476\\n\", \"133701400\\n\", \"32546132\\n\", \"112\\n\", \"85189796\\n\", \"36712636\\n\", \"89184600\\n\", \"15289696\\n\", \"6315824\\n\", \"30413528\\n\", \"157271436\\n\", \"73204340\\n\", \"1884444\\n\", \"183739004\\n\", \"222473968\\n\", \"83329040\\n\", \"7873068\\n\", \"4906272\\n\", \"132\\n\", \"156\\n\", \"3176208\\n\", \"7801316\\n\", \"172\\n\", \"26904224\\n\", \"180\\n\", \"144\\n\", \"54867628\\n\", \"63940560\\n\", \"252352\\n\", \"40583364\\n\", \"62937192\\n\", \"46860\\n\", \"16408\\n\", \"22672852\\n\", \"11561640\\n\", \"170452312\\n\", \"1756560\\n\", \"78870252\\n\", \"12539336\\n\", \"184\\n\", \"160242208\\n\", \"47415224\\n\", \"158871668\\n\", \"11358108\\n\", \"6327060\\n\", \"20535832\\n\", \"72126852\\n\", \"2320568\\n\", \"194306576\\n\", \"161541360\\n\", \"49227352\\n\", \"12981900\\n\", \"2375536\\n\", \"236\\n\", \"192\\n\", \"4506592\\n\", \"12559364\\n\", \"308\\n\", \"21783344\\n\", \"128\\n\", \"208\\n\", \"40896044\\n\", \"17002096\\n\", \"232468\\n\", \"8\\n\", \"16\\n\", \"4\\n\"]}", "source": "taco"}
|
Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:
* the Euclidean distance between A and B is one unit and neither A nor B is blocked;
* or there is some integral point C, such that A is 4-connected with C, and C is 4-connected with B.
Let's assume that the plane doesn't contain blocked points. Consider all the integral points of the plane whose Euclidean distance from the origin is no more than n, we'll name these points special. Chubby Yang wants to get the following property: no special point is 4-connected to some non-special point. To get the property she can pick some integral points of the plane and make them blocked. What is the minimum number of points she needs to pick?
Input
The first line contains an integer n (0 ≤ n ≤ 4·107).
Output
Print a single integer — the minimum number of points that should be blocked.
Examples
Input
1
Output
4
Input
2
Output
8
Input
3
Output
16
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 3\\n3 2 1\\n1 2 3\\n4 5 6\\n\", \"4 3\\n1 2 3\\n4 5 6\\n7 8 9\\n10 11 12\\n\", \"3 4\\n1 6 3 4\\n5 10 7 8\\n9 2 11 12\\n\", \"3 4\\n45240 150726 140481 81046\\n5 6 7 169420\\n50454 36955 72876 12\\n\", \"3 4\\n5 6 7 8\\n9 10 11 12\\n1 2 3 4\\n\", \"3 6\\n155286 63165 3 174888 10886 6\\n84369 8 96576 10 43333 19319\\n13 56272 34110 182368 17 64349\\n\", \"3 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n1 2 3 4 5 6\\n\", \"3 8\\n1 162585 100772 4 61260 6 68011 8\\n152705 26104 132471 137535 186316 160193 15 36618\\n15446 18 19 94134 21 139885 176988 13799\\n\", \"3 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 5 6 7 8\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 94346 14148\\n145279 56741 146667 90808\\n149476 14 66548 61472\\n22435 36909 52368 79274\\n193242 75919 23 24\\n84776 141638 98306 75212\\n\", \"7 4\\n5 6 7 8\\n9 10 11 12\\n13 14 15 16\\n17 18 19 20\\n21 22 23 24\\n25 26 27 28\\n1 2 3 4\\n\", \"7 6\\n42104 92376 101047 169739 147311 6\\n9571 14822 9 147008 108070 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 97760 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 101237\\n\", \"7 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n19 20 21 22 23 24\\n25 26 27 28 29 30\\n31 32 33 34 35 36\\n37 38 39 40 41 42\\n1 2 3 4 5 6\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 78160\\n20802 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 39 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 102522\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n25 26 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n41 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 7 8\\n\", \"5 5\\n139628 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 132566 146556 180355\\n16 67801 18 34741 17005\\n58839 22 68501 5473 25\\n\", \"7 6\\n42104 92376 101047 169739 147311 6\\n9571 14822 9 147008 108070 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 97760 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 101237\\n\", \"3 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 5 6 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 78160\\n20802 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 39 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 102522\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 94346 14148\\n145279 56741 146667 90808\\n149476 14 66548 61472\\n22435 36909 52368 79274\\n193242 75919 23 24\\n84776 141638 98306 75212\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n25 26 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n41 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 7 8\\n\", \"3 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n1 2 3 4 5 6\\n\", \"3 4\\n5 6 7 8\\n9 10 11 12\\n1 2 3 4\\n\", \"7 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n19 20 21 22 23 24\\n25 26 27 28 29 30\\n31 32 33 34 35 36\\n37 38 39 40 41 42\\n1 2 3 4 5 6\\n\", \"5 5\\n139628 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 132566 146556 180355\\n16 67801 18 34741 17005\\n58839 22 68501 5473 25\\n\", \"3 4\\n45240 150726 140481 81046\\n5 6 7 169420\\n50454 36955 72876 12\\n\", \"4 4\\n17 18 19 20\\n17 18 19 20\\n17 18 19 20\\n17 18 19 20\\n\", \"3 6\\n155286 63165 3 174888 10886 6\\n84369 8 96576 10 43333 19319\\n13 56272 34110 182368 17 64349\\n\", \"3 8\\n1 162585 100772 4 61260 6 68011 8\\n152705 26104 132471 137535 186316 160193 15 36618\\n15446 18 19 94134 21 139885 176988 13799\\n\", \"7 4\\n5 6 7 8\\n9 10 11 12\\n13 14 15 16\\n17 18 19 20\\n21 22 23 24\\n25 26 27 28\\n1 2 3 4\\n\", \"7 6\\n42104 92376 101047 169739 147311 6\\n9571 14822 9 147008 108070 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 97760 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"3 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 3 6 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 78160\\n20802 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 39 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 56741 146667 90808\\n149476 14 66548 61472\\n22435 36909 52368 79274\\n193242 75919 23 24\\n84776 141638 98306 75212\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 23 24\\n25 26 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n74 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 7 8\\n\", \"3 6\\n7 8 3 10 11 12\\n13 14 15 16 17 18\\n1 2 3 4 5 6\\n\", \"3 4\\n5 8 7 8\\n9 10 11 12\\n1 2 3 4\\n\", \"7 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n19 20 21 22 23 24\\n26 26 27 28 29 30\\n31 32 33 34 35 36\\n37 38 39 40 41 42\\n1 2 3 4 5 6\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 132566 146556 180355\\n16 67801 18 34741 17005\\n58839 22 68501 5473 25\\n\", \"3 4\\n45240 150726 140481 81046\\n5 6 7 169420\\n50454 18512 72876 12\\n\", \"4 4\\n17 18 19 20\\n17 18 19 20\\n17 18 35 20\\n17 18 19 20\\n\", \"4 3\\n1 2 3\\n4 5 6\\n7 8 9\\n10 4 12\\n\", \"3 8\\n9 10 11 17 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 3 6 7 8\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 39 24\\n25 26 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n74 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 7 8\\n\", \"3 4\\n5 8 7 8\\n9 10 11 21\\n1 2 3 4\\n\", \"7 6\\n7 8 9 10 11 12\\n13 14 15 16 17 18\\n19 20 21 22 23 24\\n26 26 27 28 29 30\\n31 0 33 34 35 36\\n37 38 39 40 41 42\\n1 2 3 4 5 6\\n\", \"3 6\\n155286 63165 3 174888 10886 6\\n84369 8 96576 16 43333 19319\\n13 53784 34110 182368 17 64349\\n\", \"4 3\\n1 2 3\\n4 5 6\\n7 16 9\\n10 4 12\\n\", \"3 4\\n5 8 7 8\\n12 10 11 21\\n1 2 3 4\\n\", \"4 3\\n1 2 3\\n4 5 9\\n7 16 9\\n10 4 12\\n\", \"3 8\\n9 9 11 17 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 1 6 7 8\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 56741 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 12386 13 24\\n84776 141638 98306 75212\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 39 24\\n25 32 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n74 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 6 8\\n\", \"3 6\\n7 1 3 15 11 12\\n13 14 15 16 17 12\\n1 2 3 4 5 6\\n\", \"4 3\\n1 2 1\\n4 5 9\\n7 16 9\\n10 4 12\\n\", \"3 6\\n5 1 3 15 11 12\\n13 14 15 16 17 12\\n1 2 3 4 5 6\\n\", \"4 3\\n1 2 1\\n5 5 9\\n7 16 9\\n10 4 12\\n\", \"3 8\\n9 9 11 17 13 14 15 16\\n17 18 33 20 21 22 15 24\\n1 2 3 4 1 4 7 8\\n\", \"3 6\\n155286 63165 3 174888 10886 6\\n84369 8 96576 10 43333 19319\\n13 53784 34110 182368 17 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 132471 137535 186316 160193 15 36618\\n15446 18 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 147311 6\\n9571 14822 9 147008 108070 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 132079\\n20802 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 39 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 56741 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 75919 23 24\\n84776 141638 98306 75212\\n\", \"3 6\\n7 8 3 10 11 12\\n13 14 15 16 17 12\\n1 2 3 4 5 6\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 243005 146556 180355\\n16 67801 18 34741 17005\\n58839 22 68501 5473 25\\n\", \"4 4\\n17 18 19 20\\n17 18 19 20\\n17 18 35 20\\n17 18 19 4\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 137535 186316 160193 15 36618\\n15446 18 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 256939 6\\n9571 14822 9 147008 108070 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"3 8\\n9 10 11 17 13 14 15 16\\n17 18 19 20 21 22 23 24\\n1 2 3 4 1 6 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 132079\\n20802 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 56741 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 12386 23 24\\n84776 141638 98306 75212\\n\", \"7 8\\n9 10 11 12 13 14 15 16\\n17 18 19 20 21 22 39 24\\n25 26 27 28 29 30 31 32\\n33 34 35 36 37 38 39 40\\n74 42 43 44 45 46 47 48\\n49 50 51 52 53 54 55 56\\n1 2 3 4 5 6 6 8\\n\", \"3 6\\n7 8 3 15 11 12\\n13 14 15 16 17 12\\n1 2 3 4 5 6\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 243005 146556 180355\\n16 51169 18 34741 17005\\n58839 22 68501 5473 25\\n\", \"4 4\\n7 18 19 20\\n17 18 19 20\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 174888 10886 6\\n84369 8 96576 16 43333 19319\\n13 53784 34110 182368 17 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 137535 186316 160193 15 59037\\n15446 18 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 256939 6\\n9571 14822 9 147008 13579 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 132079\\n23197 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 43 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"3 4\\n5 8 7 8\\n12 10 11 21\\n1 2 0 4\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 243005 146556 180355\\n16 51169 18 34741 17005\\n34511 22 68501 5473 25\\n\", \"4 4\\n7 18 19 20\\n17 18 19 34\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 247433 10886 6\\n84369 8 96576 16 43333 19319\\n13 53784 34110 182368 17 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 137535 186316 160193 15 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n153044 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"3 8\\n9 9 11 17 13 14 15 16\\n17 18 33 20 21 22 23 24\\n1 2 3 4 1 6 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 35760 132079\\n23197 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 56741 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 12521 13 24\\n84776 141638 98306 75212\\n\", \"3 4\\n5 2 7 8\\n12 10 11 21\\n1 2 0 4\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 68418\\n180173 10513 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 22 68501 5473 25\\n\", \"4 4\\n7 18 19 20\\n17 36 19 34\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 247433 10886 6\\n84369 8 96576 16 43333 3937\\n13 53784 34110 182368 17 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 137535 186316 160193 5 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 78694 117083\\n146754 101724 84463 16093 23 85271\\n125995 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"3 8\\n9 9 11 17 13 14 15 16\\n17 18 33 20 21 22 15 24\\n1 2 3 4 1 6 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 67861 132079\\n23197 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 14148\\n145279 102835 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 12521 13 24\\n84776 141638 98306 75212\\n\", \"3 6\\n5 1 3 15 11 12\\n13 14 15 16 21 12\\n1 2 3 4 5 6\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 135402\\n180173 10513 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 22 68501 5473 25\\n\", \"4 4\\n7 18 19 40\\n17 36 19 34\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 247433 10886 6\\n84369 8 96576 16 43333 3937\\n13 22483 34110 182368 17 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 192100 186316 160193 5 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n42104 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 37463 117083\\n146754 101724 84463 16093 23 85271\\n125995 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 67861 132079\\n25668 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 134957 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"7 4\\n1 60204 147610 128455\\n77665 191006 2970 24587\\n145279 102835 146667 90808\\n267304 14 66548 61472\\n22435 36909 52368 79274\\n193242 12521 13 24\\n84776 141638 98306 75212\\n\", \"3 6\\n5 1 3 15 11 12\\n13 14 15 16 21 12\\n1 2 3 4 5 4\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 135402\\n180173 10513 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 26 68501 5473 25\\n\", \"4 4\\n7 18 33 40\\n17 36 19 34\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 247433 10886 6\\n84369 8 96576 16 43333 3937\\n13 22483 34110 182368 25 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 26104 39420 192100 186316 243428 5 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n6519 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 37463 117083\\n146754 101724 84463 16093 23 85271\\n125995 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"3 8\\n9 9 11 17 13 14 15 16\\n17 7 33 20 21 22 15 24\\n1 2 3 4 1 4 7 8\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 169892 183765 84737 20941 67861 132079\\n25668 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 88829 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"3 6\\n5 1 3 15 11 12\\n13 14 15 16 24 12\\n1 2 3 4 5 4\\n\", \"5 5\\n19390 7289 133246 4 100049\\n93243 178407 150269 173728 135402\\n180173 15446 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 26 68501 5473 25\\n\", \"4 4\\n7 18 33 40\\n1 36 19 34\\n17 18 35 20\\n17 18 19 4\\n\", \"3 6\\n42197 63165 3 247433 10886 6\\n84369 8 96576 16 43333 3937\\n13 22483 34110 182368 46 64349\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 8\\n152705 50647 39420 192100 186316 243428 5 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n6519 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 37463 117083\\n146754 1272 84463 16093 23 85271\\n125995 126675 108371 28 109820 108330\\n31 199814 151856 198623 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 233834 183765 84737 20941 67861 132079\\n25668 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 197880 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 88829 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"3 6\\n5 1 3 15 11 12\\n13 14 15 16 24 12\\n1 2 3 4 7 4\\n\", \"5 5\\n19390 7289 133246 4 80326\\n93243 178407 150269 173728 135402\\n180173 15446 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 26 68501 5473 25\\n\", \"4 4\\n7 18 33 40\\n1 36 19 34\\n17 18 35 20\\n17 11 19 4\\n\", \"3 8\\n1 162585 158991 4 61260 6 68011 15\\n152705 50647 39420 192100 186316 243428 5 59037\\n15446 32 19 94134 21 139885 176988 13799\\n\", \"7 6\\n6519 92376 101047 169739 256939 6\\n9571 14822 9 147008 4993 179082\\n42935 148636 150709 15634 37463 117083\\n146754 1272 84463 16093 23 85271\\n125995 126675 108371 28 109820 108330\\n31 199814 151856 310372 36887 193019\\n22816 38 109267 70208 194429 65721\\n\", \"7 8\\n110137 66175 74657 124739 63011 153464 30956 8\\n9 62369 233834 183765 84737 20941 67861 132079\\n25668 67434 149925 53269 150062 35286 50218 112696\\n153864 26 7405 121648 170439 115181 195278 127323\\n136381 67081 57522 109132 104537 38 66 47930\\n51739 77547 48 169711 18955 88829 7223 37489\\n53153 108446 191956 52 53 31941 114019 115410\\n\", \"5 5\\n19390 7289 133246 4 80326\\n93243 178407 150269 173728 135402\\n180173 15446 243005 146556 246420\\n16 51169 18 34741 17005\\n34511 26 68501 4696 25\\n\", \"4 4\\n7 18 33 40\\n1 36 19 34\\n17 18 35 20\\n17 22 19 4\\n\", 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\"0\\n\"]}", "source": "taco"}
|
You are given a rectangular matrix of size $n \times m$ consisting of integers from $1$ to $2 \cdot 10^5$.
In one move, you can: choose any element of the matrix and change its value to any integer between $1$ and $n \cdot m$, inclusive; take any column and shift it one cell up cyclically (see the example of such cyclic shift below).
A cyclic shift is an operation such that you choose some $j$ ($1 \le j \le m$) and set $a_{1, j} := a_{2, j}, a_{2, j} := a_{3, j}, \dots, a_{n, j} := a_{1, j}$ simultaneously. [Image] Example of cyclic shift of the first column
You want to perform the minimum number of moves to make this matrix look like this: $\left. \begin{array}{|c c c c|} \hline 1 & {2} & {\ldots} & {m} \\{m + 1} & {m + 2} & {\ldots} & {2m} \\{\vdots} & {\vdots} & {\ddots} & {\vdots} \\{(n - 1) m + 1} & {(n - 1) m + 2} & {\ldots} & {nm} \\ \hline \end{array} \right.$
In other words, the goal is to obtain the matrix, where $a_{1, 1} = 1, a_{1, 2} = 2, \dots, a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, \dots, a_{n, m} = n \cdot m$ (i.e. $a_{i, j} = (i - 1) \cdot m + j$) with the minimum number of moves performed.
-----Input-----
The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5, n \cdot m \le 2 \cdot 10^5$) — the size of the matrix.
The next $n$ lines contain $m$ integers each. The number at the line $i$ and position $j$ is $a_{i, j}$ ($1 \le a_{i, j} \le 2 \cdot 10^5$).
-----Output-----
Print one integer — the minimum number of moves required to obtain the matrix, where $a_{1, 1} = 1, a_{1, 2} = 2, \dots, a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, \dots, a_{n, m} = n \cdot m$ ($a_{i, j} = (i - 1)m + j$).
-----Examples-----
Input
3 3
3 2 1
1 2 3
4 5 6
Output
6
Input
4 3
1 2 3
4 5 6
7 8 9
10 11 12
Output
0
Input
3 4
1 6 3 4
5 10 7 8
9 2 11 12
Output
2
-----Note-----
In the first example, you can set $a_{1, 1} := 7, a_{1, 2} := 8$ and $a_{1, 3} := 9$ then shift the first, the second and the third columns cyclically, so the answer is $6$. It can be shown that you cannot achieve a better answer.
In the second example, the matrix is already good so the answer is $0$.
In the third example, it is enough to shift the second column cyclically twice to obtain a good matrix, so the answer is $2$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"2\\n1\\n4\", \"2\\n1\\n3\", \"2\\n2\\n4\", \"2\\n2\\n8\", \"2\\n4\\n4\", \"2\\n2\\n7\", \"2\\n4\\n8\", \"2\\n2\\n13\", \"2\\n8\\n8\", \"2\\n2\\n26\", \"2\\n5\\n8\", \"2\\n1\\n26\", \"2\\n1\\n8\", \"2\\n1\\n41\", \"2\\n8\\n3\", \"2\\n6\\n4\", \"2\\n3\\n7\", \"2\\n4\\n13\", \"2\\n2\\n2\", \"2\\n1\\n2\", \"2\\n5\\n6\", \"2\\n1\\n14\", \"2\\n2\\n49\", \"2\\n1\\n6\", \"2\\n2\\n1\", \"2\\n3\\n23\", \"2\\n4\\n2\", \"2\\n3\\n1\", \"2\\n1\\n1\", \"2\\n5\\n1\", \"2\\n6\\n2\", \"2\\n8\\n2\", \"2\\n8\\n7\", \"2\\n1\\n72\", \"2\\n8\\n1\", \"2\\n13\\n3\", \"2\\n3\\n49\", \"2\\n6\\n23\", \"2\\n14\\n1\", \"2\\n6\\n15\", \"2\\n8\\n20\", \"2\\n13\\n5\", \"2\\n3\\n87\", \"2\\n21\\n1\", \"2\\n15\\n20\", \"2\\n21\\n2\", \"2\\n18\\n2\", \"2\\n5\\n48\", \"2\\n2\\n87\", \"2\\n14\\n8\", \"2\\n10\\n22\", \"2\\n2\\n158\", \"2\\n4\\n158\", \"2\\n9\\n43\", \"2\\n34\\n1\", \"2\\n6\\n158\", \"2\\n28\\n13\", \"2\\n12\\n191\", \"2\\n101\\n1\", \"2\\n13\\n37\", \"2\\n13\\n65\", \"2\\n8\\n237\", \"2\\n100\\n2\", \"2\\n14\\n108\", \"2\\n18\\n23\", \"2\\n23\\n4\", \"2\\n8\\n129\", \"2\\n23\\n7\", \"2\\n21\\n114\", \"2\\n25\\n193\", \"2\\n11\\n55\", \"2\\n21\\n61\", \"2\\n4\\n123\", \"2\\n21\\n8\", \"2\\n7\\n123\", \"2\\n37\\n10\", \"2\\n67\\n10\", \"2\\n38\\n107\", \"2\\n38\\n86\", \"2\\n7\\n55\", \"2\\n2\\n91\", \"2\\n1\\n158\", \"2\\n65\\n1\", \"2\\n5\\n280\", \"2\\n8\\n379\", \"2\\n14\\n204\", \"2\\n25\\n333\", \"2\\n67\\n13\", \"2\\n65\\n107\", \"2\\n28\\n35\", \"2\\n38\\n154\", \"2\\n17\\n314\", \"2\\n3\\n303\", \"2\\n35\\n4\", \"2\\n5\\n482\", \"2\\n14\\n383\", \"2\\n25\\n538\", \"2\\n21\\n24\", \"2\\n122\\n13\", \"2\\n2\\n246\", \"2\\n1\\n91\", \"2\\n1\\n4\"], \"outputs\": [\"1\\n3\", \"1\\n3\\n\", \"2\\n3\\n\", \"2\\n5\\n\", \"3\\n3\\n\", \"2\\n4\\n\", \"3\\n5\\n\", \"2\\n6\\n\", \"5\\n5\\n\", \"2\\n7\\n\", \"4\\n5\\n\", \"1\\n7\\n\", \"1\\n5\\n\", \"1\\n8\\n\", \"5\\n3\\n\", \"4\\n3\\n\", \"3\\n4\\n\", \"3\\n6\\n\", \"2\\n2\\n\", \"1\\n2\\n\", \"4\\n4\\n\", \"1\\n6\\n\", \"2\\n8\\n\", \"1\\n4\\n\", \"2\\n1\\n\", \"3\\n7\\n\", \"3\\n2\\n\", \"3\\n1\\n\", \"1\\n1\\n\", \"4\\n1\\n\", \"4\\n2\\n\", \"5\\n2\\n\", \"5\\n4\\n\", \"1\\n9\\n\", \"5\\n1\\n\", \"6\\n3\\n\", \"3\\n8\\n\", \"4\\n7\\n\", \"6\\n1\\n\", \"4\\n6\\n\", \"5\\n6\\n\", \"6\\n4\\n\", \"3\\n9\\n\", \"7\\n1\\n\", \"6\\n6\\n\", \"7\\n2\\n\", \"6\\n2\\n\", \"4\\n8\\n\", \"2\\n9\\n\", \"6\\n5\\n\", \"5\\n7\\n\", \"2\\n11\\n\", \"3\\n11\\n\", \"5\\n8\\n\", \"8\\n1\\n\", \"4\\n11\\n\", \"7\\n6\\n\", \"5\\n11\\n\", \"10\\n1\\n\", \"6\\n8\\n\", \"6\\n9\\n\", \"5\\n12\\n\", \"10\\n2\\n\", \"6\\n10\\n\", \"6\\n7\\n\", \"7\\n3\\n\", \"5\\n10\\n\", \"7\\n4\\n\", \"7\\n10\\n\", \"7\\n11\\n\", \"5\\n9\\n\", \"7\\n9\\n\", \"3\\n10\\n\", \"7\\n5\\n\", \"4\\n10\\n\", \"8\\n5\\n\", \"9\\n5\\n\", \"8\\n10\\n\", \"8\\n9\\n\", \"4\\n9\\n\", \"2\\n10\\n\", \"1\\n11\\n\", \"9\\n1\\n\", \"4\\n12\\n\", \"5\\n13\\n\", \"6\\n11\\n\", \"7\\n12\\n\", \"9\\n6\\n\", \"9\\n10\\n\", \"7\\n8\\n\", \"8\\n11\\n\", \"6\\n12\\n\", \"3\\n12\\n\", \"8\\n3\\n\", \"4\\n13\\n\", \"6\\n13\\n\", \"7\\n13\\n\", \"7\\n7\\n\", \"10\\n6\\n\", \"2\\n12\\n\", \"1\\n10\\n\", \"1\\n3\\n\"]}", "source": "taco"}
|
Read problems statements in Mandarin Chinese and Russian.
Aditi recently discovered a new magic trick. First, she gives you an integer N and asks you to think an integer between 1 and N. Then she gives you a bundle of cards each having a sorted list (in ascending order) of some distinct integers written on it. The integers in all the lists are between 1 and N. Note that the same integer may appear in more than one card. Now, she shows you these cards one by one and asks whether the number you thought is written on the card or not. After that, she immediately tells you the integer you had thought of.
Seeing you thoroughly puzzled, she explains that she can apply the trick so fast because she is just adding the first integer written on the cards that contain the integer you had thought of, and then gives the sum as the answer. She calls a bundle interesting if when the bundle is lexicographically sorted, no two consecutive cards have any number in common. Now she challenges you to find out the minimum number of cards she will need for making an interesting bundle such that the magic trick will work every time.
------ Input ------
The first line of the input contains an integer T denoting the number of test cases.
Each test case contains a line with a single integer N.
------ Output ------
For each test case, output a line containing a single integer denoting the minimum number of cards required.
------ Constraints ------
1 ≤ T ≤ 10^{5}
1 ≤ N ≤ 10^{18}
------ Sub tasks ------
Subtask #1: 1 ≤ T ≤ 10, 1 ≤ N ≤ 10 (5 points)
Subtask #2: 1 ≤ T ≤ 100, 1 ≤ N ≤ 1000 (10 points)
Subtask #3: Original Constraints (85 points)
----- Sample Input 1 ------
2
1
4
----- Sample Output 1 ------
1
3
----- explanation 1 ------
In example 1, only 1 card containing {1} will work.
In example 2, make 3 cards containing {1,4}, {2} and {3,4}.
Assume you thought of 1, then you will select the 1st card {1,4}, then she will correctly figure out the integer you thought being 1.
Assume you thought of 2, then you will select the 2nd card {2}, then she will correctly figure out the integer you thought being 2.
Assume you thought of 3, then you will select the 3rd card {3,4}, then she will correctly figure out the integer you thought being 3.
Assume you thought of 4, then you will select 1st card {1,4} and 3rd card {3,4}, then she will calculate the sum of the first integers of the two card 1 + 3 = 4, and she will answer it.
Thus her trick will work well in every case. And we can check it easily that the cards are sorted in lexicographical order and two consecutive cards have no common integers.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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1010000000\\n5 6 1000000001\\n6 7 1000000000\\n7 1 1000000000\\n\", \"6 6 5\\n1 2 1000000000\\n2 3 1000000000\\n3 6 1000000100\\n3 5 1\\n4 6 1\\n1 6 2\\n\", \"10 10 4\\n1 2 1000000000\\n2 3 1\\n3 5 1000000000\\n4 5 1000000000\\n3 6 1000001000\\n6 7 1000000000\\n7 8 1\\n8 9 1000000000\\n9 10 1000000000\\n8 10 1\\n\", \"5 5 4\\n1 2 1553634918\\n2 3 999999999\\n3 4 999999999\\n1 5 606988161\\n5 4 999999999\\n\", \"6 6 5\\n1 2 1000000000\\n2 3 1000000010\\n3 6 1000000100\\n3 5 1\\n4 6 1\\n1 6 2\\n\", \"7 7 4\\n1 2 1000000000\\n2 3 1000100000\\n3 7 2\\n7 5 1\\n3 4 1100000000\\n4 5 1000000000\\n4 7 1\\n\", \"6 6 5\\n1 2 1000000000\\n2 5 1000000010\\n3 6 1000000100\\n3 5 1\\n4 6 1\\n1 6 2\\n\", \"7 7 4\\n1 2 1000000001\\n2 3 1000100000\\n3 7 2\\n7 5 1\\n3 4 1100000000\\n4 5 1000000000\\n4 7 1\\n\", \"6 6 5\\n1 2 1000000000\\n2 5 1000000010\\n3 1 1000000100\\n3 5 1\\n4 6 1\\n1 6 2\\n\", \"6 6 5\\n1 2 1000000000\\n2 5 1000000010\\n3 1 1000000100\\n3 5 1\\n4 6 1\\n1 6 1\\n\", \"7 7 10\\n1 2 1000000000\\n2 3 1000000000\\n3 4 1000000000\\n4 5 1000000000\\n5 6 1000000000\\n6 7 1000000000\\n7 1 1000000000\\n\", \"10 10 4\\n1 2 1000000000\\n2 3 1\\n3 4 1000000000\\n4 5 1000000000\\n5 10 1000000000\\n6 7 1000000000\\n7 8 1\\n8 9 1000000000\\n9 10 1000000000\\n8 10 1\\n\", \"7 7 4\\n1 2 1000000000\\n2 3 1000000000\\n3 7 1\\n7 5 1\\n3 4 1000000000\\n3 5 1000000000\\n4 6 1\\n\", \"4 4 0\\n1 2 1\\n2 3 1\\n3 4 1\\n1 4 0\\n\", \"6 3 3\\n1 2 1000000000\\n2 3 1000000000\\n3 4 1000000000\\n\", \"6 6 4\\n1 2 947932848\\n2 5 932847264\\n3 4 994392894\\n1 5 447264976\\n5 4 983472874\\n5 6 236174687\\n\", \"5 5 4\\n1 2 999999999\\n2 3 584343222\\n3 4 999999999\\n1 5 309966577\\n5 4 999999999\\n\", \"7 5 0\\n4 1 8\\n2 4 1\\n2 1 3\\n3 4 17\\n3 1 5\\n\", \"7 7 5\\n1 2 1000000000\\n2 3 1000100000\\n3 7 2\\n7 5 1\\n3 4 1000000000\\n4 5 1000000000\\n4 6 1\\n\", \"5 5 5\\n1 2 1553634918\\n2 3 999999999\\n3 4 999999999\\n1 5 309966577\\n5 4 999999999\\n\", \"10 10 4\\n1 2 1000000000\\n2 3 1\\n3 5 1000000000\\n4 5 1000000000\\n3 6 1000001000\\n6 5 1000000000\\n7 8 1\\n8 9 1000000000\\n9 10 1000000000\\n8 10 1\\n\", \"7 7 4\\n1 2 0000000000\\n2 3 1000100000\\n3 7 2\\n7 5 1\\n3 4 1000000000\\n4 5 1000000000\\n4 7 1\\n\", \"4 5 2\\n4 1 8\\n2 4 1\\n2 1 3\\n3 4 9\\n3 1 5\\n\", \"3 3 2\\n1 2 1\\n3 2 1\\n1 3 3\\n\"], \"outputs\": [\"2\\n1 2 \", \"2\\n3 2 \", \"4\\n1 4 2 5 \", \"0\\n\", \"3\\n1 2 3 \", \"4\\n4 1 6 2 \", \"4\\n4 1 2 5 \", \"0\\n\", \"5\\n1 2 4 6 5 \", \"4\\n1 2 3 4 \", \"7\\n1 5 4 6 7 8 2 \", \"4\\n1 5 2 6 \", \"4\\n1 5 2 6 \", \"5\\n1 2 3 4 5 \", \"4\\n1 2 3 4 \", \"6\\n1 7 2 6 3 5 \", \"6\\n1 2 4 5 6 7 \", \"7\\n1 5 4 6 7 8 2 \\n\", \"4\\n4 1 2 5 \", \"6\\n1 2 4 5 6 7 \", \"4\\n4 1 6 2 \", \"6\\n1 7 2 6 3 5 \", \"5\\n1 2 4 6 5 \\n\", \"4\\n1 2 3 4 \", \"4\\n1 2 3 4 \\n\", \"0\\n\", \"4\\n1 4 2 5 \", \"4\\n1 5 2 6 \", \"5\\n1 2 3 4 5 \", \"0\\n\", \"4\\n1 5 2 6 \", \"3\\n1 2 3 \", \"4\\n1 4 2 5\\n\", \"4\\n4 6 1 5\\n\", \"6\\n1 7 2 6 3 5\\n\", \"5\\n6 5 1 3 4\\n\", \"4\\n1 2 3 5\\n\", \"4\\n1 2 3 4\\n\", \"4\\n4 1 5 2\\n\", \"5\\n1 2 3 4 5\\n\", \"0\\n\\n\", \"4\\n1 5 2 6\\n\", \"3\\n1 2 3\\n\", \"4\\n4 6 1 2\\n\", \"4\\n4 5 1 3\\n\", \"4\\n4 6 5 1\\n\", \"4\\n1 2 3 7\\n\", \"6\\n1 2 6 4 8 7\\n\", \"4\\n4 1 6 2\\n\", \"4\\n1 5 6 4\\n\", \"2\\n3 2\\n\", \"4\\n2 1 4 3\\n\", \"4\\n1 2 5 3\\n\", \"4\\n1 3 4 5\\n\", \"6\\n1 2 7 3 6 5\\n\", \"4\\n1 2 4 3\\n\", \"6\\n1 7 2 3 6 5\\n\", \"4\\n1 4 2 5\\n\", \"6\\n1 7 2 6 3 5\\n\", \"5\\n6 5 1 3 4\\n\", \"4\\n1 2 3 5\\n\", \"4\\n1 2 3 4\\n\", \"5\\n1 2 3 4 5\\n\", \"0\\n\\n\", \"4\\n1 5 2 6\\n\", \"3\\n1 2 3\\n\", \"4\\n1 4 2 5\\n\", \"6\\n1 7 2 6 3 5\\n\", \"5\\n6 5 1 3 4\\n\", \"4\\n1 2 3 5\\n\", \"4\\n4 1 5 2\\n\", \"5\\n6 5 1 3 4\\n\", \"4\\n1 2 3 7\\n\", \"5\\n6 5 1 3 4\\n\", \"4\\n1 2 3 7\\n\", \"5\\n6 5 1 3 4\\n\", \"5\\n6 5 1 3 4\\n\", \"6\\n1 7 2 6 3 5\\n\", \"4\\n1 2 3 4\\n\", \"4\\n1 2 3 4\\n\", \"0\\n\\n\", \"3\\n1 2 3\\n\", \"4\\n4 6 1 5\\n\", \"4\\n4 1 5 2\\n\", \"0\\n\\n\", \"5\\n1 2 3 4 5\\n\", \"4\\n4 5 1 3\\n\", \"4\\n1 2 3 5\\n\", \"4\\n1 2 3 7\\n\", \"2\\n3 2 \\n\", \"2\\n1 2 \"]}", "source": "taco"}
|
You are given an undirected connected weighted graph consisting of $n$ vertices and $m$ edges. Let's denote the length of the shortest path from vertex $1$ to vertex $i$ as $d_i$.
You have to erase some edges of the graph so that at most $k$ edges remain. Let's call a vertex $i$ good if there still exists a path from $1$ to $i$ with length $d_i$ after erasing the edges.
Your goal is to erase the edges in such a way that the number of good vertices is maximized.
-----Input-----
The first line contains three integers $n$, $m$ and $k$ ($2 \le n \le 3 \cdot 10^5$, $1 \le m \le 3 \cdot 10^5$, $n - 1 \le m$, $0 \le k \le m$) — the number of vertices and edges in the graph, and the maximum number of edges that can be retained in the graph, respectively.
Then $m$ lines follow, each containing three integers $x$, $y$, $w$ ($1 \le x, y \le n$, $x \ne y$, $1 \le w \le 10^9$), denoting an edge connecting vertices $x$ and $y$ and having weight $w$.
The given graph is connected (any vertex can be reached from any other vertex) and simple (there are no self-loops, and for each unordered pair of vertices there exists at most one edge connecting these vertices).
-----Output-----
In the first line print $e$ — the number of edges that should remain in the graph ($0 \le e \le k$).
In the second line print $e$ distinct integers from $1$ to $m$ — the indices of edges that should remain in the graph. Edges are numbered in the same order they are given in the input. The number of good vertices should be as large as possible.
-----Examples-----
Input
3 3 2
1 2 1
3 2 1
1 3 3
Output
2
1 2
Input
4 5 2
4 1 8
2 4 1
2 1 3
3 4 9
3 1 5
Output
2
3 2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Dima is a beginner programmer. During his working process, he regularly has to repeat the following operation again and again: to remove every second element from the array. One day he has been bored with easy solutions of this problem, and he has come up with the following extravagant algorithm.
Let's consider that initially array contains n numbers from 1 to n and the number i is located in the cell with the index 2i - 1 (Indices are numbered starting from one) and other cells of the array are empty. Each step Dima selects a non-empty array cell with the maximum index and moves the number written in it to the nearest empty cell to the left of the selected one. The process continues until all n numbers will appear in the first n cells of the array. For example if n = 4, the array is changing as follows: [Image]
You have to write a program that allows you to determine what number will be in the cell with index x (1 ≤ x ≤ n) after Dima's algorithm finishes.
-----Input-----
The first line contains two integers n and q (1 ≤ n ≤ 10^18, 1 ≤ q ≤ 200 000), the number of elements in the array and the number of queries for which it is needed to find the answer.
Next q lines contain integers x_{i} (1 ≤ x_{i} ≤ n), the indices of cells for which it is necessary to output their content after Dima's algorithm finishes.
-----Output-----
For each of q queries output one integer number, the value that will appear in the corresponding array cell after Dima's algorithm finishes.
-----Examples-----
Input
4 3
2
3
4
Output
3
2
4
Input
13 4
10
5
4
8
Output
13
3
8
9
-----Note-----
The first example is shown in the picture.
In the second example the final array is [1, 12, 2, 8, 3, 11, 4, 9, 5, 13, 6, 10, 7].
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n100 0\\n0 100\\n-100 0\\n0 -100\\n\", \"7\\n0 2\\n1 0\\n-3 0\\n0 -2\\n-1 -1\\n-1 -3\\n-2 -3\\n\", \"5\\n0 0\\n0 -1\\n3 0\\n-2 0\\n-2 1\\n\", \"5\\n0 0\\n2 0\\n0 -1\\n-2 0\\n-2 1\\n\", \"2\\n1000000000 1000000000\\n-1000000000 -1000000000\\n\", \"22\\n-1000000000 -379241\\n993438994 -993438994\\n-2792243 -997098738\\n-1000000000 -997098738\\n993927254 1000000000\\n-2792243 -1000000000\\n1000000000 -997098738\\n-1000000000 996340256\\n1000000000 -379241\\n993927254 -1000000000\\n993927254 -379241\\n-1000000000 3280503\\n-3280503 -993438994\\n-1000000000 1000000000\\n-999511740 -1000000000\\n-2792243 996340256\\n1000000000 996340256\\n-999511740 -379241\\n-1000000000 -993438994\\n3280503 -379241\\n-2792243 3280503\\n-2792243 1000000000\\n\", \"24\\n-4644147 4180336\\n-4644147 4180358\\n-4644147 4180263\\n-4644137 4180257\\n-4644147 4180326\\n-4644147 4180276\\n-4644121 4180308\\n-4644083 4180387\\n-4644021 4180308\\n-4644163 4180335\\n-4644055 4180308\\n-4644076 4180352\\n-4644167 4180276\\n-4644147 4180373\\n-4644147 4180208\\n-4644143 4180276\\n-4644148 4180208\\n-4644097 4180276\\n-4644137 4180208\\n-4644091 4180308\\n-4644147 4180308\\n-4644083 4180352\\n-4644083 4180308\\n-4644163 4180336\\n\", \"21\\n-2235473 -1822412\\n-2233347 -1822412\\n-2237427 -1819836\\n-2235793 -1822920\\n-2233226 -1821179\\n-2237815 -1822741\\n-2234032 -1820643\\n-2237697 -1819836\\n-2238771 -1821293\\n-2237815 -1823252\\n-2235473 -1821179\\n-2233347 -1822086\\n-2235458 -1822741\\n-2233347 -1822920\\n-2237697 -1821293\\n-2235793 -1822011\\n-2240159 -1821293\\n-2234032 -1822412\\n-2235458 -1821293\\n-2236502 -1822741\\n-2237934 -1822741\\n\", \"12\\n865737 66666\\n853908 65826\\n862461 66634\\n860656 66666\\n862461 67753\\n862461 76706\\n862461 66666\\n860656 61772\\n862461 70863\\n862461 72054\\n857836 66666\\n861300 66666\\n\", \"11\\n1582713 2131035\\n1582713 2130954\\n1582591 2130954\\n1582492 2130899\\n1582492 2131020\\n1582591 2131040\\n1582591 2130863\\n1582623 2130954\\n1582591 2130881\\n1582591 2130976\\n1582591 2130985\\n\", \"13\\n642780 1059073\\n642083 1062132\\n643081 1059073\\n643172 1060157\\n642083 1059073\\n642083 1059163\\n644820 1058821\\n643172 1059073\\n641626 1059073\\n644820 1059391\\n643758 1060157\\n642083 1060908\\n644820 1060318\\n\", \"24\\n-3446414 519980\\n-3446682 519752\\n-3446414 519851\\n-3446432 519536\\n-3446661 519718\\n-3446435 519752\\n-3446432 519581\\n-3446432 519717\\n-3446562 519771\\n-3446565 519752\\n-3446435 519706\\n-3446414 519752\\n-3446565 519723\\n-3446432 519752\\n-3446687 519771\\n-3446364 519752\\n-3446302 519851\\n-3446646 519771\\n-3446646 519718\\n-3446754 519718\\n-3446608 519771\\n-3446312 519851\\n-3446842 519718\\n-3446842 519681\\n\", \"26\\n-173159 -1020039\\n-174904 -1022178\\n-177226 -1022217\\n-173487 -1021789\\n-175402 -1022217\\n-173424 -1022795\\n-173487 -1019753\\n-173159 -1021557\\n-174812 -1021368\\n-173487 -1022178\\n-175345 -1021789\\n-174812 -1022741\\n-174812 -1022795\\n-173159 -1020997\\n-172034 -1019753\\n-175402 -1023393\\n-174812 -1022424\\n-175402 -1021695\\n-173487 -1023379\\n-171977 -1021789\\n-173159 -1021815\\n-175402 -1020997\\n-175402 -1021887\\n-172189 -1019753\\n-174986 -1022424\\n-174812 -1020997\\n\", \"5\\n-774946 2604878\\n-775018 2604878\\n-775018 2604957\\n-774943 2604957\\n-774861 2604957\\n\", \"5\\n783478 137368\\n783478 137395\\n784500 136450\\n784500 137368\\n783478 138286\\n\", \"28\\n-2278462 8387930\\n-2281240 8388856\\n-2280314 8387004\\n-2283092 8389782\\n-2279388 8388856\\n-2280314 8390708\\n-2284018 8390708\\n-2283092 8387930\\n-2281240 8389782\\n-2281240 8390708\\n-2279388 8387930\\n-2282166 8388856\\n-2279388 8390708\\n-2281240 8387930\\n-2280314 8389782\\n-2280314 8391634\\n-2280314 8387930\\n-2280314 8388856\\n-2284018 8389782\\n-2282166 8387930\\n-2282166 8390708\\n-2283092 8390708\\n-2283092 8388856\\n-2284018 8392560\\n-2283092 8392560\\n-2283092 8391634\\n-2282166 8389782\\n-2284018 8388856\\n\", \"3\\n587455 -1232164\\n587133 -1231842\\n587455 -1231842\\n\", \"8\\n1971603 5737002\\n1971603 5735418\\n1970811 5736210\\n1969227 5736210\\n1971603 5736210\\n1970019 5736210\\n1970019 5737002\\n1970811 5737002\\n\", \"4\\n1724432 -226596\\n1724432 -226121\\n1724432 -225646\\n1723957 -225171\\n\", \"6\\n-954200 -227581\\n-954261 -227581\\n-954261 -227642\\n-954200 -227520\\n-954139 -227642\\n-954139 -227703\\n\", \"2\\n1974595 1105366\\n1973034 1103805\\n\", \"11\\n-615244 7088010\\n-616180 7088634\\n-615868 7089570\\n-615868 7089258\\n-616180 7088946\\n-616180 7089570\\n-615868 7088634\\n-615556 7088634\\n-615244 7088322\\n-615868 7088322\\n-615868 7088946\\n\", \"21\\n3196350 998265036\\n-996504689 -1436003\\n1000000000 1000000000\\n1000000000 298961\\n999402078 -1436003\\n-999402078 1000000000\\n-298961 -1436003\\n3196350 1000000000\\n298961 298961\\n-1000000000 -1436003\\n1000000000 -1000000000\\n-1000000000 998265036\\n-996504689 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\"2435655\\n\", \"998965747\\n\", \"3128427\\n\", \"999399157\\n\", \"996719497\\n\", \"107643\\n\", \"217965\\n\", \"1734826\\n\", \"1000298961\\n\", \"893779\\n\", \"53595\\n\", \"2000000000\\n\", \"999193647\\n\", \"2\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\", \"2\", \"100\", \"2\"]}", "source": "taco"}
|
There are $n$ detachments on the surface, numbered from $1$ to $n$, the $i$-th detachment is placed in a point with coordinates $(x_i, y_i)$. All detachments are placed in different points.
Brimstone should visit each detachment at least once. You can choose the detachment where Brimstone starts.
To move from one detachment to another he should first choose one of four directions of movement (up, right, left or down) and then start moving with the constant speed of one unit interval in a second until he comes to a detachment. After he reaches an arbitrary detachment, he can repeat the same process.
Each $t$ seconds an orbital strike covers the whole surface, so at that moment Brimstone should be in a point where some detachment is located. He can stay with any detachment as long as needed.
Brimstone is a good commander, that's why he can create at most one detachment and place it in any empty point with integer coordinates he wants before his trip. Keep in mind that Brimstone will need to visit this detachment, too.
Help Brimstone and find such minimal $t$ that it is possible to check each detachment. If there is no such $t$ report about it.
-----Input-----
The first line contains a single integer $n$ $(2 \le n \le 1000)$ — the number of detachments.
In each of the next $n$ lines there is a pair of integers $x_i$, $y_i$ $(|x_i|, |y_i| \le 10^9)$ — the coordinates of $i$-th detachment.
It is guaranteed that all points are different.
-----Output-----
Output such minimal integer $t$ that it is possible to check all the detachments adding at most one new detachment.
If there is no such $t$, print $-1$.
-----Examples-----
Input
4
100 0
0 100
-100 0
0 -100
Output
100
Input
7
0 2
1 0
-3 0
0 -2
-1 -1
-1 -3
-2 -3
Output
-1
Input
5
0 0
0 -1
3 0
-2 0
-2 1
Output
2
Input
5
0 0
2 0
0 -1
-2 0
-2 1
Output
2
-----Note-----
In the first test it is possible to place a detachment in $(0, 0)$, so that it is possible to check all the detachments for $t = 100$. It can be proven that it is impossible to check all detachments for $t < 100$; thus the answer is $100$.
In the second test, there is no such $t$ that it is possible to check all detachments, even with adding at most one new detachment, so the answer is $-1$.
In the third test, it is possible to place a detachment in $(1, 0)$, so that Brimstone can check all the detachments for $t = 2$. It can be proven that it is the minimal such $t$.
In the fourth test, there is no need to add any detachments, because the answer will not get better ($t = 2$). It can be proven that it is the minimal such $t$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"10 2\\nLWL?WWDDW?\\n\", \"10 3\\nDWD?DL??LL\\n\", \"10 1\\nD??W?WL?DW\\n\", \"5 3\\n??D??\\n\", \"5 5\\n?WDDD\\n\", \"1 1\\n?\\n\", \"10 1\\nLWL?WWDDW?\\n\", \"10 2\\nD??W?WL?DW\\n\", \"20 7\\n?LLLLLWWWWW?????????\\n\", \"10 3\\nDWDLDL???L\\n\", \"3 1\\n??W\\n\", \"20 6\\n?LLLLLWWWWW?????????\\n\", \"10 3\\nLL??LD?DWD\\n\", \"10 2\\nLWL?WWDDW>\\n\", \"10 1\\nD??W?WL?DX\\n\", \"5 5\\nDDDW?\\n\", \"10 1\\n?WDDWW?LWL\\n\", \"10 2\\nWD?LW?W??D\\n\", \"10 0\\nLWL?WWDDW>\\n\", \"11 1\\nD??W?WL?DX\\n\", \"10 1\\n?WDCWW?LWL\\n\", \"10 1\\nWD?LW?W??D\\n\", \"13 1\\nD??W?WL?DX\\n\", \"15 1\\n?WDCWW?LWL\\n\", \"13 0\\nD??W?WL?DX\\n\", \"8 0\\nD??W?WL?DX\\n\", \"7 0\\nD??W?WL?DX\\n\", \"6 0\\nD??W?WL?DX\\n\", \"6 0\\nXD?LW?W??D\\n\", \"6 0\\nXD?LW?W?@D\\n\", \"2 0\\nXD?LW?W?@D\\n\", \"10 1\\nLWL?WWDDW>\\n\", \"14 1\\nD??W?WL?DW\\n\", \"1 2\\n?\\n\", \"6 1\\nW??\\n\", \"10 1\\nLWL?WVDDW?\\n\", \"11 1\\nD??W?WL?DW\\n\", \"5 10\\nDDDW?\\n\", \"5 1\\n??W\\n\", \"20 1\\n?WDDWW?LWL\\n\", \"11 0\\nD??W?WL?DX\\n\", \"10 0\\n?WDCWW?LWL\\n\", \"10 1\\nWD?LW?W?>D\\n\", \"13 1\\nXD?LW?W??D\\n\", \"13 1\\nD??W?WL?DW\\n\", \"12 0\\nD??W?WL?DX\\n\", \"6 0\\nD@?W?WL?DX\\n\", \"5 0\\nXD?LW?W??D\\n\", \"3 0\\nXD?LW?W?@D\\n\", \"14 1\\nWD?LW?W??D\\n\", \"1 4\\n?\\n\", \"6 1\\nW@?\\n\", \"10 1\\n?WDDVW?LWL\\n\", \"11 1\\nWD?LW?W??D\\n\", \"6 1\\n??W\\n\", \"20 0\\n?WDDWW?LWL\\n\", \"11 0\\nXD?LW?W??D\\n\", \"17 0\\n?WDCWW?LWL\\n\", \"10 1\\nD>?W?WL?DW\\n\", \"13 0\\nXD?LW?W??D\\n\", \"24 1\\nD??W?WL?DW\\n\", \"12 0\\nD??W?WL>DX\\n\", \"3 1\\nW??\\n\", \"3 2\\nL??\\n\", \"20 5\\n?LLLLLWWWWW?????????\\n\"], \"outputs\": [\"NO\\n\", \"DWDWDLLLLL\\n\", \"NO\\n\", \"WWDDW\\n\", \"NO\\n\", \"W\\n\", \"NO\\n\", \"DWLWLWLWDW\\n\", \"WLLLLLWWWWWWWWWWDDDW\\n\", \"DWDLDLWLLL\\n\", \"DDW\\n\", \"WLLLLLWWWWWWWWWDDDDW\\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\", \"LDL\\n\", \"WLLLLLWWWWWWWWDDDDDW\"]}", "source": "taco"}
|
Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser.
Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k.
Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost.
The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met:
* In the end the absolute difference between the number of wins and loses is equal to k;
* There is no hand such that the absolute difference before this hand was equal to k.
Help Roma to restore any such sequence.
Input
The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000).
The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence.
Output
If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO.
Otherwise print this sequence. If there are multiple answers, print any of them.
Examples
Input
3 2
L??
Output
LDL
Input
3 1
W??
Output
NO
Input
20 5
?LLLLLWWWWW?????????
Output
WLLLLLWWWWWWWWLWLWDW
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 0\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 109\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 10\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 0\\nC1 D 5\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 14\\nC1 D 13\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 84\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 17\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 90\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 14\\nC1 D 13\\nC2 L1 4\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 23\\nC1 D 13\\nC2 L1 4\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 0\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 8 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 61\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 10\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 11\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 13\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 1\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 10\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 11\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 64\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 22\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 1\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 4\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 11\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 64\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 11\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 2\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 6 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 10\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 107\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 6 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nB2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n000 70\\nH L1 5\\nC1 L1 17\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 15\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 90\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 6\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 103\\nH L1 5\\nC1 L1 14\\nC1 D 13\\nC2 L1 4\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 2 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 61\\nH L1 5\\nC1 L1 13\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 22\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 7\\nC2 D 13\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 1\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH M1 9\\nC1 D 11\\nC1 H 10\\nL1 D 10\\nC1 L1 40\\n2 1 4 6\\n100 64\\nH L1 5\\nC1 L1 12\\nC1 D 1\\nC2 L1 11\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 5\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n000 107\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 4 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 6 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 7 6\\n110 103\\nH L1 5\\nC1 L1 14\\nC1 D 13\\nC2 L1 4\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 6\\nC1 L1 20\\n2 2 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 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11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 2 6\\n100 109\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 0\\nC1 D 5\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 58\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 1 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 0\\n2 1 4 6\\n100 84\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 9\\nC1 L1 17\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 18\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 90\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC1 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 6\\nC1 L1 20\\n2 2 4 6\\n101 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 7\\nC2 L1 7\\nC2 D 13\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n110 70\\nH L1 10\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH M1 9\\nC1 D 11\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 64\\nH L1 5\\nC1 L1 4\\nC1 D 1\\nC2 L1 11\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n24\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nB2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 14\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 7\\n0 0 0 0\", \"1 1 2 5\\n37\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 6 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 83\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nB2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 1 4 6\\n000 70\\nH L1 5\\nC1 L1 17\\nC1 D 11\\nC2 L1 7\\nC2 D 14\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n110 61\\nH L1 5\\nC1 L1 13\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 111\\nH L1 5\\nC1 L1 12\\nC1 D 22\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 14\\nC2 L1 7\\nC2 D 10\\nL1 D 5\\n0 0 0 0\", \"1 1 2 5\\n27\\nH L1 5\\nC1 D 1\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 M1 20\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n13\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 2 4 6\\n100 112\\nH L1 10\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n68\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 6\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 14\\nC1 L2 24\\n2 1 4 6\\n000 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 0\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 58\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 0\\n2 1 4 6\\n100 84\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 12\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n68\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 21\\n2 1 4 6\\n100 90\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC1 D 7\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 13\\nL1 D 14\\nC1 L1 39\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 9\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 14\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 L1 10\\nC2 D -1\\nL1 D 7\\n0 0 0 0\", \"1 1 2 5\\n37\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 8 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n56\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n110 83\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nB2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 0 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n110 61\\nH L1 5\\nC1 L1 13\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n27\\nH L1 5\\nC1 D 1\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC2 M1 20\\nC1 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n13\\nH L1 18\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 24\\n2 2 4 6\\n100 112\\nH L1 10\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 12\\nL1 D 8\\n0 0 0 0\", \"1 1 4 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 2 6\\n100 109\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 M1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n29\\nH L1 9\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 1 6\\n110 130\\nH L1 5\\nC1 L1 12\\nC1 D 13\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 4\\nC1 H 13\\nL1 D 14\\nC1 L1 39\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 9\\nB1 D 11\\nC2 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n37\\nH L1 5\\nC1 D 9\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 8 6\\n110 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 10\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n27\\nH L1 5\\nC1 D 1\\nC1 H 12\\nL1 D 14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 3\\nC1 L1 12\\nB1 D 11\\nC2 M1 20\\nC1 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n68\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 31\\n2 1 8 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 6\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 18\\nL1 D 24\\nC1 L1 24\\n2 1 3 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC3 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n50\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 10\\nC1 L2 20\\n2 2 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 14\\nC2 L1 7\\nC2 D 10\\nL1 D 5\\n0 0 0 0\", \"1 1 4 5\\n68\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 31\\n2 1 8 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 6\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 20\\n2 1 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 7\\nC2 D 15\\nL1 D 8\\n0 0 0 0\"], \"outputs\": [\"1\\n-2\\n\", \"-13\\n-2\\n\", \"1\\n-41\\n\", \"1\\n12\\n\", \"1\\n-58\\n\", \"1\\n-22\\n\", \"-7\\n-22\\n\", \"1\\n-12\\n\", \"1\\n-6\\n\", \"-1\\n-2\\n\", \"7\\n-12\\n\", \"7\\n-4\\n\", \"7\\n4\\n\", \"1\\n-16\\n\", \"1\\n6\\n\", \"1\\n-74\\n\", \"1\\n-26\\n\", \"7\\n-84\\n\", \"7\\n-20\\n\", \"7\\n0\\n\", \"1\\n104\\n\", \"1\\n-13\\n\", \"7\\n-16\\n\", \"11\\n-74\\n\", \"-5\\n-22\\n\", \"-15\\n-84\\n\", \"1\\n14\\n\", \"11\\n-68\\n\", \"13\\n-22\\n\", \"-15\\n-96\\n\", \"11\\n-52\\n\", \"1\\n-66\\n\", \"1\\n68\\n\", \"1\\n-59\\n\", \"7\\n58\\n\", \"7\\n10\\n\", \"1\\n18\\n\", \"1\\n46\\n\", \"1\\n-30\\n\", \"7\\n-53\\n\", \"1\\n-68\\n\", \"1\\n-9\\n\", \"1\\n2\\n\", \"7\\n16\\n\", \"-15\\n-74\\n\", \"7\\n-52\\n\", \"-7\\n-2\\n\", \"1\\n-55\\n\", \"43\\n58\\n\", \"7\\n30\\n\", \"-7\\n-12\\n\", \"1\\n-28\\n\", \"7\\n38\\n\", \"1\\n-64\\n\", \"11\\n-64\\n\", \"11\\n-76\\n\", \"-32\\n-2\\n\", \"-13\\n-18\\n\", \"1\\n-125\\n\", \"-1\\n10\\n\", \"7\\n-136\\n\", \"-13\\n-16\\n\", \"1\\n22\\n\", \"5\\n-22\\n\", \"1\\n-38\\n\", \"1\\n-3\\n\", \"7\\n-28\\n\", \"1\\n4\\n\", \"11\\n-60\\n\", \"12\\n-2\\n\", \"-7\\n-26\\n\", \"-1\\n58\\n\", \"7\\n7\\n\", \"1\\n34\\n\", \"1\\n-15\\n\", \"1\\n-39\\n\", \"-7\\n10\\n\", \"-1\\n-22\\n\", \"23\\n-28\\n\", \"-32\\n-10\\n\", \"-7\\n-18\\n\", \"1\\n10\\n\", \"-13\\n12\\n\", \"-32\\n-38\\n\", \"-5\\n-46\\n\", \"-7\\n-34\\n\", \"-1\\n104\\n\", \"-20\\n7\\n\", \"-35\\n-15\\n\", \"-1\\n-48\\n\", \"23\\n-24\\n\", \"37\\n-125\\n\", \"7\\n-196\\n\", \"-1\\n-46\\n\", \"5\\n104\\n\", \"-1\\n-56\\n\", \"-32\\n104\\n\", \"5\\n-59\\n\", \"-22\\n10\\n\", \"4\\n104\\n\", \"1\\n-2\"]}", "source": "taco"}
|
Mr. A loves sweets, but recently his wife has told him to go on a diet. One day, when Mr. A went out from his home to the city hall, his wife recommended that he go by bicycle. There, Mr. A reluctantly went out on a bicycle, but Mr. A, who likes sweets, came up with the idea of stopping by a cake shop on the way to eat cake.
If you ride a bicycle, calories are consumed according to the mileage, but if you eat cake, you will consume that much calories. The net calories burned is the calories burned on the bike minus the calories burned by eating the cake. Therefore, the net calories burned may be less than zero.
If you buy a cake at a cake shop, Mr. A will eat all the cake on the spot. Mr. A does not stop at all cake shops, but when he passes through the point where the cake shop exists, he always stops and buys and eats one cake. However, it's really tempting to pass in front of the same cake shop many times, so each cake shop should only be visited once. In addition, you may stop by the cake shop after passing the destination city hall, and then return to the city hall to finish your work, and you may visit as many times as you like except the cake shop.
Enter the map information from Mr. A's home to the city hall, a list of calories of cakes that can be eaten at the cake shop on the way, and the calories burned by traveling a unit distance, from leaving home to entering the city hall. Create a program that outputs the minimum net calories burned.
The map shows Mr. A's home and city hall, a cake shop and a landmark building. The input data representing the map contains a line consisting of a symbol representing the two points and the distance between them, when there is a road connecting Mr. A's home, city hall, cake shop and each point of the landmark. For example, if the distance between the 5th cake shop and the 3rd landmark is 10, the input data will contain a line similar to the following:
C5 L3 10
In this way, cake shops are represented by C, and landmarks are represented by L in front of the number. Also, Mr. A's home is represented by H and the city hall is represented by D. If the input data is given two points and the distance between them, advance between the two points in either direction. For example, in the example above, you can go from a cake shop to a landmark and vice versa. In addition, you must be able to reach the city hall from your home. Other input data given are the number of cake shops m, the number of landmarks n, the calories burned per unit distance k, and the cakes that can be bought at each of the first cake shop to the mth cake shop. The total number of m data representing calories and distance data d.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by four 0 lines. Each dataset is given in the following format:
m n k d
c1 c2 ... cm
s1 t1 e1
s2 t2 e2
::
sd td ed
Number of cake shops m (1 ≤ m ≤ 6), number of landmarks n (1 ≤ n ≤ 100), calories burned per unit distance k (1 ≤ k ≤ 5), distance data on the first line The total number d (5 ≤ d ≤ 256) is given.
The second line gives the calories ci (1 ≤ ci ≤ 100) of the cake you buy at each cake shop.
The following d line is given the distance data si, ti, ei (1 ≤ ei ≤ 20) between the i-th two points.
The number of datasets does not exceed 100.
Output
Outputs the minimum total calories burned on one line for each input dataset.
Example
Input
1 1 2 5
35
H L1 5
C1 D 6
C1 H 12
L1 D 10
C1 L1 20
2 1 4 6
100 70
H L1 5
C1 L1 12
C1 D 11
C2 L1 7
C2 D 15
L1 D 8
0 0 0 0
Output
1
-2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"3\\n1 2 3\\n\", \"4\\n0 0 0 2\\n\", \"3\\n1 1 3\\n\", \"7\\n0 0 2 2 5 5 6\\n\", \"10\\n1 2 3 4 4 4 7 7 7 10\\n\", \"1\\n1\\n\", \"1\\n0\\n\", \"7\\n0 0 2 2 5 5 6\\n\", \"1\\n1\\n\", \"10\\n1 2 3 4 4 4 7 7 7 10\\n\", \"1\\n0\\n\", \"3\\n1 1 1\\n\", \"4\\n0 0 0 3\\n\", \"4\\n0 0 0 1\\n\", \"3\\n0 2 3\\n\", \"7\\n0 0 2 2 3 5 6\\n\", \"3\\n0 1 1\\n\", \"4\\n0 0 1 3\\n\", \"4\\n0 0 1 1\\n\", \"3\\n0 2 2\\n\", \"7\\n0 0 2 2 3 5 7\\n\", \"7\\n0 0 2 4 5 5 6\\n\", \"3\\n0 1 3\\n\", \"3\\n1 1 2\\n\", \"4\\n0 0 0 4\\n\", \"7\\n0 0 0 2 3 5 7\\n\", \"3\\n1 2 2\\n\", \"3\\n0 1 2\\n\", \"3\\n0 0 1\\n\", \"4\\n0 0 0 0\\n\", \"7\\n0 0 2 2 3 3 6\\n\", \"3\\n0 0 3\\n\", \"3\\n0 0 2\\n\", \"7\\n0 0 2 3 3 3 6\\n\", \"3\\n0 0 0\\n\", \"7\\n0 0 2 3 3 4 6\\n\", \"7\\n0 0 2 2 5 5 7\\n\", \"4\\n0 1 1 2\\n\", \"4\\n0 1 1 3\\n\", \"7\\n0 0 2 2 2 3 6\\n\", \"7\\n0 0 3 3 3 3 6\\n\", \"4\\n0 1 1 4\\n\", \"7\\n0 0 2 2 2 3 4\\n\", \"7\\n0 0 2 3 5 5 6\\n\", \"4\\n0 0 2 3\\n\", \"7\\n0 0 1 2 3 5 7\\n\", \"7\\n0 0 2 3 3 5 6\\n\", \"7\\n0 0 2 3 3 4 7\\n\", \"7\\n0 0 0 2 5 5 7\\n\", \"4\\n1 1 1 3\\n\", \"7\\n0 0 2 2 2 2 6\\n\", \"4\\n0 0 1 4\\n\", \"7\\n0 0 1 2 2 5 7\\n\", \"7\\n0 0 0 4 5 5 7\\n\", \"7\\n0 0 0 2 2 2 6\\n\", \"4\\n0 0 2 4\\n\", \"7\\n0 0 1 2 2 4 7\\n\", \"7\\n0 0 0 0 2 2 6\\n\", \"4\\n0 0 2 2\\n\", \"7\\n0 0 0 0 0 2 6\\n\", \"7\\n0 0 2 3 4 5 6\\n\", \"4\\n0 1 1 1\\n\", \"7\\n0 0 2 3 5 5 7\\n\", \"4\\n1 1 1 2\\n\", \"4\\n1 1 1 4\\n\", \"4\\n0 0 3 3\\n\", \"7\\n0 0 1 2 3 5 6\\n\", \"4\\n1 1 2 3\\n\", \"4\\n0 0 1 2\\n\", \"7\\n0 1 1 2 2 4 7\\n\", \"7\\n0 0 2 4 5 5 7\\n\", \"7\\n1 1 1 2 2 4 7\\n\", \"7\\n1 1 1 2 3 4 7\\n\", \"7\\n1 1 1 1 3 4 7\\n\", \"7\\n1 1 1 1 3 5 7\\n\", \"7\\n1 1 1 2 3 5 7\\n\", \"4\\n1 1 1 1\\n\", \"7\\n0 0 0 2 3 5 6\\n\", \"7\\n0 1 2 2 3 5 7\\n\", \"7\\n0 0 2 2 3 6 6\\n\", \"7\\n0 1 1 2 3 5 6\\n\", \"7\\n0 0 0 3 5 5 7\\n\", \"7\\n0 0 0 0 2 2 7\\n\", \"4\\n0 1 3 3\\n\", \"7\\n0 0 1 4 5 5 7\\n\", \"7\\n1 1 1 2 4 5 7\\n\", \"7\\n0 0 0 1 3 5 6\\n\", \"7\\n0 1 1 2 2 5 6\\n\", \"7\\n0 1 1 2 4 5 7\\n\", \"7\\n0 1 1 1 3 5 6\\n\", \"7\\n0 0 2 2 3 4 6\\n\", \"7\\n0 1 3 3 3 3 6\\n\", \"3\\n1 2 3\\n\", \"3\\n1 1 3\\n\", \"4\\n0 0 0 2\\n\"], \"outputs\": [\"0 1 2 \", \"1 3 4 0 \", \"0 2 1 \", \"1 3 0 4 2 7 5 \", \"0 1 2 3 5 6 4 8 9 7 \", \"0 \", \"1 \", \"1 3 0 4 2 7 5\\n\", \"0\\n\", \"0 1 2 3 5 6 4 8 9 7\\n\", \"1\\n\", \"0 2 3 \\n\", \"1 2 4 0 \\n\", \"2 3 4 0 \\n\", \"1 0 2 \\n\", \"1 4 0 7 2 3 5 \\n\", \"2 0 3 \\n\", \"2 4 0 1 \\n\", \"2 3 0 4 \\n\", \"1 0 3 \\n\", \"1 4 0 6 2 3 5 \\n\", \"1 3 0 2 4 7 5 \\n\", \"2 0 1 \\n\", \"0 3 1 \\n\", \"1 2 3 0 \\n\", \"1 4 6 0 2 3 5 \\n\", \"0 1 3 \\n\", \"3 0 1 \\n\", \"2 3 0 \\n\", \"1 2 3 4 \\n\", \"1 4 0 5 2 7 3 \\n\", \"1 2 0 \\n\", \"1 3 0 \\n\", \"1 4 0 2 5 7 3 \\n\", \"1 2 3 \\n\", \"1 5 0 2 7 3 4 \\n\", \"1 3 0 4 2 6 5 \\n\", \"3 0 4 1 \\n\", \"2 0 4 1 \\n\", \"1 4 0 5 7 2 3 \\n\", \"1 2 0 4 5 7 3 \\n\", \"2 0 3 1 \\n\", \"1 5 0 6 7 2 3 \\n\", \"1 4 0 2 3 7 5 \\n\", \"1 4 0 2 \\n\", \"4 6 0 1 2 3 5 \\n\", \"1 4 0 2 7 3 5 \\n\", \"1 5 0 2 6 3 4 \\n\", \"1 3 4 0 2 6 5 \\n\", \"0 2 4 1 \\n\", \"1 3 0 4 5 7 2 \\n\", \"2 3 0 1 \\n\", \"3 4 0 1 6 2 5 \\n\", \"1 2 3 0 4 6 5 \\n\", \"1 3 4 0 5 7 2 \\n\", \"1 3 0 2 \\n\", \"3 5 0 1 6 2 4 \\n\", \"1 3 4 5 0 7 2 \\n\", \"1 3 0 4 \\n\", \"1 3 4 5 7 0 2 \\n\", \"1 7 0 2 3 4 5 \\n\", \"2 0 3 4 \\n\", \"1 4 0 2 3 6 5 \\n\", \"0 3 4 1 \\n\", \"0 2 3 1 \\n\", \"1 2 0 4 \\n\", \"4 7 0 1 2 3 5 \\n\", \"0 4 1 2 \\n\", \"3 4 0 1 \\n\", \"3 0 5 1 6 2 4 \\n\", \"1 3 0 2 4 6 5 \\n\", \"0 3 5 1 6 2 4 \\n\", \"0 5 6 1 2 3 4 \\n\", \"0 2 5 6 1 3 4 \\n\", \"0 2 4 6 1 3 5 \\n\", \"0 4 6 1 2 3 5 \\n\", \"0 2 3 4 \\n\", \"1 4 7 0 2 3 5 \\n\", \"4 0 1 6 2 3 5 \\n\", \"1 4 0 5 2 3 7 \\n\", \"4 0 7 1 2 3 5 \\n\", \"1 2 4 0 3 6 5 \\n\", \"1 3 4 5 0 6 2 \\n\", \"2 0 1 4 \\n\", \"2 3 0 1 4 6 5 \\n\", \"0 3 6 1 2 4 5 \\n\", \"2 4 7 0 1 3 5 \\n\", \"3 0 4 1 7 2 5 \\n\", \"3 0 6 1 2 4 5 \\n\", \"2 0 4 7 1 3 5 \\n\", \"1 5 0 7 2 3 4 \\n\", \"2 0 1 4 5 7 3 \\n\", \"0 1 2\\n\", \"0 2 1\\n\", \"1 3 4 0\\n\"]}", "source": "taco"}
|
Given an array $a$ of length $n$, find another array, $b$, of length $n$ such that:
for each $i$ $(1 \le i \le n)$ $MEX(\{b_1$, $b_2$, $\ldots$, $b_i\})=a_i$.
The $MEX$ of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 10^5$) — the length of the array $a$.
The second line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_n$ ($0 \le a_i \le i$) — the elements of the array $a$. It's guaranteed that $a_i \le a_{i+1}$ for $1\le i < n$.
-----Output-----
If there's no such array, print a single line containing $-1$.
Otherwise, print a single line containing $n$ integers $b_1$, $b_2$, $\ldots$, $b_n$ ($0 \le b_i \le 10^6$)
If there are multiple answers, print any.
-----Examples-----
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
-----Note-----
In the second test case, other answers like $[1,1,1,0]$, for example, are valid.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n5 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 6\\n10 8\\n\\n2 4\\n6 5 2 1\\n7 9 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n5 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 6\\n10 8\\n\\n2 4\\n6 5 2 1\\n7 3 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n5 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 6\\n10 13\\n\\n2 4\\n6 4 2 1\\n7 3 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n0 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 12\\n10 13\\n\\n2 4\\n6 4 2 1\\n7 3 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n0 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 12\\n12 13\\n\\n2 4\\n6 4 2 1\\n7 3 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 2 3\\n\\n2 3\\n0 3 4\\n2 5 1\\n\\n4 2\\n7 9\\n8 1\\n9 12\\n4 13\\n\\n2 4\\n6 4 2 1\\n7 3 7 2\\n\", 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13\\n\\n2 4\\n6 4 2 1\\n7 -1 7 0\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 1 3\\n\\n2 3\\n0 3 4\\n2 5 0\\n\\n4 2\\n7 9\\n8 1\\n9 12\\n18 13\\n\\n2 4\\n6 4 2 1\\n7 3 7 3\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 5 1\\n3 1 1\\n1 2 2\\n1 2 3\\n\\n2 3\\n0 8 4\\n5 2 1\\n\\n4 2\\n7 6\\n8 1\\n9 1\\n1 13\\n\\n2 4\\n6 4 2 1\\n7 -1 7 0\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 3 1\\n3 1 1\\n1 2 2\\n1 0 3\\n\\n2 3\\n5 3 4\\n4 5 1\\n\\n4 2\\n7 9\\n8 3\\n9 6\\n19 2\\n\\n2 4\\n6 5 2 1\\n7 4 7 2\\n\", \"5\\n\\n2 2\\n1 2\\n3 4\\n\\n4 3\\n1 5 1\\n3 1 1\\n1 2 2\\n0 2 3\\n\\n2 3\\n0 3 4\\n2 2 1\\n\\n4 2\\n0 9\\n8 2\\n9 3\\n2 13\\n\\n2 4\\n6 7 2 1\\n0 -2 7 0\\n\", \"5\\n\\n2 2\\n2 2\\n3 2\\n\\n4 3\\n1 5 1\\n0 1 0\\n2 2 2\\n2 2 3\\n\\n2 3\\n0 4 4\\n3 2 1\\n\\n4 2\\n7 3\\n8 -1\\n9 1\\n2 23\\n\\n2 4\\n6 6 2 1\\n7 -1 5 0\\n\", \"5\\n\\n2 2\\n2 2\\n3 3\\n\\n4 3\\n1 5 1\\n0 1 0\\n2 2 2\\n2 2 3\\n\\n2 3\\n0 4 4\\n3 2 1\\n\\n4 2\\n14 15\\n8 -1\\n9 1\\n2 23\\n\\n2 4\\n6 6 2 1\\n7 -1 9 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|
Vlad has $n$ friends, for each of whom he wants to buy one gift for the New Year.
There are $m$ shops in the city, in each of which he can buy a gift for any of his friends. If the $j$-th friend ($1 \le j \le n$) receives a gift bought in the shop with the number $i$ ($1 \le i \le m$), then the friend receives $p_{ij}$ units of joy. The rectangular table $p_{ij}$ is given in the input.
Vlad has time to visit at most $n-1$ shops (where $n$ is the number of friends). He chooses which shops he will visit and for which friends he will buy gifts in each of them.
Let the $j$-th friend receive $a_j$ units of joy from Vlad's gift. Let's find the value $\alpha=\min\{a_1, a_2, \dots, a_n\}$. Vlad's goal is to buy gifts so that the value of $\alpha$ is as large as possible. In other words, Vlad wants to maximize the minimum of the joys of his friends.
For example, let $m = 2$, $n = 2$. Let the joy from the gifts that we can buy in the first shop: $p_{11} = 1$, $p_{12}=2$, in the second shop: $p_{21} = 3$, $p_{22}=4$.
Then it is enough for Vlad to go only to the second shop and buy a gift for the first friend, bringing joy $3$, and for the second — bringing joy $4$. In this case, the value $\alpha$ will be equal to $\min\{3, 4\} = 3$
Help Vlad choose gifts for his friends so that the value of $\alpha$ is as high as possible. Please note that each friend must receive one gift. Vlad can visit at most $n-1$ shops (where $n$ is the number of friends). In the shop, he can buy any number of gifts.
-----Input-----
The first line of the input contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases in the input.
An empty line is written before each test case. Then there is a line containing integers $m$ and $n$ ($2 \le n$, $2 \le n \cdot m \le 10^5$) separated by a space — the number of shops and the number of friends, where $n \cdot m$ is the product of $n$ and $m$.
Then $m$ lines follow, each containing $n$ numbers. The number in the $i$-th row of the $j$-th column $p_{ij}$ ($1 \le p_{ij} \le 10^9$) is the joy of the product intended for friend number $j$ in shop number $i$.
It is guaranteed that the sum of the values $n \cdot m$ over all test cases in the test does not exceed $10^5$.
-----Output-----
Print $t$ lines, each line must contain the answer to the corresponding test case — the maximum possible value of $\alpha$, where $\alpha$ is the minimum of the joys from a gift for all of Vlad's friends.
-----Examples-----
Input
5
2 2
1 2
3 4
4 3
1 3 1
3 1 1
1 2 2
1 1 3
2 3
5 3 4
2 5 1
4 2
7 9
8 1
9 6
10 8
2 4
6 5 2 1
7 9 7 2
Output
3
2
4
8
2
-----Note-----
None
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [[0], [1], [2], [3], [4], [5], [6], [10], [20], [50]], \"outputs\": [[1], [10], [55], [220], [715], [2002], [5005], [92378], [10015005], [12565671261]]}", "source": "taco"}
|
An `non decreasing` number is one containing no two consecutive digits (left to right), whose the first is higer than the second. For example, 1235 is an non decreasing number, 1229 is too, but 123429 isn't.
Write a function that finds the number of non decreasing numbers up to `10**N` (exclusive) where N is the input of your function. For example, if `N=3`, you have to count all non decreasing numbers from 0 to 999.
You'll definitely need something smarter than brute force for large values of N!
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"8 3\\n3 3 1 2 2 1 1 3\\n3 1 1\\n\", \"6 5\\n1 2 4 2 4 3\\n0 0 1 0 0\\n\", \"1 1\\n1\\n1\\n\", \"2 1\\n1 1\\n1\\n\", \"2 1\\n1 1\\n2\\n\", \"2 2\\n1 2\\n1 1\\n\", \"2 2\\n2 2\\n1 1\\n\", \"3 3\\n3 3 2\\n0 0 1\\n\", \"4 4\\n4 4 4 4\\n0 1 1 1\\n\", \"2 2\\n1 1\\n1 0\\n\", \"3 3\\n3 3 3\\n0 0 1\\n\", \"4 4\\n2 4 4 3\\n0 1 0 0\\n\", \"2 2\\n2 1\\n0 1\\n\", \"3 3\\n3 1 1\\n1 1 1\\n\", \"4 4\\n1 3 1 4\\n1 0 0 1\\n\", \"2 2\\n2 1\\n1 0\\n\", \"3 3\\n3 1 1\\n2 0 0\\n\", \"4 4\\n4 4 2 2\\n1 1 1 1\\n\", \"2 2\\n1 2\\n0 2\\n\", \"3 3\\n3 2 3\\n0 2 1\\n\", \"4 4\\n1 2 4 2\\n0 0 1 0\\n\", \"4 4\\n4 2 1 2\\n1 2 0 1\\n\", \"5 5\\n4 4 2 4 2\\n0 2 0 3 0\\n\", \"6 6\\n4 3 5 4 5 2\\n0 1 0 1 2 0\\n\", \"4 4\\n4 3 3 2\\n0 0 2 0\\n\", \"5 5\\n3 4 5 1 4\\n1 0 1 1 1\\n\", \"6 6\\n1 1 3 2 2 2\\n1 0 0 0 0 0\\n\", \"4 4\\n4 1 1 3\\n2 0 0 1\\n\", \"5 5\\n3 4 1 1 5\\n2 0 1 1 0\\n\", \"6 6\\n4 3 5 6 5 5\\n0 0 1 1 0 0\\n\", \"4 4\\n1 3 4 2\\n1 0 0 0\\n\", \"5 5\\n4 1 3 3 3\\n0 0 0 1 0\\n\", \"6 6\\n6 2 6 2 5 4\\n0 1 0 0 0 1\\n\", \"4 4\\n3 2 1 3\\n0 1 0 0\\n\", \"5 5\\n3 4 1 4 2\\n1 0 0 1 0\\n\", \"6 6\\n4 1 6 6 3 5\\n1 0 1 1 1 2\\n\", \"2 2\\n1 1\\n1 0\\n\", \"6 6\\n4 1 6 6 3 5\\n1 0 1 1 1 2\\n\", \"6 6\\n6 2 6 2 5 4\\n0 1 0 0 0 1\\n\", \"4 4\\n3 2 1 3\\n0 1 0 0\\n\", \"2 2\\n1 2\\n1 1\\n\", \"4 4\\n4 2 1 2\\n1 2 0 1\\n\", \"4 4\\n4 4 2 2\\n1 1 1 1\\n\", \"3 3\\n3 3 3\\n0 0 1\\n\", \"3 3\\n3 3 2\\n0 0 1\\n\", \"4 4\\n2 4 4 3\\n0 1 0 0\\n\", \"5 5\\n3 4 1 1 5\\n2 0 1 1 0\\n\", \"2 2\\n1 2\\n0 2\\n\", \"1 1\\n1\\n1\\n\", \"5 5\\n3 4 1 4 2\\n1 0 0 1 0\\n\", \"4 4\\n4 1 1 3\\n2 0 0 1\\n\", \"3 3\\n3 2 3\\n0 2 1\\n\", \"4 4\\n1 3 1 4\\n1 0 0 1\\n\", \"5 5\\n3 4 5 1 4\\n1 0 1 1 1\\n\", \"2 2\\n2 1\\n0 1\\n\", \"5 5\\n4 1 3 3 3\\n0 0 0 1 0\\n\", \"3 3\\n3 1 1\\n2 0 0\\n\", \"4 4\\n1 3 4 2\\n1 0 0 0\\n\", \"3 3\\n3 1 1\\n1 1 1\\n\", \"2 1\\n1 1\\n2\\n\", \"6 5\\n1 2 4 2 4 3\\n0 0 1 0 0\\n\", \"4 4\\n1 2 4 2\\n0 0 1 0\\n\", \"2 1\\n1 1\\n1\\n\", \"5 5\\n4 4 2 4 2\\n0 2 0 3 0\\n\", \"4 4\\n4 4 4 4\\n0 1 1 1\\n\", \"6 6\\n4 3 5 4 5 2\\n0 1 0 1 2 0\\n\", \"2 2\\n2 2\\n1 1\\n\", \"6 6\\n1 1 3 2 2 2\\n1 0 0 0 0 0\\n\", \"2 2\\n2 1\\n1 0\\n\", \"6 6\\n4 3 5 6 5 5\\n0 0 1 1 0 0\\n\", \"4 4\\n4 3 3 2\\n0 0 2 0\\n\", \"6 6\\n6 2 6 2 3 4\\n0 1 0 0 0 1\\n\", \"5 5\\n3 4 1 2 5\\n2 0 1 1 0\\n\", \"8 3\\n3 3 1 2 2 1 1 3\\n3 0 1\\n\", \"6 6\\n6 2 6 2 3 4\\n0 1 0 1 0 1\\n\", \"2 2\\n2 2\\n0 2\\n\", \"5 5\\n3 4 5 1 4\\n1 0 1 2 1\\n\", \"3 3\\n3 1 2\\n2 0 0\\n\", \"4 4\\n1 2 1 2\\n0 0 1 0\\n\", \"5 5\\n4 4 2 4 2\\n0 3 0 3 0\\n\", \"4 4\\n4 4 4 4\\n0 1 1 2\\n\", \"6 6\\n4 3 5 4 5 2\\n0 0 0 1 2 0\\n\", \"6 6\\n1 1 3 2 2 2\\n1 0 0 1 0 0\\n\", \"5 5\\n3 4 1 2 5\\n2 1 1 1 0\\n\", \"2 2\\n2 2\\n0 1\\n\", \"5 5\\n3 4 5 1 4\\n1 0 1 2 2\\n\", \"3 3\\n3 1 2\\n2 0 1\\n\", \"4 4\\n1 2 1 1\\n0 0 1 0\\n\", \"8 3\\n3 3 1 1 2 1 1 3\\n3 0 1\\n\", \"3 3\\n1 1 2\\n2 0 1\\n\", \"4 4\\n1 3 1 1\\n0 0 1 0\\n\", \"4 4\\n1 2 1 3\\n0 1 0 0\\n\", \"2 2\\n2 1\\n1 1\\n\", \"4 4\\n4 2 2 2\\n1 2 0 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0\\n\", \"5 5\\n5 4 1 4 5\\n2 0 1 1 0\\n\", \"4 4\\n2 3 1 1\\n0 1 1 0\\n\", \"4 4\\n1 4 1 3\\n0 1 0 1\\n\", \"4 4\\n4 2 1 3\\n0 0 0 2\\n\", \"5 5\\n3 4 5 1 4\\n1 1 1 0 2\\n\", \"8 3\\n3 3 1 2 2 1 1 3\\n3 1 1\\n\"], \"outputs\": [\"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\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\", \"0\", \"0\", \"0\", \"0\", \"0\", \"-1\", \"0\", \"0\", \"0\", \"0\", \"-1\", \"0\", \"0\", \"0\", \"-1\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"-1\", \"0\", \"0\", \"-1\", \"0\", \"0\", \"-1\", \"0\", \"-1\", \"0\", \"0\", \"0\", \"0\\n\", \"0\\n\", \"-1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"-1\\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\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1\"]}", "source": "taco"}
|
There is unrest in the Galactic Senate. Several thousand solar systems have declared their intentions to leave the Republic. Master Heidi needs to select the Jedi Knights who will go on peacekeeping missions throughout the galaxy. It is well-known that the success of any peacekeeping mission depends on the colors of the lightsabers of the Jedi who will go on that mission.
Heidi has n Jedi Knights standing in front of her, each one with a lightsaber of one of m possible colors. She knows that for the mission to be the most effective, she needs to select some contiguous interval of knights such that there are exactly k_1 knights with lightsabers of the first color, k_2 knights with lightsabers of the second color, ..., k_{m} knights with lightsabers of the m-th color.
However, since the last time, she has learned that it is not always possible to select such an interval. Therefore, she decided to ask some Jedi Knights to go on an indefinite unpaid vacation leave near certain pits on Tatooine, if you know what I mean. Help Heidi decide what is the minimum number of Jedi Knights that need to be let go before she is able to select the desired interval from the subsequence of remaining knights.
-----Input-----
The first line of the input contains n (1 ≤ n ≤ 2·10^5) and m (1 ≤ m ≤ n). The second line contains n integers in the range {1, 2, ..., m} representing colors of the lightsabers of the subsequent Jedi Knights. The third line contains m integers k_1, k_2, ..., k_{m} (with $1 \leq \sum_{i = 1}^{m} k_{i} \leq n$) – the desired counts of Jedi Knights with lightsabers of each color from 1 to m.
-----Output-----
Output one number: the minimum number of Jedi Knights that need to be removed from the sequence so that, in what remains, there is an interval with the prescribed counts of lightsaber colors. If this is not possible, output - 1.
-----Example-----
Input
8 3
3 3 1 2 2 1 1 3
3 1 1
Output
1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"6\\n2 1 4 6 2 2\\n\", \"7\\n3 3 3 1 3 3 3\\n\", \"7\\n5128 5672 5805 5452 5882 5567 5032\\n\", \"10\\n1 2 2 3 5 5 5 4 2 1\\n\", \"14\\n20 20 20 20 20 20 3 20 20 20 20 20 20 20\\n\", \"50\\n3 2 4 3 5 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 5 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 5 4\\n\", \"1\\n1\\n\", \"1\\n1000000000\\n\", \"2\\n1 1\\n\", \"2\\n1049 1098\\n\", \"2\\n100 100\\n\", \"5\\n1 2 3 2 1\\n\", \"15\\n2 2 1 1 2 2 2 2 2 2 2 2 2 1 2\\n\", \"28\\n415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\\n\", \"45\\n3 12 13 11 13 13 10 11 14 15 15 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 14 10 11 14 13 14 11 11 11 12 15 1 10 15 12 14 14 14\\n\", \"84\\n1 3 4 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 7 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\"45\\n3 12 13 11 13 13 10 11 14 15 15 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 14 10 11 14 13 14 11 11 11 12 15 1 10 15 12 14 14 14\\n\", \"84\\n1 3 4 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 7 9 3 4 4 4 2 2 1 6 4 9 5 9 9 10 7 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 5 9 8 5 3 3 2\\n\", \"2\\n1049 1098\\n\", \"1\\n1\\n\", \"15\\n2 2 1 1 2 2 2 2 2 2 2 2 2 1 2\\n\", \"28\\n415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\\n\", \"5\\n1 2 3 2 1\\n\", \"50\\n3 2 4 3 5 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 5 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 5 4\\n\", \"2\\n100 100\\n\", \"10\\n1 2 2 3 5 5 1 4 2 1\\n\", \"14\\n20 2 20 20 20 20 3 20 20 20 20 20 20 20\\n\", \"7\\n5128 5672 9144 5452 5882 5567 5032\\n\", \"2\\n1 2\\n\", \"45\\n3 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1 2 1 3 3 2 1 2 1 1 1 2 3 4 5 4 3 2 1 1 2 1 2 3 4 3 2 1\\n\", \"7\\n5128 10315 9144 5452 5882 5567 5032\\n\", \"2\\n4 2\\n\", \"1\\n0100000001\\n\", \"45\\n3 12 13 11 13 13 10 11 14 15 1 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 21 10 11 14 13 14 11 11 11 12 15 1 10 15 22 14 14 14\\n\", \"84\\n1 3 4 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 8 9 3 4 4 5 2 2 1 6 4 9 5 9 9 10 7 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 1 9 8 5 3 3 2\\n\", \"2\\n685 1085\\n\", \"15\\n2 2 1 1 2 2 0 2 2 2 0 2 2 2 2\\n\", \"28\\n415546599 415546599 415546599 415546599 415546599 269614167 415546599 415546599 712281815 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1153224769 1 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\\n\", \"50\\n3 2 4 3 2 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 10 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 3 4\\n\", \"2\\n010 101\\n\", \"6\\n4 1 0 6 2 2\\n\", \"7\\n3 4 3 2 3 3 3\\n\", \"10\\n2 2 2 3 10 5 1 4 2 0\\n\", \"14\\n20 2 20 12 20 20 3 20 20 20 23 24 20 20\\n\", \"170\\n1 2 1 2 1 1 1 1 2 3 2 1 1 2 2 1 2 1 2 1 1 2 3 3 2 1 1 1 1 1 1 1 1 2 1 2 3 3 2 1 2 2 1 2 3 2 1 1 2 3 2 1 2 1 1 1 2 3 3 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 3 2 1 1 2 3 4 4 3 2 0 2 1 2 1 2 3 3 2 1 2 1 1 1 0 1 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2 2 1 2 1 1 1 2 2 1 2 1 3 3 2 1 2 1 1 1 2 3 4 5 4 3 2 1 2 2 1 2 3 4 3 2 1\\n\", \"7\\n2133 10315 9144 5452 5882 5567 5032\\n\", \"2\\n2 0\\n\", \"1\\n1100010001\\n\", \"45\\n3 12 13 11 13 13 10 11 14 15 1 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 21 10 11 14 13 14 11 11 11 12 10 1 10 15 22 14 14 14\\n\", \"84\\n1 3 0 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 8 9 3 4 4 5 2 2 1 6 4 9 5 9 9 10 7 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 1 9 8 5 3 3 2\\n\", \"2\\n1053 1085\\n\", \"15\\n2 2 1 1 2 4 0 2 2 2 0 2 2 2 2\\n\", \"28\\n415546599 415546599 415546599 415546599 415546599 269614167 415546599 415546599 712281815 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1153224769 1 781075398 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\\n\", \"50\\n3 0 4 3 2 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 10 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 3 4\\n\", \"2\\n011 101\\n\", \"6\\n4 1 0 6 3 2\\n\", \"7\\n3 4 3 2 2 3 3\\n\", \"10\\n1 2 2 3 10 5 1 4 2 0\\n\", \"14\\n35 2 20 12 20 20 3 20 20 20 23 24 20 20\\n\", \"170\\n1 2 1 2 1 1 1 1 2 3 2 1 1 2 2 1 2 1 2 1 1 2 3 3 2 1 1 1 1 1 1 1 1 2 1 2 3 3 2 1 4 2 1 2 3 2 1 1 2 3 2 1 2 1 1 1 2 3 3 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 3 2 1 1 2 3 4 4 3 2 0 2 1 2 1 2 3 3 2 1 2 1 1 1 0 1 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2 2 1 2 1 1 1 2 2 1 2 1 3 3 2 1 2 1 1 1 2 3 4 5 4 3 2 1 2 2 1 2 3 4 3 2 1\\n\", \"7\\n2133 10315 4589 5452 5882 5567 5032\\n\", \"1\\n1100001001\\n\", \"45\\n3 12 13 11 13 13 10 11 14 15 1 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 21 10 11 14 13 14 11 11 11 15 10 1 10 15 22 14 14 14\\n\", \"84\\n1 3 0 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 8 9 3 4 4 5 2 2 1 6 4 9 5 9 9 10 14 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 1 9 8 5 3 3 2\\n\", \"2\\n1682 1085\\n\", \"15\\n2 2 1 2 2 4 0 2 2 2 0 2 2 2 2\\n\", \"28\\n415546599 415546599 415546599 415546599 415546599 269614167 415546599 415546599 712281815 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1153224769 1 1111238211 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\\n\", \"50\\n3 0 4 3 2 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 10 2 2 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 3 4\\n\", \"2\\n011 001\\n\", \"6\\n4 1 0 4 3 2\\n\", \"7\\n3 4 3 2 2 2 3\\n\", \"10\\n1 2 2 3 10 6 1 4 2 0\\n\", \"14\\n35 2 20 12 20 20 3 31 20 20 23 24 20 20\\n\", \"170\\n1 2 1 2 1 1 1 1 2 3 2 1 1 2 2 1 2 1 2 1 1 2 3 3 2 1 1 1 1 1 1 1 1 2 1 2 3 3 2 1 4 2 1 2 3 2 1 1 2 3 2 1 2 1 1 1 2 3 3 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 3 2 1 1 2 3 4 4 3 2 0 2 1 2 1 2 3 3 2 1 2 1 1 1 0 1 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2 2 1 2 1 1 1 2 2 1 2 1 3 3 2 1 4 1 1 1 2 3 4 5 4 3 2 1 2 2 1 2 3 4 3 2 1\\n\", \"7\\n2133 10315 4589 5452 8455 5567 5032\\n\", \"1\\n1000001001\\n\", \"45\\n3 12 13 11 13 13 10 11 14 15 1 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 21 10 11 14 13 14 11 11 11 15 10 1 0 15 22 14 14 14\\n\", \"84\\n1 3 0 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 8 9 3 4 4 5 2 2 1 6 4 9 5 9 9 10 14 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 2 9 8 5 3 3 2\\n\", \"2\\n1682 967\\n\", \"6\\n2 1 4 6 2 2\\n\", \"7\\n3 3 3 1 3 3 3\\n\"], \"outputs\": [\"3\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"6\\n\", \"13\\n\", \"8\\n\", \"5\\n\", \"1\\n\", \"5\", \"5\", \"5\", \"4\", \"1\", \"1\", \"1\", \"13\", \"8\", \"1\", \"1\", \"2\", \"6\", \"3\", \"4\", \"1\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"2\\n\", \"6\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"12\\n\", \"7\\n\", \"1\\n\", \"3\", \"2\"]}", "source": "taco"}
|
Limak is a little bear who loves to play. Today he is playing by destroying block towers. He built n towers in a row. The i-th tower is made of h_{i} identical blocks. For clarification see picture for the first sample.
Limak will repeat the following operation till everything is destroyed.
Block is called internal if it has all four neighbors, i.e. it has each side (top, left, down and right) adjacent to other block or to the floor. Otherwise, block is boundary. In one operation Limak destroys all boundary blocks. His paws are very fast and he destroys all those blocks at the same time.
Limak is ready to start. You task is to count how many operations will it take him to destroy all towers.
-----Input-----
The first line contains single integer n (1 ≤ n ≤ 10^5).
The second line contains n space-separated integers h_1, h_2, ..., h_{n} (1 ≤ h_{i} ≤ 10^9) — sizes of towers.
-----Output-----
Print the number of operations needed to destroy all towers.
-----Examples-----
Input
6
2 1 4 6 2 2
Output
3
Input
7
3 3 3 1 3 3 3
Output
2
-----Note-----
The picture below shows all three operations for the first sample test. Each time boundary blocks are marked with red color. [Image] After first operation there are four blocks left and only one remains after second operation. This last block is destroyed in third operation.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"test\", 10], [\"test\", 10, \"x\"], [\"test\", 10, \"xO\"], [\"test\", 10, \"xO-\"], [\"some other test\", 10, \"nope\"], [\"some other test\", 10, \"> \"], [\"test\", 7, \">nope\"], [\"test\", 7, \"^more complex\"], [\"test\", 7, \"\"], [\"test\", 10, \"< \"], [\"test\", 3], [\"test\", 3, \"> \"], [\"test\", 10, \"\"], [\"test\", 10, \">\"], [\"test\", 10, \"^\"], [\"test\", 0, \"> \"], [\"test\", 0, \"^ \"], [\"test\", 0, \"< \"]], \"outputs\": [[\" test\"], [\"xxxxxxtest\"], [\"xOxOxOtest\"], [\"xO-xO-test\"], [\"other test\"], [\"some other\"], [\"testnop\"], [\"motestm\"], [\"test\"], [\" test\"], [\"est\"], [\"tes\"], [\"test\"], [\"test\"], [\"test\"], [\"\"], [\"\"], [\"\"]]}", "source": "taco"}
|
In the wake of the npm's `left-pad` debacle, you decide to write a new super padding method that superceds the functionality of `left-pad`. Your version will provide the same functionality, but will additionally add right, and justified padding of string -- the `super_pad`.
Your function `super_pad` should take three arguments: the string `string`, the width of the final string `width`, and a fill character `fill`. However, the fill character can be enriched with a format string resulting in different padding strategies. If `fill` begins with `'<'` the string is padded on the left with the remaining fill string and if `fill` begins with `'>'` the string is padded on the right. Finally, if `fill` begins with `'^'` the string is padded on the left and the right, where the left padding is always greater or equal to the right padding. The `fill` string can contain more than a single char, of course.
Some examples to clarify the inner workings:
- `super_pad("test", 10)` returns " test"
- `super_pad("test", 10, "x")` returns `"xxxxxxtest"`
- `super_pad("test", 10, "xO")` returns `"xOxOxOtest"`
- `super_pad("test", 10, "xO-")` returns `"xO-xO-test"`
- `super_pad("some other test", 10, "nope")` returns `"other test"`
- `super_pad("some other test", 10, "> ")` returns `"some other"`
- `super_pad("test", 7, ">nope")` returns `"testnop"`
- `super_pad("test", 7, "^more complex")` returns `"motestm"`
- `super_pad("test", 7, "")` returns `"test"`
The `super_pad` method always returns a string of length `width` if possible. We expect the `width` to be positive (including 0) and the fill could be also an empty string.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"76 72\\n29 4 64 68 20 8 12 50 42 46 0 70 11 37 75 47 45 29 17 19 73 9 41 31 35 67 65 39 51 55\\n25 60 32 48 42 8 6 9 7 31 19 25 5 33 51 61 67 55 49 27 29 53 39 65 35 13\\n\", \"2 3\\n1 0\\n2 0 2\\n\", \"69 72\\n18 58 46 52 43 1 55 16 7 4 38 68 14 32 53 41 29 2 59\\n21 22 43 55 13 70 4 7 31 10 23 56 44 62 17 50 53 5 41 11 65 32\\n\", \"75 90\\n60 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74\\n72 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 75 77 78 79 80 82 83 84 85 87 88 89\\n\", \"20 20\\n9 0 3 4 6 7 8 10 12 13\\n10 1 2 5 9 11 14 15 16 18 19\\n\", \"55 79\\n5 51 27 36 45 53\\n30 15 28 0 5 38 3 34 30 35 1 32 12 27 42 39 69 33 10 63 16 29 76 19 60 70 67 31 78 68 45\\n\", \"16 88\\n6 5 14 2 0 12 7\\n30 21 64 35 79 74 39 63 44 81 73 0 27 33 69 12 86 46 20 25 55 52 7 58 23 5 60 32 41 50 82\\n\", \"80 40\\n27 0 41 44 45 6 47 8 10 52 13 14 16 17 18 59 21 62 23 64 26 68 29 32 75 37 78 39\\n13 2 3 9 11 15 20 25 27 30 31 33 34 36\\n\", \"41 2\\n1 33\\n0\\n\", \"90 25\\n26 55 30 35 20 15 26 6 1 41 81 76 46 57 17 12 67 77 27 47 62 8 43 63 3 48 19\\n9 10 16 21 7 17 12 13 19 9\\n\", \"100 50\\n31 52 54 8 60 61 62 63 64 16 19 21 73 25 76 77 79 30 81 32 33 34 37 88 39 40 91 42 94 95 96 98\\n18 0 1 3 5 6 7 9 15 18 20 22 24 28 35 36 43 47 49\\n\", \"7 72\\n1 4\\n3 49 32 28\\n\", \"66 66\\n24 2 35 3 36 4 5 10 45 14 48 18 51 19 21 55 22 23 24 25 26 63 31 65 32\\n21 0 1 37 6 40 7 8 42 45 13 15 16 50 53 23 24 60 28 62 63 31\\n\", \"100 99\\n1 99\\n0\\n\", \"100 40\\n25 61 42 2 3 25 46 66 68 69 49 9 10 50 91 72 92 33 73 53 14 15 55 96 36 39\\n12 0 22 3 23 4 6 27 11 35 37 38 39\\n\", \"5 7\\n1 0\\n1 0\\n\", \"98 98\\n23 6 81 90 28 38 51 23 69 13 95 15 16 88 58 10 26 42 44 54 92 27 45 39\\n18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57\\n\", \"100 100\\n50 0 1 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\\n50 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 84 36 37 38 39 40 41 42 44 45 46 48 98 49\\n34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"40 40\\n23 0 2 3 4 5 7 11 15 16 17 18 19 22 25 28 29 30 31 32 34 35 36 37\\n16 1 6 8 9 10 12 13 14 20 21 23 24 26 27 38 39\\n\", \"50 49\\n1 49\\n0\\n\", \"3 20\\n0\\n1 19\\n\", \"66 99\\n23 33 35 36 38 8 10 44 11 45 46 47 50 19 54 22 55 23 58 59 27 61 30 65\\n32 33 67 69 4 70 38 6 39 7 74 42 9 43 12 13 14 15 81 82 84 85 20 87 89 90 24 58 59 27 95 97 31\\n\", \"66 66\\n26 0 54 6 37 43 13 25 38 2 32 56 20 50 39 27 51 9 64 4 16 17 65 11 5 47 23\\n15 6 24 43 49 25 20 14 63 27 3 58 52 53 11 41\\n\", \"52 91\\n13 26 1 3 43 17 19 32 46 33 48 23 37 50\\n25 78 26 1 40 2 67 42 4 56 30 70 84 32 20 85 59 8 86 34 73 23 10 88 24 11\\n\", \"76 28\\n10 24 13 61 45 29 57 41 21 37 11\\n2 12 9\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 63 64 15 16 18 19 20 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 32 34 35 38 40 41 49\\n\", \"4 5\\n3 0 1 3\\n4 0 1 3 4\\n\", \"6 54\\n1 5\\n14 13 49 31 37 44 2 15 51 52 22 28 10 35 47\\n\", \"39 87\\n16 18 15 30 33 21 9 3 31 16 10 34 20 35 8 26 23\\n36 33 75 81 24 42 54 78 39 57 60 30 36 63 4 76 25 1 40 73 22 58 49 85 31 74 59 20 44 83 65 23 41 71 47 14 35\\n\", \"50 50\\n14 7 8 12 16 18 22 23 24 28 30 35 40 46 49\\n35 0 1 2 3 4 5 6 9 10 11 13 14 15 17 19 20 21 25 26 27 29 31 32 33 34 36 37 38 39 41 43 44 45 47 48\\n\", \"4 1\\n1 3\\n0\\n\", \"30 44\\n3 8 26 28\\n6 2 30 38 26 8 6\\n\", \"24 60\\n4 0 2 19 23\\n15 12 24 49 2 14 3 52 28 5 6 19 32 33 34 35\\n\", \"79 23\\n35 31 62 14 9 46 18 68 69 42 13 50 77 23 76 5 53 40 16 32 74 54 38 25 45 39 26 37 66 78 3 48 10 17 56 59\\n13 16 0 8 6 18 14 21 11 20 4 15 13 22\\n\", \"96 36\\n34 84 24 0 48 85 13 61 37 62 38 86 75 3 16 64 40 28 76 53 5 17 42 6 7 91 67 55 68 92 57 11 71 35 59\\n9 1 14 15 17 18 30 6 8 35\\n\", \"98 98\\n43 49 1 51 3 53 4 55 56 8 9 10 60 11 12 61 64 16 65 17 19 20 21 72 24 74 25 77 78 31 34 35 36 37 87 88 89 42 92 43 44 94 46 96\\n34 50 2 52 5 54 9 62 63 15 18 68 70 22 72 75 26 27 77 30 81 82 83 35 36 37 87 88 89 90 41 93 95 96 48\\n\", \"75 75\\n19 48 3 5 67 23 8 70 45 63 36 38 56 15 10 37 52 11 9 27\\n21 13 9 45 28 59 36 30 43 5 38 27 40 50 17 41 71 8 51 63 1 33\\n\", \"27 31\\n4 25 5 19 20\\n26 5 28 17 2 1 0 26 23 12 29 6 4 25 19 15 13 20 24 8 27 22 30 3 10 9 7\\n\", \"99 84\\n66 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83 84 86 87 89 90 92 93 95 96 98\\n56 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83\\n\", \"75 75\\n33 30 74 57 23 19 42 71 11 44 29 58 43 48 61 63 13 27 50 17 18 70 64 39 12 32 36 10 40 51 49 1 54 73\\n8 43 23 0 7 63 47 74 28\\n\", \"26 52\\n8 0 14 16 17 7 9 10 11\\n15 39 15 2 41 42 30 17 18 31 6 21 35 48 50 51\\n\", \"100 1\\n1 99\\n0\\n\", \"98 49\\n33 0 51 52 6 57 10 12 63 15 16 19 20 21 72 73 74 76 77 78 30 31 81 33 83 37 38 39 40 92 44 45 95 97\\n15 4 5 7 9 11 13 17 18 22 26 35 36 41 42 47\\n\", \"3 50\\n0\\n1 49\\n\", \"36 100\\n10 0 32 4 5 33 30 18 14 35 7\\n29 60 32 20 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 67 75 35 95 43 79 3 27\\n\", \"75 30\\n18 46 47 32 33 3 34 35 21 51 7 9 54 39 72 42 59 29 14\\n8 0 17 5 6 23 26 27 13\\n\", \"90 30\\n27 15 16 2 32 78 49 64 65 50 6 66 21 22 82 23 39 84 85 10 86 56 27 87 13 58 44 74\\n7 19 4 20 24 25 12 27\\n\", \"50 50\\n0\\n0\\n\", \"65 75\\n15 25 60 12 62 37 22 47 52 3 63 58 13 14 49 34\\n18 70 10 2 52 22 47 72 57 38 48 13 73 3 19 4 74 49 34\\n\", \"91 98\\n78 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89\\n84 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89 91 92 93 94 95 96\\n\", \"100 100\\n50 0 1 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\\n49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"2 3\\n1 0\\n2 1 2\\n\", \"69 72\\n18 58 46 52 43 1 55 16 7 4 38 68 14 32 53 41 29 2 59\\n21 22 43 55 13 70 4 7 31 10 23 56 44 62 17 50 53 2 41 11 65 32\\n\", \"75 90\\n60 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74\\n72 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 24 74 75 77 78 79 80 82 83 84 85 87 88 89\\n\", \"20 20\\n9 0 3 4 11 7 8 10 12 13\\n10 1 2 5 9 11 14 15 16 18 19\\n\", \"55 79\\n5 51 27 36 45 53\\n30 15 28 0 5 38 3 34 30 17 1 32 12 27 42 39 69 33 10 63 16 29 76 19 60 70 67 31 78 68 45\\n\", \"80 40\\n27 0 41 44 45 6 47 8 10 52 13 14 16 17 18 59 21 62 23 64 26 68 29 32 75 37 78 39\\n13 2 3 1 11 15 20 25 27 30 31 33 34 36\\n\", \"41 3\\n1 33\\n0\\n\", \"90 25\\n26 55 30 35 20 15 26 6 1 41 81 76 46 57 17 12 67 77 27 47 62 8 43 63 3 48 19\\n9 10 16 21 7 17 12 3 19 9\\n\", \"7 72\\n1 4\\n3 49 50 28\\n\", \"100 40\\n25 61 42 2 3 25 46 66 68 69 49 9 10 50 91 72 92 33 73 53 14 15 55 96 36 39\\n12 0 9 3 23 4 6 27 11 35 37 38 39\\n\", \"98 98\\n23 6 81 90 28 38 51 23 69 13 95 15 16 88 58 10 26 42 75 54 92 27 45 39\\n18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57\\n\", \"100 100\\n50 0 1 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\\n50 50 51 52 53 54 55 56 57 58 59 60 61 62 63 20 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 33 36 37 38 39 40 41 42 44 45 46 48 98 49\\n34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"40 40\\n23 0 2 3 4 5 7 11 15 16 17 18 19 22 25 28 29 30 31 32 34 35 36 37\\n16 1 6 8 9 10 12 13 14 20 21 0 24 26 27 38 39\\n\", \"50 49\\n1 19\\n0\\n\", \"3 20\\n0\\n1 14\\n\", \"66 66\\n26 0 54 6 37 43 13 25 38 2 32 56 20 50 39 27 51 9 64 4 16 17 65 11 5 47 23\\n15 2 24 43 49 25 20 14 63 27 3 58 52 53 11 41\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 63 64 15 16 18 19 20 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"6 54\\n1 5\\n14 13 49 31 37 44 2 15 51 52 22 28 10 35 5\\n\", \"39 87\\n16 18 15 30 33 21 9 3 19 16 10 34 20 35 8 26 23\\n36 33 75 81 24 42 54 78 39 57 60 30 36 63 4 76 25 1 40 73 22 58 49 85 31 74 59 20 44 83 65 23 41 71 47 14 35\\n\", \"30 44\\n3 8 20 28\\n6 2 30 38 26 8 6\\n\", \"79 23\\n35 31 62 14 9 46 18 68 69 42 13 50 77 23 76 2 53 40 16 32 74 54 38 25 45 39 26 37 66 78 3 48 10 17 56 59\\n13 16 0 8 6 18 14 21 11 20 4 15 13 22\\n\", \"96 36\\n34 84 24 0 48 85 13 61 37 62 38 86 26 3 16 64 40 28 76 53 5 17 42 6 7 91 67 55 68 92 57 11 71 35 59\\n9 1 14 15 17 18 30 6 8 35\\n\", \"98 98\\n43 49 1 51 3 53 4 55 56 8 9 10 60 11 12 37 64 16 65 17 19 20 21 72 24 74 25 77 78 31 34 35 36 37 87 88 89 42 92 43 44 94 46 96\\n34 50 2 52 5 54 9 62 63 15 18 68 70 22 72 75 26 27 77 30 81 82 83 35 36 37 87 88 89 90 41 93 95 96 48\\n\", \"75 75\\n19 48 3 5 67 23 8 70 45 63 36 38 56 15 10 37 52 11 9 27\\n21 13 9 45 28 59 36 37 43 5 38 27 40 50 17 41 71 8 51 63 1 33\\n\", \"27 31\\n4 25 5 19 20\\n26 5 28 11 2 1 0 26 23 12 29 6 4 25 19 15 13 20 24 8 27 22 30 3 10 9 7\\n\", \"75 75\\n33 30 74 57 23 19 42 71 11 44 29 58 43 48 61 63 13 27 50 17 18 70 64 39 12 32 36 10 40 51 49 1 54 73\\n8 43 23 0 7 63 47 74 19\\n\", \"26 52\\n8 0 14 16 17 7 9 10 11\\n15 39 15 2 41 0 30 17 18 31 6 21 35 48 50 51\\n\", \"100 2\\n1 99\\n0\\n\", \"36 100\\n10 0 32 4 5 33 30 18 14 35 7\\n29 60 32 20 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 65 75 35 95 43 79 3 27\\n\", \"75 30\\n18 46 47 32 33 3 34 35 21 51 7 15 54 39 72 42 59 29 14\\n8 0 17 5 6 23 26 27 13\\n\", \"90 30\\n27 15 16 2 32 78 49 64 65 50 6 66 21 22 82 23 39 84 85 10 86 56 42 87 13 58 44 74\\n7 19 4 20 24 25 12 27\\n\", \"82 50\\n0\\n0\\n\", \"65 75\\n15 25 60 12 62 37 22 47 52 3 63 58 6 14 49 34\\n18 70 10 2 52 22 47 72 57 38 48 13 73 3 19 4 74 49 34\\n\", \"91 98\\n78 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 10 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89\\n84 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89 91 92 93 94 95 96\\n\", \"100 100\\n50 0 1 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\\n49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 51 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"2 4\\n1 0\\n1 0\\n\", \"2 4\\n1 0\\n2 1 2\\n\", \"69 72\\n18 58 46 52 43 0 55 16 7 4 38 68 14 32 53 41 29 2 59\\n21 22 43 55 13 70 4 7 31 10 23 56 44 62 17 50 53 2 41 11 65 32\\n\", \"20 20\\n9 0 3 4 11 7 8 10 12 13\\n10 1 2 5 9 15 14 15 16 18 19\\n\", \"90 25\\n26 55 30 35 20 15 26 6 1 41 81 76 46 57 17 12 67 77 27 47 79 8 43 63 3 48 19\\n9 10 16 21 7 17 12 3 19 9\\n\", \"98 98\\n23 6 81 90 28 38 51 23 69 13 95 15 16 83 58 10 26 42 75 54 92 27 45 39\\n18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57\\n\", \"100 100\\n50 0 1 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\\n50 50 51 52 51 54 55 56 57 58 59 60 61 62 63 20 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 33 36 37 42 39 40 41 42 44 45 46 48 98 49\\n34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"4 20\\n0\\n1 14\\n\", \"66 66\\n26 0 54 6 37 43 13 25 38 2 32 56 20 50 39 27 51 9 64 4 16 17 65 14 5 47 23\\n15 2 24 43 49 25 20 14 63 27 3 58 52 53 11 41\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 19 20 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"79 23\\n35 31 62 14 9 46 18 68 69 42 13 50 77 23 76 2 53 40 16 32 74 54 38 25 45 39 26 37 66 78 5 48 10 17 56 59\\n13 16 0 8 6 18 14 21 11 20 4 15 13 22\\n\", \"96 36\\n34 84 24 0 48 85 13 61 37 62 38 86 26 3 16 64 40 28 76 53 5 17 42 6 7 91 67 55 68 92 57 11 71 35 59\\n9 1 17 15 17 18 30 6 8 35\\n\", \"98 98\\n43 49 1 51 3 53 4 55 56 8 9 10 60 11 12 37 64 16 65 17 19 20 21 72 24 74 25 77 78 31 34 35 36 37 87 88 89 42 92 43 50 94 46 96\\n34 50 2 52 5 54 9 62 63 15 18 68 70 22 72 75 26 27 77 30 81 82 83 35 36 37 87 88 89 90 41 93 95 96 48\\n\", \"75 75\\n33 30 74 57 23 19 42 71 11 44 29 58 43 48 61 63 13 27 50 17 18 70 64 39 12 32 36 10 40 51 49 1 54 73\\n8 73 23 0 7 63 47 74 19\\n\", \"26 52\\n8 0 14 16 17 7 9 10 11\\n15 39 15 2 41 0 30 17 18 31 6 21 29 48 50 51\\n\", \"100 2\\n1 66\\n0\\n\", \"36 100\\n10 0 32 4 5 33 30 18 14 35 7\\n29 60 32 20 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 65 75 35 95 43 78 3 27\\n\", \"75 30\\n18 46 47 32 33 3 34 35 21 51 7 15 54 39 72 42 59 29 14\\n8 0 3 5 6 23 26 27 13\\n\", \"82 100\\n0\\n0\\n\", \"91 98\\n78 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 10 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89\\n84 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 0 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89 91 92 93 94 95 96\\n\", \"2 4\\n1 0\\n2 2 2\\n\", \"69 72\\n18 58 46 52 43 0 55 16 7 4 38 68 14 32 53 41 29 2 59\\n21 22 43 55 13 70 4 7 34 10 23 56 44 62 17 50 53 2 41 11 65 32\\n\", \"20 20\\n9 0 3 4 11 7 8 14 12 13\\n10 1 2 5 9 15 14 15 16 18 19\\n\", \"90 25\\n26 55 30 35 20 15 26 6 1 41 81 76 46 57 17 12 67 75 27 47 79 8 43 63 3 48 19\\n9 10 16 21 7 17 12 3 19 9\\n\", \"98 98\\n23 6 81 90 28 38 51 23 69 13 95 15 16 83 58 10 26 67 75 54 92 27 45 39\\n18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 33 36 37 42 39 40 41 42 44 45 46 48 98 92\\n34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 20 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"96 36\\n34 84 24 0 48 85 13 61 37 62 38 86 26 3 16 64 40 28 76 53 5 17 42 6 7 91 67 55 68 92 57 11 71 35 59\\n9 0 17 15 17 18 30 6 8 35\\n\", \"75 75\\n33 30 74 57 23 19 42 71 11 44 29 58 43 48 61 63 13 27 50 17 18 70 64 39 12 3 36 10 40 51 49 1 54 73\\n8 73 23 0 7 63 47 74 19\\n\", \"26 52\\n8 0 14 16 17 7 9 10 11\\n15 39 15 0 41 0 30 17 18 31 6 21 29 48 50 51\\n\", \"100 2\\n1 55\\n0\\n\", \"36 100\\n10 0 32 4 5 33 30 18 14 35 7\\n29 60 32 29 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 65 75 35 95 43 78 3 27\\n\", \"75 30\\n18 46 47 32 33 3 34 35 21 51 7 15 54 39 69 42 59 29 14\\n8 0 3 5 6 23 26 27 13\\n\", \"23 100\\n0\\n0\\n\", \"69 72\\n18 58 46 52 43 0 55 16 7 4 38 68 14 32 53 41 29 2 59\\n21 22 43 55 13 70 4 6 34 10 23 56 44 62 17 50 53 2 41 11 65 32\\n\", \"20 20\\n9 0 3 4 11 7 8 14 12 13\\n10 1 2 5 9 15 14 15 16 11 19\\n\", \"98 98\\n23 6 81 90 28 38 51 23 69 13 95 15 16 83 58 10 26 67 75 54 92 27 45 39\\n18 20 70 38 82 72 61 37 78 74 23 15 3 59 35 93 64 28 57\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 97 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 33 36 37 42 39 40 41 42 44 45 46 48 98 92\\n34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 1 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"96 36\\n34 84 24 0 48 85 13 61 37 62 38 86 26 3 16 64 40 28 76 53 5 17 42 6 7 91 16 55 68 92 57 11 71 35 59\\n9 0 17 15 17 18 30 6 8 35\\n\", \"26 52\\n8 0 14 16 17 7 9 9 11\\n15 39 15 0 41 0 30 17 18 31 6 21 29 48 50 51\\n\", \"100 2\\n1 38\\n0\\n\", \"36 100\\n10 0 32 4 5 33 30 18 14 35 7\\n29 67 32 29 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 65 75 35 95 43 78 3 27\\n\", \"75 30\\n18 46 47 32 33 3 22 35 21 51 7 15 54 39 69 42 59 29 14\\n8 0 3 5 6 23 26 27 13\\n\", \"35 100\\n0\\n0\\n\", \"20 20\\n9 0 3 4 11 7 8 14 12 13\\n10 1 4 5 9 15 14 15 16 11 19\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 97 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 33 36 37 42 39 40 41 42 44 45 46 48 98 92\\n34 50 1 2 52 3 54 56 1 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 1 5 73 27 79 83 86 87 89 42 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"26 52\\n8 0 14 16 17 7 9 9 11\\n15 39 15 0 41 0 30 17 18 31 5 21 29 48 50 51\\n\", \"100 2\\n1 23\\n0\\n\", \"100 100\\n45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 97 17 18 20 21 22 22 25 27 78 28 29 30 31 82 83 33 33 36 37 42 39 40 41 42 44 45 46 48 98 92\\n34 50 1 2 52 3 54 56 1 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 1 5 73 27 79 83 86 87 89 58 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 25 26 28 30 31 6 34 35 38 40 41 49\\n\", \"26 52\\n8 0 14 16 17 7 9 9 11\\n15 39 15 0 41 0 30 24 18 31 5 21 29 48 50 51\\n\", \"100 2\\n1 24\\n0\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 1 5 73 27 79 83 86 87 89 58 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 17 26 28 30 31 6 34 35 38 40 41 49\\n\", \"26 52\\n8 0 14 16 11 7 9 9 11\\n15 39 15 0 41 0 30 24 18 31 5 21 29 48 50 51\\n\", \"100 3\\n1 24\\n0\\n\", \"100 50\\n30 50 54 7 8 59 60 61 62 86 64 15 16 18 27 1 5 73 27 79 83 86 87 89 58 93 94 45 46 97 98\\n20 1 2 3 5 6 17 21 24 17 26 28 30 28 6 34 35 38 40 41 49\\n\", \"26 65\\n8 0 14 16 11 7 9 9 11\\n15 39 15 0 41 0 30 24 18 31 5 21 29 48 50 51\\n\", \"100 3\\n1 42\\n0\\n\", \"100 3\\n1 32\\n0\\n\", \"75 90\\n60 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74\\n72 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 75 77 78 79 80 82 83 25 85 87 88 89\\n\", \"55 79\\n5 51 27 36 45 53\\n30 15 28 0 5 38 3 34 30 35 1 32 12 27 42 39 69 33 10 63 16 29 66 19 60 70 67 31 78 68 45\\n\", \"2 3\\n0\\n1 0\\n\", \"2 3\\n1 0\\n1 1\\n\", \"2 4\\n1 0\\n1 2\\n\"], \"outputs\": [\"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\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\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\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\", \"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\", \"Yes\\n\", \"Yes\\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\", \"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\", \"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\", \"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\", \"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\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\"]}", "source": "taco"}
|
Drazil has many friends. Some of them are happy and some of them are unhappy. Drazil wants to make all his friends become happy. So he invented the following plan.
There are n boys and m girls among his friends. Let's number them from 0 to n - 1 and 0 to m - 1 separately. In i-th day, Drazil invites <image>-th boy and <image>-th girl to have dinner together (as Drazil is programmer, i starts from 0). If one of those two people is happy, the other one will also become happy. Otherwise, those two people remain in their states. Once a person becomes happy (or if he/she was happy originally), he stays happy forever.
Drazil wants to know whether he can use this plan to make all his friends become happy at some moment.
Input
The first line contains two integer n and m (1 ≤ n, m ≤ 100).
The second line contains integer b (0 ≤ b ≤ n), denoting the number of happy boys among friends of Drazil, and then follow b distinct integers x1, x2, ..., xb (0 ≤ xi < n), denoting the list of indices of happy boys.
The third line conatins integer g (0 ≤ g ≤ m), denoting the number of happy girls among friends of Drazil, and then follow g distinct integers y1, y2, ... , yg (0 ≤ yj < m), denoting the list of indices of happy girls.
It is guaranteed that there is at least one person that is unhappy among his friends.
Output
If Drazil can make all his friends become happy by this plan, print "Yes". Otherwise, print "No".
Examples
Input
2 3
0
1 0
Output
Yes
Input
2 4
1 0
1 2
Output
No
Input
2 3
1 0
1 1
Output
Yes
Note
By <image> we define the remainder of integer division of i by k.
In first sample case:
* On the 0-th day, Drazil invites 0-th boy and 0-th girl. Because 0-th girl is happy at the beginning, 0-th boy become happy at this day.
* On the 1-st day, Drazil invites 1-st boy and 1-st girl. They are both unhappy, so nothing changes at this day.
* On the 2-nd day, Drazil invites 0-th boy and 2-nd girl. Because 0-th boy is already happy he makes 2-nd girl become happy at this day.
* On the 3-rd day, Drazil invites 1-st boy and 0-th girl. 0-th girl is happy, so she makes 1-st boy happy.
* On the 4-th day, Drazil invites 0-th boy and 1-st girl. 0-th boy is happy, so he makes the 1-st girl happy. So, all friends become happy at this moment.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"2\\n1 2\\n3 2\\n\", \"3\\n8 3\\n0 1\\n4 8\\n\", \"1\\n1 1\\n\", \"2\\n1 3\\n3 1\", \"1\\n0 0\", \"2\\n1 5\\n5 1\", \"3\\n8 3\\n-1 1\\n5 8\", \"2\\n0 2\\n3 1\", \"2\\n0 1\\n3 2\", \"2\\n1 4\\n5 2\", \"3\\n8 3\\n-1 0\\n4 8\", \"1\\n2 2\", \"1\\n-1 -1\", \"2\\n1 0\\n1 2\", \"2\\n2 3\\n2 1\", \"1\\n3 3\", \"1\\n-2 -2\", \"2\\n1 0\\n2 3\", \"2\\n-1 2\\n4 1\", \"2\\n2 3\\n3 2\", \"1\\n-3 -3\", \"2\\n2 1\\n2 3\", \"2\\n0 2\\n4 2\", \"2\\n0 0\\n2 2\", \"2\\n0 4\\n5 1\", \"2\\n2 5\\n5 2\", \"2\\n1 3\\n4 2\", \"2\\n1 1\\n1 1\", \"2\\n-2 2\\n4 0\", \"2\\n2 2\\n3 3\", \"2\\n1 2\\n2 1\", \"2\\n2 0\\n1 3\", \"2\\n1 1\\n0 0\", \"2\\n-2 1\\n4 1\", \"2\\n0 1\\n1 0\", \"3\\n11 3\\n-1 1\\n2 8\", \"2\\n0 3\\n4 1\", \"2\\n0 2\\n2 0\", \"2\\n2 2\\n2 2\", \"1\\n-6 -6\", \"2\\n2 2\\n1 1\", \"1\\n-4 -4\", \"2\\n-1 0\\n2 1\", \"2\\n-4 1\\n6 1\", \"2\\n1 1\\n2 2\", \"2\\n0 0\\n1 1\", \"2\\n2 1\\n1 2\", \"2\\n0 1\\n2 1\", \"2\\n2 4\\n3 1\", \"2\\n2 2\\n4 4\", \"2\\n0 0\\n4 4\", \"2\\n3 0\\n0 3\", \"2\\n1 2\\n0 -1\", \"2\\n1 0\\n0 1\", \"2\\n1 -1\\n1 3\", \"2\\n1 4\\n3 0\", \"2\\n1 0\\n3 4\", \"2\\n0 0\\n3 3\", \"2\\n0 -1\\n1 2\", \"2\\n1 3\\n2 0\", \"2\\n2 0\\n0 2\", \"2\\n1 -1\\n0 2\", \"2\\n0 0\\n0 0\", \"2\\n-1 1\\n1 -1\", \"2\\n1 1\\n3 3\", \"2\\n-1 -1\\n1 1\", \"2\\n4 4\\n2 2\", \"1\\n4 4\", \"2\\n2 0\\n2 4\", \"2\\n0 1\\n0 -1\", \"2\\n-1 2\\n2 -1\", \"2\\n2 2\\n0 0\", \"2\\n1 2\\n1 0\", \"2\\n-1 -1\\n0 0\", \"2\\n0 3\\n3 0\", \"2\\n0 3\\n2 -1\", \"2\\n2 -1\\n-1 2\", \"2\\n0 2\\n1 -1\", \"2\\n-1 1\\n2 0\", \"2\\n2 1\\n-1 0\", \"2\\n-1 2\\n3 0\", \"2\\n1 5\\n6 2\", \"2\\n1 0\\n4 5\", \"2\\n1 2\\n4 3\", \"2\\n2 4\\n2 0\", \"1\\n0 0\", \"1\\n-1 -1\", \"1\\n2 2\", \"2\\n0 2\\n4 2\", \"1\\n-2 -2\", \"1\\n-3 -3\", \"2\\n0 3\\n4 1\", \"2\\n1 2\\n1 0\", \"2\\n1 4\\n4 1\", \"1\\n4 4\", \"2\\n0 1\\n3 2\", \"1\\n3 3\", \"1\\n-4 -4\", \"2\\n1 2\\n2 1\", \"2\\n0 0\\n3 3\", \"2\\n1 4\\n3 0\", \"2\\n1 1\\n3 3\", \"2\\n1 3\\n3 1\", \"3\\n8 3\\n0 1\\n4 8\", \"1\\n1 1\", \"2\\n1 2\\n3 2\"], \"outputs\": [\"2\\n\", \"9\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"5\\n\", \"9\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"8\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"4\\n\", \"5\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"9\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"5\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"3\\n\", \"9\", \"0\", \"2\"]}", "source": "taco"}
|
You are given sequences A and B consisting of non-negative integers.
The lengths of both A and B are N, and the sums of the elements in A and B are equal.
The i-th element in A is A_i, and the i-th element in B is B_i.
Tozan and Gezan repeats the following sequence of operations:
- If A and B are equal sequences, terminate the process.
- Otherwise, first Tozan chooses a positive element in A and decrease it by 1.
- Then, Gezan chooses a positive element in B and decrease it by 1.
- Then, give one candy to Takahashi, their pet.
Tozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible.
Find the number of candies given to Takahashi when both of them perform the operations optimally.
-----Constraints-----
- 1 \leq N \leq 2 × 10^5
- 0 \leq A_i,B_i \leq 10^9(1\leq i\leq N)
- The sums of the elements in A and B are equal.
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
-----Output-----
Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.
-----Sample Input-----
2
1 2
3 2
-----Sample Output-----
2
When both Tozan and Gezan perform the operations optimally, the process will proceed as follows:
- Tozan decreases A_1 by 1.
- Gezan decreases B_1 by 1.
- One candy is given to Takahashi.
- Tozan decreases A_2 by 1.
- Gezan decreases B_1 by 1.
- One candy is given to Takahashi.
- As A and B are equal, the process is terminated.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1\\n28\\n13\", \"3\\n19 15 5\\n0 0 0\", \"3\\n23 10 14\\n0 3 4\", \"2\\n8 13\\n5 10\", \"1\\n28\\n11\", \"3\\n23 10 14\\n0 4 4\", \"1\\n28\\n3\", \"3\\n23 10 26\\n0 4 4\", \"2\\n8 13\\n0 2\", \"1\\n28\\n5\", \"3\\n6 10 26\\n0 4 4\", \"1\\n28\\n10\", \"3\\n6 12 26\\n0 4 4\", \"2\\n14 13\\n0 3\", \"3\\n6 12 26\\n1 4 4\", \"2\\n14 13\\n1 3\", \"3\\n6 12 26\\n1 4 5\", \"3\\n7 12 26\\n1 4 5\", \"2\\n8 13\\n1 13\", \"3\\n23 10 14\\n1 3 4\", \"3\\n19 21 5\\n1 0 0\", \"3\\n23 10 16\\n0 4 4\", \"3\\n23 10 26\\n0 4 7\", \"2\\n8 5\\n0 2\", \"1\\n28\\n8\", \"3\\n6 11 26\\n0 4 4\", \"1\\n28\\n4\", \"2\\n14 13\\n0 5\", \"3\\n11 12 26\\n1 4 4\", \"2\\n14 12\\n1 3\", \"3\\n6 12 26\\n1 4 3\", \"3\\n7 12 26\\n1 3 5\", \"3\\n19 5 14\\n0 0 1\", \"2\\n12 13\\n1 13\", \"3\\n23 10 14\\n2 3 4\", \"3\\n19 21 5\\n2 0 0\", \"3\\n23 10 16\\n0 4 6\", \"2\\n8 7\\n0 3\", \"2\\n3 5\\n0 2\", \"1\\n24\\n8\", \"3\\n0 11 26\\n0 4 4\", \"3\\n11 12 26\\n1 4 1\", \"3\\n6 12 26\\n1 0 3\", \"3\\n7 23 26\\n3 6 5\", \"3\\n23 10 31\\n0 4 6\", \"3\\n0 11 26\\n0 4 8\", \"1\\n49\\n3\", \"3\\n6 28 26\\n0 0 4\", \"3\\n18 12 26\\n1 4 1\", \"3\\n6 12 16\\n1 0 3\", \"3\\n14 12 26\\n1 3 3\", \"3\\n7 23 23\\n3 6 5\", \"3\\n8 12 47\\n2 3 5\", \"3\\n1 20 25\\n1 8 5\", \"3\\n2 12 26\\n0 3 5\", \"1\\n0\\n0\", \"3\\n32 5 14\\n0 1 1\", \"3\\n23 10 31\\n1 4 6\", \"3\\n25 39 10\\n1 1 0\", \"2\\n3 14\\n1 3\", \"3\\n14 20 26\\n1 3 3\", \"3\\n7 24 23\\n3 6 5\", \"3\\n32 5 14\\n0 1 2\", \"3\\n6 10 31\\n1 4 6\", \"2\\n3 21\\n1 3\", \"3\\n14 20 26\\n1 3 5\", \"3\\n7 24 23\\n3 6 6\", \"3\\n6 9 31\\n1 4 6\", \"3\\n14 20 26\\n2 3 5\", \"2\\n10 21\\n1 3\", \"3\\n18 18 16\\n1 0 2\", \"3\\n0 37 25\\n0 8 0\", \"3\\n10 9 31\\n1 4 4\", \"1\\n22\\n8\", \"3\\n2 20 26\\n2 0 5\", \"3\\n3 15 7\\n1 5 0\", \"1\\n11\\n4\", \"1\\n22\\n9\", \"3\\n3 13 7\\n1 5 0\", \"3\\n45 14 14\\n0 3 2\", \"1\\n20\\n4\", \"2\\n14 29\\n1 3\", \"1\\n20\\n8\", \"3\\n2 10 33\\n2 1 9\", \"2\\n8 29\\n1 3\", \"3\\n2 20 33\\n2 1 9\", \"1\\n23\\n4\", \"3\\n2 20 33\\n2 2 13\", \"2\\n1 12\\n0 1\", \"3\\n21 19 6\\n2 1 2\", \"4\\n2 1 1 8\\n2 0 1 8\", \"3\\n19 21 5\\n0 0 0\", \"2\\n8 13\\n0 10\", \"3\\n16 21 5\\n0 0 0\", \"3\\n26 21 5\\n0 0 0\", \"2\\n14 13\\n0 2\", \"3\\n25 21 5\\n0 0 0\", \"3\\n7 12 26\\n1 6 5\", \"3\\n7 12 26\\n2 6 5\", \"3\\n7 12 26\\n2 10 5\", \"1\\n50\\n13\", \"3\\n19 15 14\\n0 0 0\", \"3\\n19 10 14\\n0 3 4\", \"4\\n2 0 1 8\\n2 0 1 8\", \"2\\n8 13\\n5 13\"], \"outputs\": [\"32768\\n\", \"2\\n\", \"162\\n\", \"-1\\n\", \"131072\\n\", \"96\\n\", \"32\\n\", \"2114\\n\", \"144\\n\", \"33024\\n\", \"2112\\n\", \"262144\\n\", \"2306\\n\", \"34\\n\", \"2336\\n\", \"40\\n\", \"416\\n\", \"388\\n\", \"36\\n\", \"164\\n\", \"6\\n\", \"66\\n\", \"524354\\n\", \"10\\n\", \"1024\\n\", \"2178\\n\", \"64\\n\", \"258\\n\", \"2308\\n\", \"516\\n\", \"800\\n\", \"644\\n\", \"42\\n\", \"132\\n\", \"160\\n\", \"138\\n\", \"1090\\n\", \"16\\n\", \"8\\n\", \"65536\\n\", \"2176\\n\", \"288\\n\", \"546\\n\", \"131216\\n\", \"66114\\n\", \"640\\n\", \"1088\\n\", \"2050\\n\", \"292\\n\", \"560\\n\", \"548\\n\", \"131152\\n\", \"576\\n\", \"5120\\n\", \"642\\n\", \"0\\n\", \"44\\n\", \"66112\\n\", \"4\\n\", \"2052\\n\", \"2660\\n\", \"528\\n\", \"12\\n\", \"66144\\n\", \"68\\n\", \"2244\\n\", \"131600\\n\", \"66080\\n\", \"2240\\n\", \"72\\n\", \"136\\n\", \"525314\\n\", \"544\\n\", \"16384\\n\", \"130\\n\", \"1030\\n\", \"128\\n\", \"8192\\n\", \"262\\n\", \"2056\\n\", \"256\\n\", \"1096\\n\", \"4096\\n\", \"4104\\n\", \"1124\\n\", \"4132\\n\", \"4224\\n\", \"1048584\\n\", \"134\\n\", \"280\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"144\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"137438953472\", \"2\", \"160\", \"0\", \"-1\"]}", "source": "taco"}
|
Aoki is playing with a sequence of numbers a_{1}, a_{2}, ..., a_{N}. Every second, he performs the following operation :
* Choose a positive integer k. For each element of the sequence v, Aoki may choose to replace v with its remainder when divided by k, or do nothing with v. The cost of this operation is 2^{k} (regardless of how many elements he changes).
Aoki wants to turn the sequence into b_{1}, b_{2}, ..., b_{N} (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.
Constraints
* 1 \leq N \leq 50
* 0 \leq a_{i}, b_{i} \leq 50
* All values in the input are integers.
Input
Input is given from Standard Input in the following format:
N
a_{1} a_{2} ... a_{N}
b_{1} b_{2} ... b_{N}
Output
Print the minimum cost required to turn the original sequence into b_{1}, b_{2}, ..., b_{N}. If the task is impossible, output -1 instead.
Examples
Input
3
19 10 14
0 3 4
Output
160
Input
3
19 15 14
0 0 0
Output
2
Input
2
8 13
5 13
Output
-1
Input
4
2 0 1 8
2 0 1 8
Output
0
Input
1
50
13
Output
137438953472
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n6\\n3 2 5 6\\n2 4 6\\n3 1 3 4\\n2 1 3\\n4 1 2 4 6\\n5\\n2 2 3\\n2 1 2\\n2 1 4\\n2 4 5\\n7\\n3 1 2 6\\n4 1 3 5 6\\n2 1 2\\n3 4 5 7\\n6 1 2 3 4 5 6\\n3 1 3 6\\n2\\n2 1 2\\n5\\n2 2 5\\n3 2 3 5\\n4 2 3 4 5\\n5 1 2 3 4 5\\n\", \"1\\n6\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 5\\n6 1 2 3 4 5 6\\n\", \"1\\n6\\n4 2 3 4 5\\n2 1 3\\n2 3 5\\n2 2 5\\n6 1 2 3 4 5 6\\n\", \"1\\n6\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 2 3 4 5 6\\n\", \"1\\n6\\n4 1 3 4 5\\n2 1 3\\n2 3 5\\n2 2 5\\n6 1 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 5\\n7 2 2 3 6 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 2 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 2 2 3 4 1 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 6 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 0 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 4 1 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n8 0 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 2 3 4 5 12\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 2 2 3 3 1 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 4 2 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 4 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 4 3 4 5 12\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 0 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 1 3 0 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 2 3 4 2 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 0 2 3 4 10 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 1 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 6 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n11 1 4 3 4 5 12\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -2 2 3 1 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 1 3 6 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 1 3 6 3 11\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 4 5 4\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 0 2 3 4 5 5\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 2 3 4 2 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n2 -1 2 3 0 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n8 1 2 3 4 2 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 0 1 3 4 10 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n9 -1 2 3 1 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -2 3 3 1 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 1 3 7 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 0 3 6 3 11\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n8 1 2 3 4 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -2 3 3 1 9 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -2 3 3 0 9 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 2 2 3 4 5 5\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n10 2 2 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n8 0 3 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 2 2 3 3 1 4\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 4 5 1\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 1 3 0 5 0\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 0 3 4 2 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 2 1 3 0 3 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n7 0 0 3 6 3 11\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n8 1 3 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -1 2 3 5 5 1\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 -2 2 3 5 5 1\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 1 0 3 4 5 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n2 2 2 3 4 1 6\\n\", \"1\\n5\\n4 2 3 4 5\\n2 1 2\\n2 3 5\\n2 2 3\\n6 0 4 3 4 5 6\\n\", \"5\\n6\\n3 2 5 6\\n2 4 6\\n3 1 3 4\\n2 1 3\\n4 1 2 4 6\\n5\\n2 2 3\\n2 1 2\\n2 1 4\\n2 4 5\\n7\\n3 1 2 6\\n4 1 3 5 6\\n2 1 2\\n3 4 5 7\\n6 1 2 3 4 5 6\\n3 1 3 6\\n2\\n2 1 2\\n5\\n2 2 5\\n3 2 3 5\\n4 2 3 4 5\\n5 1 2 3 4 5\\n\"], \"outputs\": [\"3 1 4 6 2 5 \\n3 2 1 4 5 \\n2 1 6 3 5 4 7 \\n1 2 \\n2 5 3 4 1 \\n\", \"1 2 5 3 4 6 \\n\", \"1 3 5 2 4 6\\n\", \"1 2 3 5 4 6\\n\", \"1 2 3 5 4\\n\", \"2 5 3 1 4 6\\n\", \"1 2 5 3 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"1 2 3 5 4\\n\", \"3 1 4 6 2 5 \\n3 2 1 4 5 \\n2 1 6 3 5 4 7 \\n1 2 \\n2 5 3 4 1 \\n\"]}", "source": "taco"}
|
We guessed a permutation $p$ consisting of $n$ integers. The permutation of length $n$ is the array of length $n$ where each element from $1$ to $n$ appears exactly once. This permutation is a secret for you.
For each position $r$ from $2$ to $n$ we chose some other index $l$ ($l < r$) and gave you the segment $p_l, p_{l + 1}, \dots, p_r$ in sorted order (i.e. we rearranged the elements of this segment in a way that the elements of this segment are sorted). Thus, you are given exactly $n-1$ segments of the initial permutation but elements inside each segment are sorted. The segments are given to you in random order.
For example, if the secret permutation is $p=[3, 1, 4, 6, 2, 5]$ then the possible given set of segments can be: $[2, 5, 6]$ $[4, 6]$ $[1, 3, 4]$ $[1, 3]$ $[1, 2, 4, 6]$
Your task is to find any suitable permutation (i.e. any permutation corresponding to the given input data). It is guaranteed that the input data corresponds to some permutation (i.e. such permutation exists).
You have to answer $t$ independent test cases.
-----Input-----
The first line of the input contains one integer $t$ ($1 \le t \le 100$) — the number of test cases. Then $t$ test cases follow.
The first line of the test case contains one integer $n$ ($2 \le n \le 200$) — the length of the permutation.
The next $n-1$ lines describe given segments.
The $i$-th line contains the description of the $i$-th segment. The line starts with the integer $k_i$ ($2 \le k_i \le n$) — the length of the $i$-th segment. Then $k_i$ integers follow. All integers in a line are distinct, sorted in ascending order, between $1$ and $n$, inclusive.
It is guaranteed that the required $p$ exists for each test case.
It is also guaranteed that the sum of $n$ over all test cases does not exceed $200$ ($\sum n \le 200$).
-----Output-----
For each test case, print the answer: $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$, all $p_i$ should be distinct) — any suitable permutation (i.e. any permutation corresponding to the test case input).
-----Example-----
Input
5
6
3 2 5 6
2 4 6
3 1 3 4
2 1 3
4 1 2 4 6
5
2 2 3
2 1 2
2 1 4
2 4 5
7
3 1 2 6
4 1 3 5 6
2 1 2
3 4 5 7
6 1 2 3 4 5 6
3 1 3 6
2
2 1 2
5
2 2 5
3 2 3 5
4 2 3 4 5
5 1 2 3 4 5
Output
3 1 4 6 2 5
3 2 1 4 5
2 1 6 3 5 4 7
1 2
2 5 3 4 1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"Hello\"], [314159], [\"314159\"], [[]], [{}], [true], [[1, 2, 3]]], \"outputs\": [[\"olleH\"], [951413], [\"951413\"], [[]], [{}], [true], [[1, 2, 3]]]}", "source": "taco"}
|
You have to create a function named reverseIt.
Write your function so that in the case a string or a number is passed in as the data , you will return the data in reverse order. If the data is any other type, return it as it is.
Examples of inputs and subsequent outputs:
```
"Hello" -> "olleH"
"314159" -> "951413"
[1,2,3] -> [1,2,3]
```
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n1 4 1 1\\n\", \"5\\n1 0 1 0 1\\n\", \"1\\n1000000000\\n\", \"4\\n3 3 3 3\\n\", \"4\\n3 3 2 3\\n\", \"16\\n1 1 2 3 3 4 5 6 6 6 4 3 2 1 1 1\\n\", \"1\\n1\\n\", \"20\\n1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2\\n\", \"1\\n0\\n\", \"2\\n0 1\\n\", \"4\\n3 3 3 3\\n\", \"1\\n0\\n\", \"16\\n1 1 2 3 3 4 5 6 6 6 4 3 2 1 1 1\\n\", \"1\\n1\\n\", \"20\\n1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2\\n\", \"2\\n0 1\\n\", \"4\\n3 3 2 3\\n\", \"1\\n1000000000\\n\", \"4\\n3 4 3 3\\n\", \"16\\n1 1 2 3 3 4 5 6 6 6 4 3 0 1 1 1\\n\", \"1\\n2\\n\", \"20\\n1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3\\n\", \"4\\n3 3 2 2\\n\", \"5\\n1 0 1 0 0\\n\", \"20\\n1 2 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 3\\n\", \"16\\n1 1 2 3 3 1 5 6 6 6 4 1 0 1 1 1\\n\", \"16\\n1 1 2 3 0 1 5 6 6 6 4 1 0 1 1 1\\n\", \"20\\n1 2 2 6 1 2 0 2 1 2 0 2 1 2 1 2 0 2 1 0\\n\", \"2\\n0 0\\n\", \"16\\n1 1 2 3 3 4 5 6 6 6 4 3 0 1 1 2\\n\", \"2\\n0 2\\n\", \"4\\n1 4 2 1\\n\", \"4\\n3 4 3 5\\n\", \"16\\n1 1 2 3 3 4 5 6 6 6 4 1 0 1 1 1\\n\", \"4\\n3 3 2 1\\n\", \"4\\n1 4 3 1\\n\", \"4\\n6 4 3 5\\n\", \"20\\n1 2 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 0\\n\", \"4\\n3 3 3 1\\n\", \"4\\n1 7 3 1\\n\", \"4\\n6 4 3 8\\n\", \"20\\n1 2 1 4 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 0\\n\", \"4\\n3 3 5 1\\n\", \"4\\n1 5 3 1\\n\", \"4\\n6 4 3 7\\n\", \"16\\n1 1 2 3 0 1 5 6 6 6 7 1 0 1 1 1\\n\", \"20\\n1 2 2 4 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 0\\n\", \"4\\n3 3 4 1\\n\", \"4\\n1 5 1 1\\n\", \"4\\n6 1 3 7\\n\", \"16\\n1 1 2 3 0 0 5 6 6 6 7 1 0 1 1 1\\n\", \"20\\n1 2 2 6 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 0\\n\", \"4\\n3 4 4 1\\n\", \"4\\n1 0 1 1\\n\", \"4\\n6 0 3 7\\n\", \"16\\n1 1 2 3 0 0 5 6 6 6 7 2 0 1 1 1\\n\", \"20\\n1 2 2 6 1 2 0 2 1 2 1 2 1 2 1 2 0 2 1 0\\n\", \"4\\n3 4 4 2\\n\", \"4\\n2 0 1 1\\n\", \"4\\n6 0 3 1\\n\", \"16\\n1 1 2 3 0 0 8 6 6 6 7 2 0 1 1 1\\n\", \"4\\n5 4 4 2\\n\", \"4\\n6 0 3 0\\n\", \"16\\n1 1 2 3 0 0 8 6 6 6 9 2 0 1 1 1\\n\", \"4\\n5 8 4 2\\n\", \"16\\n1 1 2 4 0 0 8 6 6 6 9 2 0 1 1 1\\n\", \"4\\n5 8 4 1\\n\", \"16\\n1 2 2 4 0 0 8 6 6 6 9 2 0 1 1 1\\n\", \"4\\n4 8 4 1\\n\", \"16\\n1 2 2 4 0 0 8 6 6 2 9 2 0 1 1 1\\n\", \"4\\n7 8 4 1\\n\", \"16\\n0 2 2 4 0 0 8 6 6 2 9 2 0 1 1 1\\n\", \"4\\n7 4 4 1\\n\", \"16\\n0 2 2 4 0 0 1 6 6 2 9 2 0 1 1 1\\n\", \"4\\n7 5 4 1\\n\", \"16\\n0 2 2 4 0 0 1 6 6 3 9 2 0 1 1 1\\n\", \"4\\n7 5 1 1\\n\", \"4\\n7 10 1 1\\n\", \"4\\n7 10 2 1\\n\", \"4\\n7 13 2 1\\n\", \"4\\n7 13 3 1\\n\", \"4\\n2 13 3 1\\n\", \"4\\n2 26 3 1\\n\", \"4\\n2 26 3 2\\n\", \"4\\n2 46 3 2\\n\", \"4\\n2 46 3 0\\n\", \"4\\n2 6 3 0\\n\", \"4\\n3 3 1 3\\n\", \"1\\n3\\n\", \"16\\n1 1 2 3 3 4 10 6 6 6 4 3 2 1 1 1\\n\", \"1\\n4\\n\", \"20\\n1 2 1 2 1 2 1 2 1 0 1 2 1 2 1 2 1 2 1 2\\n\", \"4\\n0 3 2 3\\n\", \"4\\n1 4 1 0\\n\", \"5\\n1 1 1 0 1\\n\", \"4\\n3 4 1 3\\n\", \"1\\n6\\n\", \"20\\n1 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 1 2 1 3\\n\", \"2\\n1 2\\n\", \"4\\n1 4 1 1\\n\", \"5\\n1 0 1 0 1\\n\"], \"outputs\": [\"2\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"6\\n\", \"1\\n\", \"11\\n\", \"0\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"6\\n\", \"1\\n\", \"11\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"4\\n\", \"7\\n\", \"1\\n\", \"11\\n\", \"3\\n\", \"2\\n\", \"12\\n\", \"9\\n\", \"10\\n\", \"13\\n\", \"0\\n\", \"8\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"7\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"11\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"11\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"10\\n\", \"11\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"10\\n\", \"11\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"10\\n\", \"12\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"10\\n\", \"4\\n\", \"2\\n\", \"10\\n\", \"4\\n\", \"10\\n\", \"4\\n\", \"10\\n\", \"4\\n\", \"10\\n\", \"4\\n\", \"10\\n\", \"4\\n\", \"9\\n\", \"4\\n\", \"10\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"11\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"1\\n\", \"10\\n\", \"2\\n\", \"2\\n\", \"3\\n\"]}", "source": "taco"}
|
You have a multiset containing several integers. Initially, it contains $a_1$ elements equal to $1$, $a_2$ elements equal to $2$, ..., $a_n$ elements equal to $n$.
You may apply two types of operations: choose two integers $l$ and $r$ ($l \le r$), then remove one occurrence of $l$, one occurrence of $l + 1$, ..., one occurrence of $r$ from the multiset. This operation can be applied only if each number from $l$ to $r$ occurs at least once in the multiset; choose two integers $i$ and $x$ ($x \ge 1$), then remove $x$ occurrences of $i$ from the multiset. This operation can be applied only if the multiset contains at least $x$ occurrences of $i$.
What is the minimum number of operations required to delete all elements from the multiset?
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 5000$).
The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($0 \le a_i \le 10^9$).
-----Output-----
Print one integer — the minimum number of operations required to delete all elements from the multiset.
-----Examples-----
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n1 1\\n\", \"3\\n3 4 2\\n\", \"1\\n1\\n\", \"1\\n1000000000\\n\", \"3\\n1 2 3\\n\", \"2\\n2 3\\n\", \"5\\n1 4 2 1 1\\n\", \"15\\n2 72 77 69 62 73 58 9 4 95 97 14 41 79 34\\n\", \"1\\n1\\n\", \"10\\n529280935 122195401 684409084 743180136 724768643 211207376 167236398 696535490 425348743 1\\n\", \"8\\n1 870540358 821874877 223725489 367257956 1 105870869 267059674\\n\", \"5\\n483078839 692549116 1 458438081 1\\n\", \"6\\n1 1 423308752 1 1 1\\n\", \"7\\n150616203 306436158 391126478 164096410 558820207 878798937 310121836\\n\", \"50\\n1 3083990 976356336 922018335 1 170272482 1 547248035 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 942696777 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"96\\n1 1 1 1 1 1 1 943302667 1 1 1 1 1 1 1 1 422145309 1 1 848134211 1 1 1 1 182511245 1 1 1 1 826044915 1 1 1 1 778749310 1 1 1 1 1 1 1 1 1 1 1 1 1 274149110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 291019191 1 1 1 1 1 1 1 1 1 1 1 532064146 1 1 1 1 1 1 772234680 1 1 1 1 1 1 1\\n\", \"10\\n529280935 122195401 684409084 743180136 724768643 211207376 167236398 696535490 425348743 1\\n\", \"5\\n483078839 692549116 1 458438081 1\\n\", \"15\\n2 72 77 69 62 73 58 9 4 95 97 14 41 79 34\\n\", \"50\\n1 3083990 976356336 922018335 1 170272482 1 547248035 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 942696777 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"7\\n150616203 306436158 391126478 164096410 558820207 878798937 310121836\\n\", \"1\\n1\\n\", \"6\\n1 1 423308752 1 1 1\\n\", \"5\\n1 4 2 1 1\\n\", \"2\\n2 3\\n\", \"3\\n1 2 3\\n\", \"8\\n1 870540358 821874877 223725489 367257956 1 105870869 267059674\\n\", \"1\\n1000000000\\n\", \"96\\n1 1 1 1 1 1 1 943302667 1 1 1 1 1 1 1 1 422145309 1 1 848134211 1 1 1 1 182511245 1 1 1 1 826044915 1 1 1 1 778749310 1 1 1 1 1 1 1 1 1 1 1 1 1 274149110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 291019191 1 1 1 1 1 1 1 1 1 1 1 532064146 1 1 1 1 1 1 772234680 1 1 1 1 1 1 1\\n\", \"5\\n483078839 348093611 1 458438081 1\\n\", \"15\\n2 72 77 54 62 73 58 9 4 95 97 14 41 79 34\\n\", \"50\\n1 3083990 976356336 650365630 1 170272482 1 547248035 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 942696777 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"7\\n150616203 306436158 391126478 82886680 558820207 878798937 310121836\\n\", \"1\\n2\\n\", \"6\\n2 1 423308752 1 1 1\\n\", \"5\\n1 5 2 1 1\\n\", \"2\\n2 2\\n\", \"3\\n1 2 4\\n\", \"8\\n1 870540358 821874877 223725489 367257956 1 105870869 473512028\\n\", \"5\\n323193204 348093611 1 458438081 1\\n\", \"15\\n2 72 77 54 62 73 36 9 4 95 97 14 41 79 34\\n\", \"50\\n1 3083990 976356336 650365630 1 170272482 1 349492670 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 942696777 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"7\\n150616203 306436158 391126478 13755300 558820207 878798937 310121836\\n\", \"6\\n2 1 236308097 1 1 1\\n\", \"8\\n1 870540358 821874877 223725489 367257956 1 105870869 200236427\\n\", \"5\\n532329217 348093611 1 458438081 1\\n\", \"15\\n2 72 77 54 62 73 36 9 4 95 97 14 53 79 34\\n\", \"50\\n1 3083990 976356336 650365630 1 170272482 1 349492670 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 185208167 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"7\\n150616203 306436158 391126478 18041268 558820207 878798937 310121836\\n\", \"2\\n2 7\\n\", \"8\\n1 870540358 821874877 223725489 526411279 1 105870869 200236427\\n\", \"5\\n532329217 348093611 1 213704341 1\\n\", \"15\\n2 72 77 54 62 73 36 9 4 95 97 14 18 79 34\\n\", \"50\\n1 3083990 976356336 650365630 1 170272482 1 349492670 1 1 1 1 1 732217245 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 185208167 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"2\\n4 7\\n\", \"8\\n1 206069219 821874877 223725489 526411279 1 105870869 200236427\\n\", \"15\\n2 72 77 54 62 73 36 9 4 95 97 14 18 71 34\\n\", \"50\\n1 3083990 976356336 650365630 1 170272482 1 349492670 1 1 1 1 1 732217245 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 194289952 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"15\\n2 72 77 54 62 73 36 9 4 95 97 14 18 64 34\\n\", \"50\\n1 3083990 976356336 542741725 1 170272482 1 349492670 1 1 1 1 1 732217245 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 194289952 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"15\\n2 72 29 54 62 73 36 9 4 95 97 14 18 64 34\\n\", \"50\\n1 3083990 976356336 542741725 1 170272482 1 349492670 1 1 1 1 1 732217245 1 1 1 270052499 315045369 1 2 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 194289952 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 313704390 1 1 957736320 771147030 458205965 497342117\\n\", \"15\\n2 72 29 54 62 73 36 9 4 95 97 12 18 64 34\\n\", \"15\\n1 72 29 54 62 73 36 9 4 95 97 12 18 64 34\\n\", \"15\\n1 72 29 54 62 73 36 9 4 95 86 12 18 64 34\\n\", \"15\\n1 72 29 54 56 73 36 9 4 95 86 12 18 64 34\\n\", \"15\\n1 72 29 54 56 73 36 9 4 95 86 23 18 64 34\\n\", \"15\\n1 72 9 54 56 73 36 9 4 95 86 23 18 64 34\\n\", \"10\\n778941740 122195401 684409084 743180136 724768643 211207376 167236398 696535490 425348743 1\\n\", \"5\\n312909297 692549116 1 458438081 1\\n\", \"15\\n2 72 35 69 62 73 58 9 4 95 97 14 41 79 34\\n\", \"50\\n1 3083990 976356336 922018335 1 170272482 1 547248035 1 1 1 1 1 928379588 1 1 1 270052499 315045369 1 1 556091215 1 655608230 424079072 1 1 185387009 77360256 1 1 942696777 228860271 1 487787709 1 437229749 167886535 1 1 904578415 319694007 1 218169824 1 1 957736320 771147030 458205965 497342117\\n\", \"7\\n150616203 207194989 391126478 164096410 558820207 878798937 310121836\\n\", \"1\\n3\\n\", \"8\\n1 870540358 821874877 223725489 367257956 1 131395668 267059674\\n\", \"1\\n1000000001\\n\", \"3\\n3 8 2\\n\", \"15\\n1 72 77 54 62 73 58 9 4 95 97 14 41 79 34\\n\", \"3\\n3 1 2\\n\", \"2\\n2 4\\n\", \"2\\n4 2\\n\", \"2\\n4 1\\n\", \"2\\n2 5\\n\", \"3\\n1 2 5\\n\", \"2\\n2 1\\n\", \"3\\n3 4 2\\n\", \"2\\n1 1\\n\"], \"outputs\": [\"0\\n\", \"13\\n\", \"0\\n\", \"999999999\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"944598823\\n\", \"0\\n\", \"391882076\\n\", \"945207649\\n\", \"723940136\\n\", \"423308751\\n\", \"650844459\\n\", \"768215804\\n\", \"870354739\\n\", \"391882076\", \"723940136\", \"944598823\", \"768215804\", \"650844459\", \"0\", \"423308751\", \"5\", \"4\", \"4\", \"945207649\", \"999999999\", \"870354739\", \"764258501\\n\", \"236107225\\n\", \"817336984\\n\", \"848312664\\n\", \"1\\n\", \"423308752\\n\", \"6\\n\", \"3\\n\", \"5\\n\", \"151659996\\n\", \"863947180\\n\", \"753198551\\n\", \"619581619\\n\", \"402332178\\n\", \"236308097\\n\", \"878384402\\n\", \"813508879\\n\", \"234157465\\n\", \"557228378\\n\", \"177428362\\n\", \"8\\n\", \"37537718\\n\", \"568775139\\n\", \"753117508\\n\", \"361066035\\n\", \"18\\n\", \"268771733\\n\", \"753117500\\n\", \"652521025\\n\", \"753117493\\n\", \"301366472\\n\", \"970097858\\n\", \"301366474\\n\", \"38217036\\n\", \"561097563\\n\", \"370070157\\n\", \"396758728\\n\", \"39300406\\n\", \"953666201\\n\", \"641542881\\n\", \"301726511\\n\", \"563770099\\n\", \"672681238\\n\", \"358691126\\n\", \"2\\n\", \"543640646\\n\", \"1000000000\\n\", \"17\\n\", \"67220024\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"6\\n\", \"6\\n\", \"1\\n\", \"13\", \"0\"]}", "source": "taco"}
|
Long ago, Vasily built a good fence at his country house. Vasily calls a fence good, if it is a series of n consecutively fastened vertical boards of centimeter width, the height of each in centimeters is a positive integer. The house owner remembers that the height of the i-th board to the left is h_{i}.
Today Vasily decided to change the design of the fence he had built, by cutting his top connected part so that the fence remained good. The cut part should consist of only the upper parts of the boards, while the adjacent parts must be interconnected (share a non-zero length before cutting out of the fence).
You, as Vasily's curious neighbor, will count the number of possible ways to cut exactly one part as is described above. Two ways to cut a part are called distinct, if for the remaining fences there is such i, that the height of the i-th boards vary.
As Vasily's fence can be very high and long, get the remainder after dividing the required number of ways by 1 000 000 007 (10^9 + 7).
-----Input-----
The first line contains integer n (1 ≤ n ≤ 1 000 000) — the number of boards in Vasily's fence.
The second line contains n space-separated numbers h_1, h_2, ..., h_{n} (1 ≤ h_{i} ≤ 10^9), where h_{i} equals the height of the i-th board to the left.
-----Output-----
Print the remainder after dividing r by 1 000 000 007, where r is the number of ways to cut exactly one connected part so that the part consisted of the upper parts of the boards and the remaining fence was good.
-----Examples-----
Input
2
1 1
Output
0
Input
3
3 4 2
Output
13
-----Note-----
From the fence from the first example it is impossible to cut exactly one piece so as the remaining fence was good.
All the possible variants of the resulting fence from the second sample look as follows (the grey shows the cut out part): [Image]
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"-12 -35\\n\", \"-215 -996\\n\", \"-96 -556\\n\", \"-1000 0\\n\", \"20 -21\\n\", \"0 0\\n\", \"207 -224\\n\", \"-668 970\\n\", \"-496 -644\\n\", \"253 -204\\n\", \"-129 489\\n\", \"15 -8\\n\", \"-589 952\\n\", \"0 2\\n\", \"-216 -90\\n\", \"-72 -646\\n\", \"280 342\\n\", \"0 1000\\n\", \"875 -129\\n\", \"-201 278\\n\", \"-196 -484\\n\", \"-4 -4\\n\", \"-677 492\\n\", \"377 -902\\n\", \"-441 572\\n\", \"217 221\\n\", \"4 4\\n\", \"117 -44\\n\", \"3 3\\n\", \"351 -280\\n\", \"1000 -1000\\n\", \"-211 243\\n\", \"0 -1000\\n\", \"12 5\\n\", \"-796 -365\\n\", \"658 198\\n\", \"72 -154\\n\", \"128 -504\\n\", \"4 -4\\n\", \"902 479\\n\", \"-206 -518\\n\", \"-673 -270\\n\", \"-4 4\\n\", \"0 72\\n\", \"12 -5\\n\", \"189 -387\\n\", \"64 0\\n\", \"132 224\\n\", \"-399 -40\\n\", \"165 -738\\n\", \"0 1\\n\", \"-180 -432\\n\", \"61 -175\\n\", \"-469 -36\\n\", \"-281 -552\\n\", \"17 144\\n\", \"847 -294\\n\", \"8 882\\n\", \"60 -448\\n\", \"-220 208\\n\", \"-40 198\\n\", \"-693 -929\\n\", \"555 319\\n\", \"168 -26\\n\", \"-42 389\\n\", \"-192 -256\\n\", \"1000 0\\n\", \"-12 -49\\n\", \"-299 -996\\n\", \"-46 -556\\n\", \"-330 0\\n\", \"27 -21\\n\", \"-1 0\\n\", \"207 -376\\n\", \"-668 1077\\n\", \"-368 -644\\n\", \"156 -204\\n\", \"-50 489\\n\", \"9 -8\\n\", \"-589 1107\\n\", \"1 2\\n\", \"-216 -70\\n\", \"-64 -646\\n\", \"99 342\\n\", \"1 1000\\n\", \"1336 -129\\n\", \"-388 278\\n\", \"-196 -146\\n\", \"-4 -3\\n\", \"-1093 492\\n\", \"626 -902\\n\", \"-477 572\\n\", \"410 221\\n\", \"4 6\\n\", \"117 -30\\n\", \"2 3\\n\", \"237 -280\\n\", \"0000 -1000\\n\", \"-211 366\\n\", \"0 -1649\\n\", \"12 0\\n\", \"-694 -365\\n\", \"658 349\\n\", \"87 -154\\n\", \"230 -504\\n\", \"2 -4\\n\", \"-206 -838\\n\", \"-123 -270\\n\", \"-4 2\\n\", \"0 116\\n\", \"1 -5\\n\", \"189 -746\\n\", \"35 0\\n\", \"132 381\\n\", \"-399 -5\\n\", \"165 -1083\\n\", \"0 -1\\n\", \"-180 -861\\n\", \"61 -291\\n\", \"-641 -36\\n\", \"-409 -552\\n\", \"17 105\\n\", \"847 -226\\n\", \"8 1385\\n\", \"108 -448\\n\", \"-47 208\\n\", \"-76 198\\n\", \"-1059 -929\\n\", \"555 173\\n\", \"168 -9\\n\", \"-42 272\\n\", \"-192 -499\\n\", \"1000 1\\n\", \"-2 0\\n\", \"5 3\\n\", \"3 1\\n\", \"-12 -93\\n\", \"-66 -556\\n\", \"-330 -1\\n\", \"27 -40\\n\", \"1 0\\n\", \"207 -601\\n\", \"-26 1077\\n\", \"-368 -875\\n\", \"159 -204\\n\", \"-50 93\\n\", \"3 -8\\n\", \"-512 1107\\n\", \"1 4\\n\", \"-216 -26\\n\", \"-25 -646\\n\", \"99 59\\n\", \"1 1100\\n\", \"1336 -229\\n\", \"-470 278\\n\", \"-196 -50\\n\", \"-7 -3\\n\", \"-1085 492\\n\", \"626 -1338\\n\", \"-857 572\\n\", \"666 221\\n\", \"-2 1\\n\", \"4 3\\n\", \"2 1\\n\"], \"outputs\": [\"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"white\\n\", \"black\\n\", \"black\\n\", \"white\\n\", \"white\\n\", \"white\\n\", \"black\\n\", \"black\\n\"]}", "source": "taco"}
|
Not so long ago as a result of combat operations the main Berland place of interest — the magic clock — was damaged. The cannon's balls made several holes in the clock, that's why the residents are concerned about the repair. The magic clock can be represented as an infinite Cartesian plane, where the origin corresponds to the clock center. The clock was painted two colors as is shown in the picture:
<image>
The picture shows only the central part of the clock. This coloring naturally extends to infinity.
The balls can be taken to be points on the plane. Your task is to find the color of the area, damaged by the given ball.
All the points located on the border of one of the areas have to be considered painted black.
Input
The first and single line contains two integers x and y — the coordinates of the hole made in the clock by the ball. Each of the numbers x and y has an absolute value that does not exceed 1000.
Output
Find the required color.
All the points between which and the origin of coordinates the distance is integral-value are painted black.
Examples
Input
-2 1
Output
white
Input
2 1
Output
black
Input
4 3
Output
black
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 0 0\\n1 2\\n2 3\\n\", \"2 1 0\\n1 2\\n2 2\\n\", \"2 5 7\\n3 4\\n14 4\\n\", \"2 0 1\\n1 2\\n2 2\\n\", \"2 1 1\\n0 0\\n1 1\\n\", \"5 5 5\\n0 0 0 0 0\\n0 0 0 0 0\\n\", \"3 4 5\\n1 2 3\\n3 2 1\\n\", \"3 1000 0\\n1 2 3\\n-1000 -1000 -1000\\n\", \"10 300 517\\n-6 -2 6 5 -3 8 9 -10 8 6\\n5 -9 -2 6 1 4 6 -2 5 -3\\n\", \"10 819 133\\n87 22 30 89 82 -97 -52 25 76 -22\\n-20 95 21 25 2 -3 45 -7 -98 -56\\n\", \"10 10 580\\n302 -553 -281 -299 -270 -890 -989 -749 -418 486\\n735 330 6 725 -984 209 -855 -786 -502 967\\n\", \"10 403 187\\n9691 -3200 3016 3540 -9475 8840 -4705 7940 6293 -2631\\n-2288 9129 4067 696 -6754 9869 -5747 701 3344 -3426\\n\", \"10 561 439\\n76639 67839 10670 -23 -18393 65114 46538 67596 86615 90480\\n50690 620 -33631 -75857 75634 91321 -81662 -93668 -98557 -43621\\n\", \"10 765 62\\n-929885 -995154 254071 -370672 -435272 584846 -301610 -234118 -82557 743536\\n-36327 439149 -977780 -821019 -585558 953598 -151943 140715 -311253 -383103\\n\", \"22 334 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|
You are given two arrays A and B, each of size n. The error, E, between these two arrays is defined $E = \sum_{i = 1}^{n}(a_{i} - b_{i})^{2}$. You have to perform exactly k_1 operations on array A and exactly k_2 operations on array B. In one operation, you have to choose one element of the array and increase or decrease it by 1.
Output the minimum possible value of error after k_1 operations on array A and k_2 operations on array B have been performed.
-----Input-----
The first line contains three space-separated integers n (1 ≤ n ≤ 10^3), k_1 and k_2 (0 ≤ k_1 + k_2 ≤ 10^3, k_1 and k_2 are non-negative) — size of arrays and number of operations to perform on A and B respectively.
Second line contains n space separated integers a_1, a_2, ..., a_{n} ( - 10^6 ≤ a_{i} ≤ 10^6) — array A.
Third line contains n space separated integers b_1, b_2, ..., b_{n} ( - 10^6 ≤ b_{i} ≤ 10^6)— array B.
-----Output-----
Output a single integer — the minimum possible value of $\sum_{i = 1}^{n}(a_{i} - b_{i})^{2}$ after doing exactly k_1 operations on array A and exactly k_2 operations on array B.
-----Examples-----
Input
2 0 0
1 2
2 3
Output
2
Input
2 1 0
1 2
2 2
Output
0
Input
2 5 7
3 4
14 4
Output
1
-----Note-----
In the first sample case, we cannot perform any operations on A or B. Therefore the minimum possible error E = (1 - 2)^2 + (2 - 3)^2 = 2.
In the second sample case, we are required to perform exactly one operation on A. In order to minimize error, we increment the first element of A by 1. Now, A = [2, 2]. The error is now E = (2 - 2)^2 + (2 - 2)^2 = 0. This is the minimum possible error obtainable.
In the third sample case, we can increase the first element of A to 8, using the all of the 5 moves available to us. Also, the first element of B can be reduced to 8 using the 6 of the 7 available moves. Now A = [8, 4] and B = [8, 4]. The error is now E = (8 - 8)^2 + (4 - 4)^2 = 0, but we are still left with 1 move for array B. Increasing the second element of B to 5 using the left move, we get B = [8, 5] and E = (8 - 8)^2 + (4 - 5)^2 = 1.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
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\"wbbmmsnnpdduuwwrnjjoooovveennyyuukkmzoovllvzzhvvtruhiinbhyudkrrvimjden\", \"etq\\n\", \"cceeggrrrrwwwwwwyyzz\\n\", \"ddyy\\n\", \"baab\\n\", \"esq\\n\", \"eeyy\\n\", \"wae\\n\", \"z\\n\", \"eqt\\n\", \"babb\\n\", \"eexx\\n\", \"eeww\\n\", \"ddww\\n\", \"cj\\n\", \"dy\\n\", \"ert\\n\", \"daarkkcnay\\n\", \"bk\\n\", \"rrttttrrppfaabbkka\\n\", \"bbaa\\n\", \"eqs\\n\", \"ex\\n\", \"ck\\n\", \"cy\\n\", \"errtt\\n\", \"daarkkdnay\\n\", \"ey\\n\", \"eerrtt\\n\", \"xae\\n\", \"aaaabbbbddmmsswwwwxx\\n\", \"y\\n\", \"uru\\n\", \"ffffggnypigmo\\n\", \"aabbba\\n\", \"we\\n\", \"ci\\n\", \"ffyy\\n\", \"aabb\\n\", \"eqqss\\n\", \"cckk\\n\", \"eevv\\n\", \"ccii\\n\", \"yc\\n\", \"ic\\n\", \"qlsujxrszs\\n\", \"ffffggnypggiimo\\n\", \"ers\\n\", \"vae\\n\", \"wd\\n\", \"eezz\\n\", \"dz\\n\", \"etr\\n\", \"ch\\n\", \"qlsuzxrsjjs\\n\", \"sre\\n\", \"ze\\n\", \"zd\\n\", \"trfaaaatrkbbp\\n\", \"equ\\n\", \"qet\\n\", \"ddxx\\n\", \"daarkkcnaay\\n\", \"kb\\n\", \"darkdnay\\n\", \"ccjj\\n\", \"jc\\n\", \"yd\\n\", \"ye\\n\", \"qte\\n\", \"rte\\n\", \"xd\\n\", \"baaaab\\n\", \"aawe\\n\", \"kc\\n\", \"fy\\n\", \"ez\\n\", \"xea\\n\", \"darkcnay\\n\", \"qltujxrszs\\n\", \"rtf\\n\", \"fz\\n\", \"bj\\n\", \"baaba\\n\", \"ffxx\\n\", \"bbba\\n\", \"tru\\n\", \"ccyy\\n\", \"ib\\n\", \"xad\\n\", \"xc\\n\", \"qlsuzxrsjs\\n\", \"uqe\\n\", \"aave\\n\", \"aaxe\\n\", \"gz\\n\", \"eax\\n\", \"caaba\\n\", \"axe\\n\", \"awe\\n\", \"wad\\n\", \"wbe\\n\", \"eesstt\\n\", \"eeqqtt\\n\", \"ffffgnypgimo\\n\", \"eettrr\\n\", \"euq\\n\", \"jb\\n\", \"eav\\n\", \"ew\\n\", \"ffww\\n\", \"baaca\\n\", \"utr\\n\", \"ffgnypigmo\\n\", \"x\\n\", \"xe\\n\", \"zc\\n\", \"frs\\n\", \"qlsuzsrxjjs\\n\", \"trfaaaatrkbp\\n\", \"dnaydark\\n\", \"wae\\n\", \"z\\n\", \"eeyy\\n\", \"eeyy\\n\", \"bk\\n\", \"y\\n\", \"cy\\n\", \"ey\\n\", \"eerrtt\\n\", \"ci\\n\", \"xae\\n\", \"yc\\n\", \"ch\\n\", \"wd\\n\", \"qlsujxrszs\\n\", \"vae\\n\", \"ze\\n\", \"qet\\n\", \"y\\n\", \"yd\\n\", \"we\\n\", \"ic\\n\", \"ers\\n\", \"we\\n\", \"xae\\n\", \"z\\n\", \"ye\\n\", \"rrttttrrppfaabbkka\\n\", \"qte\\n\", \"ddww\\n\", \"yd\\n\", \"xad\\n\", \"ddww\\n\", \"caaba\\n\", \"caaba\\n\", \"fy\\n\", \"ffxx\\n\", \"ye\\n\", \"ic\\n\", \"ze\\n\", \"ddxx\\n\", \"darkdnay\\n\", \"etr\\n\", \"xd\\n\", \"y\\n\", \"baaaab\\n\", \"yd\\n\", \"wae\\n\", \"ze\\n\", \"yc\\n\", \"esq\\n\", \"eeww\\n\", \"kc\\n\", \"ert\\n\", \"wd\\n\", \"ze\\n\", \"eexx\\n\", \"ccjj\\n\", \"baaaab\", \"darkcyan\", \"daarkkcyan\"]}", "source": "taco"}
|
A binary tree of n nodes is given. Nodes of the tree are numbered from 1 to n and the root is the node 1. Each node can have no child, only one left child, only one right child, or both children. For convenience, let's denote l_u and r_u as the left and the right child of the node u respectively, l_u = 0 if u does not have the left child, and r_u = 0 if the node u does not have the right child.
Each node has a string label, initially is a single character c_u. Let's define the string representation of the binary tree as the concatenation of the labels of the nodes in the in-order. Formally, let f(u) be the string representation of the tree rooted at the node u. f(u) is defined as follows: $$$ f(u) = \begin{cases} <empty string>, & if u = 0; \\\ f(l_u) + c_u + f(r_u) & otherwise, \end{cases} where +$$$ denotes the string concatenation operation.
This way, the string representation of the tree is f(1).
For each node, we can duplicate its label at most once, that is, assign c_u with c_u + c_u, but only if u is the root of the tree, or if its parent also has its label duplicated.
You are given the tree and an integer k. What is the lexicographically smallest string representation of the tree, if we can duplicate labels of at most k nodes?
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5).
The second line contains a string c of n lower-case English letters, where c_i is the initial label of the node i for 1 ≤ i ≤ n. Note that the given string c is not the initial string representation of the tree.
The i-th of the next n lines contains two integers l_i and r_i (0 ≤ l_i, r_i ≤ n). If the node i does not have the left child, l_i = 0, and if the node i does not have the right child, r_i = 0.
It is guaranteed that the given input forms a binary tree, rooted at 1.
Output
Print a single line, containing the lexicographically smallest string representation of the tree if at most k nodes have their labels duplicated.
Examples
Input
4 3
abab
2 3
0 0
0 4
0 0
Output
baaaab
Input
8 2
kadracyn
2 5
3 4
0 0
0 0
6 8
0 7
0 0
0 0
Output
daarkkcyan
Input
8 3
kdaracyn
2 5
0 3
0 4
0 0
6 8
0 7
0 0
0 0
Output
darkcyan
Note
The images below present the tree for the examples. The number in each node is the node number, while the subscripted letter is its label. To the right is the string representation of the tree, with each letter having the same color as the corresponding node.
Here is the tree for the first example. Here we duplicated the labels of nodes 1 and 3. We should not duplicate the label of node 2 because it would give us the string "bbaaab", which is lexicographically greater than "baaaab".
<image>
In the second example, we can duplicate the labels of nodes 1 and 2. Note that only duplicating the label of the root will produce a worse result than the initial string.
<image>
In the third example, we should not duplicate any character at all. Even though we would want to duplicate the label of the node 3, by duplicating it we must also duplicate the label of the node 2, which produces a worse result.
<image>
There is no way to produce string "darkkcyan" from a tree with the initial string representation "darkcyan" :(.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 11 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 5 4 8 2 9 1 7\\n0\", \"3\\n1010 5 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 11 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 9 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 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10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 6 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 13 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 8 2 8 1\\n3335 10 10 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10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 2 9 0\\n1200 5 3 9 1 9 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 0 10 6 2 4 6 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 6 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 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10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 0 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 11 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 12 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 14 1 7 3 5 4 8 2 9 1 7\\n0\", \"3\\n1010 1 3 10 7 1 0 7 9 1 10 6 2 3 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 11 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 0 10 6 2 4 6 9 1 14 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n0010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 7 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 13 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 16\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 8 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 12 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 14 1 7 1 5 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 0 10 6 2 4 6 9 1 14 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 6 6 4 8 2 9 1 7\\n0\", \"3\\n0010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 7 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 13 1 8 2 9\\n1001 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 16\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3\\n4\\n3321 3 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 8 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 12 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 13 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 14 1 7 1 5 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n4912 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 0 10 6 2 4 6 9 1 14 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 10\\n1101 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 0 7 6 6 4 8 2 9 1 7\\n0\", \"3\\n0010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 7 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 13 1 8 2 9\\n1001 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 6 2 9 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 16\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3\\n4\\n3321 3 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 1 10 9 1 4 1 9 0 10 10 7 1 8 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 10 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 12 1 0 0 12 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 13 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 0 4 8 2 8 2 14 1 7 1 5 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 2 3 16 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 2 10 10 4 3 9 1 8 2 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10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n4912 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n0010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 7 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 13 1 8 2 9\\n1001 3 3 3 3 3 3 6 3 2 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 6 2 11 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 2 3 16 1 9 0\\n1200 5 3 9 1 1 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n4912 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 1 9 1 7\\n0\", \"3\\n0010 6 3 10 7 1 0 7 9 1 10 6 2 4 6 7 1 9 0\\n1200 5 3 9 1 7 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10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 0 7 3 6 4 8 2 6 2 11 0 7 3 6 4 8 2 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 2 3 16 1 9 0\\n1200 5 3 9 1 1 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n2526 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 1 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 2 3 16 1 9 0\\n1200 5 3 9 1 1 1 0 0 8 2 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 6 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 4 8 0\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n2399 8 2 7 3 0 4 8 2 8 2 9 1 7 3 6 4 8 1 9 1 7\\n0\", \"3\\n1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0\\n1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9\\n1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n4\\n3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10\\n3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1\\n3335 10 10 10 10 10 10 10 10 10 10 10 10\\n3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7\\n0\"], \"outputs\": [\"1200 127\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 155\\n3332 122\\n\", \"1200 127\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 167\\n3332 122\\n\", \"1200 137\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 155\\n3332 122\\n\", \"1200 127\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 164\\n3332 122\\n\", \"1200 137\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 145\\n3332 122\\n\", \"1200 127\\n1010 122\\n1101 60\\n3335 300\\n3321 200\\n3340 164\\n3332 122\\n\", \"1200 131\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 175\\n3332 122\\n\", \"1200 127\\n1010 121\\n1101 60\\n3335 300\\n3321 200\\n3340 155\\n3332 122\\n\", \"1200 127\\n1010 123\\n1101 59\\n3335 300\\n3321 200\\n3340 167\\n3332 122\\n\", \"1200 131\\n1010 115\\n1101 60\\n3335 300\\n3321 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200\\n3340 172\\n3332 133\\n\", \"1200 127\\n1010 124\\n1101 60\\n3335 300\\n3321 207\\n3340 164\\n3332 122\\n\", \"1200 141\\n1010 123\\n1101 61\\n3335 300\\n3321 200\\n3340 145\\n3332 122\\n\", \"1200 127\\n1010 118\\n1101 60\\n5825 300\\n3321 200\\n3340 164\\n3332 122\\n\", \"1200 131\\n1010 123\\n1101 60\\n3335 300\\n3321 203\\n3340 166\\n3332 122\\n\", \"1200 136\\n1010 121\\n1101 60\\n3335 300\\n3321 200\\n3340 155\\n3332 122\\n\", \"1200 131\\n1010 115\\n1101 63\\n3335 300\\n3321 200\\n3340 175\\n3332 121\\n\", \"10 135\\n1200 108\\n1101 59\\n3335 300\\n3321 200\\n3340 167\\n3332 122\\n\", \"1200 134\\n1010 123\\n1101 60\\n3335 300\\n3321 203\\n3340 175\\n3332 133\\n\", \"1200 142\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 148\\n3332 122\\n\", \"1200 127\\n1010 117\\n1101 60\\n3335 300\\n3321 200\\n3340 164\\n3332 143\\n\", \"1200 138\\n1010 121\\n1101 60\\n3335 300\\n3321 200\\n3340 154\\n3332 124\\n\", \"1010 134\\n1200 127\\n1101 59\\n3335 300\\n3321 200\\n3340 167\\n3332 114\\n\", \"1200 123\\n10 122\\n1101 59\\n3335 300\\n3321 200\\n3340 155\\n3332 122\\n\", \"1200 134\\n1010 123\\n1101 62\\n3335 300\\n3321 200\\n3340 164\\n3332 133\\n\", \"1200 138\\n1010 121\\n1101 60\\n3335 280\\n3321 200\\n3340 155\\n3332 123\\n\", \"1200 123\\n10 122\\n1001 59\\n3335 300\\n3321 200\\n3340 160\\n3332 122\\n\", \"1200 134\\n1010 123\\n1101 63\\n3335 300\\n3321 185\\n3340 175\\n3332 133\\n\", \"1200 141\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 143\\n3332 126\\n\", \"1200 135\\n1010 121\\n1101 60\\n3335 300\\n3321 200\\n4912 155\\n3332 123\\n\", \"1200 123\\n10 122\\n1001 59\\n3335 300\\n3321 192\\n3340 154\\n3332 122\\n\", \"1200 134\\n1010 115\\n1101 62\\n3335 300\\n3321 185\\n3340 175\\n3332 134\\n\", \"1200 141\\n1010 112\\n1101 60\\n3335 300\\n3321 191\\n3340 141\\n3332 126\\n\", \"1200 138\\n1010 119\\n1101 60\\n3335 300\\n3321 200\\n4912 155\\n3332 125\\n\", \"1200 123\\n10 122\\n1001 60\\n3335 300\\n3321 200\\n3340 154\\n3332 122\\n\", \"1200 126\\n1010 119\\n1101 61\\n3335 300\\n3321 200\\n4912 155\\n3332 123\\n\", \"1200 126\\n1010 119\\n1101 60\\n3335 300\\n3321 200\\n4912 145\\n3332 131\\n\", \"1200 123\\n10 122\\n1001 63\\n3335 300\\n3321 200\\n3340 147\\n3332 122\\n\", \"1200 126\\n1010 119\\n1101 58\\n3335 300\\n3321 200\\n2526 145\\n3332 123\\n\", \"1200 126\\n1010 119\\n1101 63\\n3335 300\\n3321 200\\n2399 145\\n3332 123\\n\", \"1200 127\\n1010 123\\n1101 60\\n3335 300\\n3321 200\\n3340 175\\n3332 122\"]}", "source": "taco"}
|
I decided to do bowling as a recreation of the class. Create a program that inputs the pitching information for each participant and outputs the grade information in descending order of score. If there is a tie, output in ascending order of student ID number. However, it is assumed that the number of participants is 3 or more and 40 or less, and one game is thrown per person.
Bowling is a sport in which the player rolls the ball toward 10 pins arranged in an equilateral triangle with the vertices facing the player and knocks down the pins. The case where all the players fall in the first pitch is called a strike, and only that pitch advances to the next frame. If it is not a strike, leave the remaining pins and make a second pitch. A spare is when all the pitches have fallen on the second pitch. After the second pitch, proceed to the next frame.
One game consists of 10 frames, and each of the 1st to 9th frames can be pitched twice. At the beginning of each frame, all 10 pins are upright. In the 10th frame, if there is a strike or a spare, a total of 3 pitches will be thrown, otherwise 2 pitches will be made and the game will end.
Score example 1
<image>
Score example 2 (when the maximum score is 300 points)
<image>
How to calculate the score
* If there are no spares or strikes in each frame, the number of pins defeated in two pitches will be the score for that frame. (4th and 8th frames of score example 1)
* If you give a spare, in addition to the number of defeated 10 points, the number of defeated pins in the next pitch will be added to the score of this frame. (Relationship between the 1st frame and the 2nd frame of the score example 1) In the 1st frame of the score example 1, 20 points including 10 points (points) defeated by 1 throw of the 2nd frame will be scored. The calculation method is the same for the third frame.
* If you strike, the number of pins you defeated in the next two pitches will be added to the number of defeated 10 points. (Relationship between the 2nd frame and the 3rd frame of score example 1) Of course, there may be a strike during the following 2 throws. (Relationship between the 5th frame and the 6th and 7th frames of score example 1)
* If you give a spare or strike only in the 10th frame, the total number of pins you have thrown and defeated will be added as the score in the 10th frame.
* The total score of each frame is the score of one game, and the maximum score is 300 points.
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:
m
score1
score2
::
scorem
The number of participants m (3 ≤ m ≤ 40) is given in the first line, and the i-th participant information scorei is given in the following m lines. Each participant information is given in the following format, one line at a time.
id s1 s2 ... sn
The student ID number id (0 ≤ id ≤ 9999) is given first, followed by the number of fall pins of the jth throw sj (0 ≤ sj ≤ 10). It is assumed that the total number of pitches n is 12 or more and 21 or less, and the number of pins required for score calculation is given in just proportion.
Output
For each input dataset, the student ID number and score are output in descending order of score (if there is a tie, the student ID number is in ascending order). Please separate your student ID number and score with one space and output them on one line.
Example
Input
3
1010 6 3 10 7 1 0 7 9 1 10 6 2 4 3 9 1 9 0
1200 5 3 9 1 7 1 0 0 8 1 10 10 4 3 9 1 8 2 9
1101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
4
3321 8 2 10 9 1 7 0 10 10 10 0 8 10 10 10 10
3332 5 0 10 9 1 4 1 9 0 10 10 7 1 5 2 8 1
3335 10 10 10 10 10 10 10 10 10 10 10 10
3340 8 2 7 3 6 4 8 2 8 2 9 1 7 3 6 4 8 2 9 1 7
0
Output
1200 127
1010 123
1101 60
3335 300
3321 200
3340 175
3332 122
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"abrakadabrabrakadabra\\n\", \"acacacaca\\n\", \"abcabc\\n\", \"abababab\\n\", \"tatbt\\n\", \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n\", \"r\\n\", \"zaz\\n\", \"zaza\\n\", \"gg\\n\", \"gagaga\\n\", \"hhhh\\n\", \"sssss\\n\", \"nxnxnx\\n\", \"vygvygv\\n\", \"rlrlrlrl\\n\", \"zyzyzyzyz\\n\", \"jjjjjjjjjj\\n\", \"kkhuskkhusk\\n\", \"gzgzgzgzgzgz\\n\", \"vkyxvkyxvkyxv\\n\", \"uuuuuuuuuuuuuu\\n\", \"esxwpesxwpesxwp\\n\", \"qltrajqltrajqltr\\n\", \"alxalxalxalxalxal\\n\", \"ijtojrijtojrijtojr\\n\", \"yhbhamyhbhamyhbhamy\\n\", \"cdrcuccdrcuccdrcuccd\\n\", \"ddoaxeaddoaxeaddoaxea\\n\", \"ejfrayejfrayejfrayejfr\\n\", \"oxciazoxciazoxciazoxcia\\n\", \"zfusxizfusxizfusxizfusxi\\n\", \"kqkqkqkqkqkqkqkqkqkqkqkqk\\n\", \"mrmrmrmrmrmrmrmrmrmrmrmrmr\\n\", \"wnwnwnwnwnwnwnwnwnwnwnwnwnw\\n\", \"zchvhrmcrzchvhrmcrzchvhrmcrz\\n\", \"hngryskhngryskhngryskhngryskh\\n\", \"papapapapapapapapapapapapapapa\\n\", 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\"axquczgfdshcpqjcqaxquczgfdshcpqjcqaxquczgfdshcpqjcqaxquczxfdshcpqjcqaxquczgfdshcpqjcqaxquc\\n\", \"vyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvyhsqvvshsqvvyhsqvv\\n\", \"bpqxbraxrcxwdoftbpqxbraxryxwdoftbpqxbraxrcxwdoftbpqxbraxrcxwdoftbpqxbraxrcxwdoftbpqxbraxrcxw\\n\", \"renpsuotrenpsuotrenpsuotrenpsuotrenpsuotrenpsuoprenpsuotrenpsuotrenpsuotrenpsuotrenpsuotrenps\\n\", \"qqeemdmddqddkmudbmaabaedquqmqqdqqqeemdmddqddkmudbmaabaedquqmqqdqqqeemdmddqddkmudbmaabaedquqmqq\\n\", \"gfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpis\\n\", \"nnsssnnngsbnngnsnnbgbgnbnbnnsssnnngsbnngnsnnbgbgnbnbnnsssnnngsbnngnbnnbgbgnbnbnnsssnnngsbnngnsnn\\n\", \"qimxxxojmmjqmxqfxfqiximjxqimxxxojqmjqmxqfxfqiximjxqimxxxojmmjqmxqfxfqiximjxqimxxxojmmjqmxqfxfqixi\\n\", \"otjwmbgahamrbbhnttmoqahohbhbjxwkbtotjwmbgahamrbbhnttmoqahohbhyjxwkbtotjwmbgahamrbbhnttmoqahohbhbjx\\n\", \"hligdsxyzyjejeskxapshligdsxyzyjejeskxapshligdsxyzyjejeskxapshligdsxyzyjejeskxapshligdsxyzljejeskxap\\n\", \"ooogesrsajsnzroyhabbckrnovooogesrsajsnzroyhabbckrnovooogesrsajsnzroyhabbckrnovooogesrsajsnzroyhadbck\\n\"], \"outputs\": [\"YES\\nabrakadabra\\n\", \"YES\\nacaca\\n\", \"NO\\n\", \"YES\\nababab\\n\", \"NO\\n\", \"YES\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\ngaga\\n\", \"YES\\nhhh\\n\", \"YES\\nsss\\n\", \"YES\\nnxnx\\n\", \"YES\\nvygv\\n\", \"YES\\nrlrlrl\\n\", \"YES\\nzyzyz\\n\", \"YES\\njjjjjj\\n\", \"YES\\nkkhusk\\n\", \"YES\\ngzgzgzgz\\n\", \"YES\\nvkyxvkyxv\\n\", \"YES\\nuuuuuuuu\\n\", \"YES\\nesxwpesxwp\\n\", \"YES\\nqltrajqltr\\n\", \"YES\\nalxalxalxal\\n\", \"YES\\nijtojrijtojr\\n\", \"YES\\nyhbhamyhbhamy\\n\", \"YES\\ncdrcuccdrcuccd\\n\", \"YES\\nddoaxeaddoaxea\\n\", \"YES\\nejfrayejfrayejfr\\n\", \"YES\\noxciazoxciazoxcia\\n\", \"YES\\nzfusxizfusxizfusxi\\n\", \"YES\\nkqkqkqkqkqkqk\\n\", \"YES\\nmrmrmrmrmrmrmr\\n\", \"YES\\nwnwnwnwnwnwnwnw\\n\", \"YES\\nzchvhrmcrzchvhrmcrz\\n\", \"YES\\nhngryskhngryskh\\n\", \"YES\\npapapapapapapapa\\n\", \"YES\\nqqgedqkewrelydzq\\n\", \"YES\\nmtphoncwmtphoncwmtphoncw\\n\", \"YES\\nsypfetgsuhifxzsypfe\\n\", \"YES\\navhiggygrtudeavhiggyg\\n\", \"YES\\nhphhiattwnahphhiattwnahp\\n\", \"YES\\nlpuilpuilpuilpuilpui\\n\", \"YES\\nbbztwlxbocpbbztwlxbocpbbzt\\n\", \"YES\\ndvdvdvdvdvdvdvdvdvdv\\n\", \"YES\\nmnvkmnvkmnvkmnvkmnvkmnv\\n\", \"YES\\nugugugugugugugugugugug\\n\", \"YES\\nnyilpgayabfzpqifnyilpgaya\\n\", \"YES\\nawxmegcmrkzawxmegcmrkzawxmegcmr\\n\", \"YES\\nugduygugduygugduygugduygu\\n\", \"YES\\ndkwelorlspdltsdkwelorlspdltsdk\\n\", \"YES\\nxwyxssvcedrwtpgxwyxssvcedrwtpg\\n\", \"YES\\npwjkpwjkpwjkpwjkpwjkpwjkpw\\n\", \"YES\\nvxumrzwwzrzzfuvxumrzwwzrzzfuvxumr\\n\", \"YES\\nkkkkrhhkkkkrhhkkkkrhhkkkkrh\\n\", \"YES\\nlfbpinxnjsfvjsfbshblyvlfbpi\\n\", \"YES\\nsqdrmjqbfbmjmqfbcemrjtsqdrmj\\n\", \"YES\\neeaiaeeaiaeeaiaeeaiaeeaiae\\n\", \"YES\\nfhfhfhfhfhfhfhfhfhfhfhfhfhfh\\n\", \"YES\\nouygsznbnotbouygsznbnotbouygs\\n\", \"YES\\nwtqqagwaguqgaffuqgqtwtwawtqqag\\n\", \"YES\\nsogoiyexpwmpaixsogoiyexpwmpaixsogoiyexpw\\n\", \"YES\\nvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\n\", \"YES\\nhlyjflfbvbtvtqtsjklkfsbqthvsh\\n\", \"YES\\nmlymfzfkmkfjomlymfzfkmkfjomlymfz\\n\", \"YES\\nswylxswylxswylxswylxswylxswylxswyl\\n\", \"YES\\ncifcifcifcifcifcifcifcifcifcifcif\\n\", \"YES\\nlvifmwwfkvewsezsufghillvifmwwfkvewsezsu\\n\", \"YES\\nmhgbtgdmhgbtgdmhgbtgdmhgbtgdmhgbtg\\n\", \"YES\\nszfsdufuduiofckbszfsdufuduiofckbszfsdufuduiofck\\n\", \"YES\\nceypvrszdqljkzezlcceypvrszdqljkzezlcceypvrszdq\\n\", \"YES\\nojmtpzmojamdjydojmtpzmojamdjydojmtp\\n\", \"YES\\nuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu\\n\", \"YES\\nuhkuqbhrhlqjhgbshsvtqouquhkuqbhrhlqjhgbshsv\\n\", \"YES\\nxcgtgdpomjvngwdtrvrttldigxcgtgdpomjvngwdtrv\\n\", \"YES\\nvuuovdvktdjvuaafiguzdrrtratjyvuuovdvktdj\\n\", \"YES\\nyukcccrccccyukcccrccccyukcccrccccyukc\\n\", \"YES\\nrrriiiiaaainnrrrainniiarirrriiiiaaainnrrrainni\\n\", \"YES\\nxmxxumdfubrcsbccxmxxumdfubrcsbccxmxxumdf\\n\", \"YES\\nxovouvxuxtcvvovpxnhruswcphrstctxovouvxuxtc\\n\", \"YES\\nhowwwscoebckiatfzarhowwwscoebckiatfzarhowwwscoebckiatfz\\n\", \"YES\\nickpakvkbaljifqdifjfcdxpashuickpakvkbaljifqdifj\\n\", \"YES\\nzgzwgwggzggwzzwwwhzgzgzwgwggzggwzzwwwhzgzgzwgwggzggwzzww\\n\", \"YES\\nppdbpyheotppdbpyheotppdbpyheotppdbpyheotppdbpyh\\n\", \"YES\\nitlmmmqfkflfamdaqekrjlocitlmmmqfkflfamdaqekrjlocitlmmm\\n\", \"YES\\nyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqyqy\\n\", \"YES\\nijdghvidfbqqpajplojvtlppdiftzvhuqatijdghvidfb\\n\", \"YES\\njozbicochmmtmmhogkgrfutknpjozbicochmmtmmhogkgrfutknpjoz\\n\", \"YES\\ntvsyxhopzmbebwoimyxhjbjuyszplhhggftvsyxhopzmbebw\\n\", \"YES\\nkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk\\n\", \"YES\\nzyqxlypnlpavjxuydvxcnnzszyqxlypnlpavjxuydvxcnnzszyqxlypnlpav\\n\", \"YES\\nirlgpgsejirlgpgsejirlgpgsejirlgpgsejirlgpgsejirlg\\n\", \"YES\\nhthththththththththththththththththththththt\\n\", \"YES\\nwlladflfanfmlljbbldamdjabtfbnftawbfnllfjwlladfl\\n\", \"YES\\nfrxafrxafrxafrxafrxafrxafrxafrxafrxafrxafrxafrxa\\n\", \"YES\\nuzdcgbifcuzdcgbifcuzdcgbifcuzdcgbifcuzdcgbifcuzdcgbif\\n\", \"YES\\ndzpttoozpoqsjywqnzokdzpttoozpoqsjywqnzokdzpttoozpo\\n\", \"YES\\navqriqniaavqriqniaavqriqniaavqriqniaavqriqniaa\\n\", \"YES\\nqqpppqqpqqqqqpqqpqpqqqpqpqqqqqqqpppqqpqqqqqpqqpqpqqqpqpqqqqqqq\\n\", \"YES\\nmnmxvxqrfnjxnmnmxvxqrfnjxnmnmxvxqrfnjxnmnmxvxqrfnjxnmn\\n\", \"YES\\nqzcgreoroxoxqzwvvoeiggriwrzotcxizqzcgreoroxoxqzwvvoeiggriwrzo\\n\", \"YES\\npymvkuoucpujkekgnjrvnkrvodtszsbkmoabtlgdbpymvkuoucpujk\\n\", \"YES\\nyguclskcmiuobsgckhotgkzqykebvttqaqmtzsyguclskcmiuobsgckhot\\n\", \"YES\\nkowiovfyffitkipvmccesjhatgyqaekowiovfyffitkipvmccesjhatgyqaekowiovf\\n\", \"YES\\nmrjdrepsprwlwwjewemrjdrepsprwlwwjewemrjdrepsprwlwwjewemrjdreps\\n\", \"YES\\nhgxenqnawiyiirinhraywlhgxenqnawiyiirinhraywlhgxenqnawiy\\n\", \"YES\\nfoxywhckxuiipgfoxywhckxuiipgfoxywhckxuiipgfoxywhckxuiipgfo\\n\", \"YES\\nbkwdegdnxtnvtczozttjitzmfienbtxhoipldptluxbtvhmybkwd\\n\", \"YES\\ncftorbxtglokyoxsemzlysptutvldtlzqbhawyecivljlcftorbxtgl\\n\", \"YES\\ntwfflboprkkjobbgoubmybfkbmmconrjhsktwfflboprkkjobbgoubmybfkbmmcon\\n\", \"YES\\nwajaubjjlsvvatkrwphykszmkwajaubjjlsvvatkrwphykszmkwajaubjjlsvvatkrwphykszmk\\n\", \"YES\\nppppppppppppppppppppppppppppppppppppppppppppppppppp\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nqqeemdmddqddkmudbmaabaedquqmqqdqqqeemdmddqddkmudbmaabaedquqmqq\\n\", \"YES\\ngfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpiskgfpis\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\"]}", "source": "taco"}
|
В Берляндском государственном университете локальная сеть между серверами не всегда работает без ошибок. При передаче двух одинаковых сообщений подряд возможна ошибка, в результате которой эти два сообщения сливаются в одно. При таком слиянии конец первого сообщения совмещается с началом второго. Конечно, совмещение может происходить только по одинаковым символам. Длина совмещения должна быть положительным числом, меньшим длины текста сообщения.
Например, при передаче двух сообщений «abrakadabra» подряд возможно, что оно будет передано с ошибкой описанного вида, и тогда будет получено сообщение вида «abrakadabrabrakadabra» или «abrakadabrakadabra» (в первом случае совмещение произошло по одному символу, а во втором — по четырем).
По полученному сообщению t определите, возможно ли, что это результат ошибки описанного вида работы локальной сети, и если возможно, определите возможное значение s.
Не следует считать ошибкой ситуацию полного наложения друга на друга двух сообщений. К примеру, если получено сообщение «abcd», следует считать, что в нём ошибки нет. Аналогично, простое дописывание одного сообщения вслед за другим не является признаком ошибки. Например, если получено сообщение «abcabc», следует считать, что в нём ошибки нет.
-----Входные данные-----
В единственной строке выходных данных следует непустая строка t, состоящая из строчных букв латинского алфавита. Длина строки t не превосходит 100 символов.
-----Выходные данные-----
Если сообщение t не может содержать ошибки, выведите «NO» (без кавычек) в единственную строку выходных данных.
В противном случае в первой строке выведите «YES» (без кавычек), а в следующей строке выведите строку s — возможное сообщение, которое могло привести к ошибке. Если возможных ответов несколько, разрешается вывести любой из них.
-----Примеры-----
Входные данные
abrakadabrabrakadabra
Выходные данные
YES
abrakadabra
Входные данные
acacacaca
Выходные данные
YES
acaca
Входные данные
abcabc
Выходные данные
NO
Входные данные
abababab
Выходные данные
YES
ababab
Входные данные
tatbt
Выходные данные
NO
-----Примечание-----
Во втором примере подходящим ответом также является строка acacaca.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[\"\"], [\"FFFFF\"], [\"FFFFFLFFFFFLFFFFFLFFFFFL\"], [\"LFFFFFRFFFRFFFRFFFFFFF\"], [\"LF5RF3RF3RF7\"], [\"FFFLLFFFFFFRRFFFLFFFRRFFFFFFFF\"], [\"F3L2F6R2F3LF3R2F8\"], [\"F2FLLF3F3R2FFFLF2FRRF3F2F2F\"], [\"FFLFFFLFFFFLFFFFFLFFFFFFLFFFFFFFLFFFFFFFFLFFFFFFFFFLFFFFFFFFFF\"], [\"F2LF3LF4LF5LF6LF7LF8LF9LF10\"], [\"FFFFLFFFFRFFFFRFFFFLFFFFLFFFFRFFFFRFFFFLFFFFLFFFFRFFFFRFFFF\"], [\"F4LF4RF4RF4LF4LF4RF4RF4LF4LF4RF4RF4\"]], \"outputs\": [[\"*\"], [\"******\"], [\"******\\r\\n* *\\r\\n* *\\r\\n* *\\r\\n* *\\r\\n******\"], [\" ****\\r\\n * *\\r\\n * *\\r\\n********\\r\\n * \\r\\n * \"], [\" ****\\r\\n * *\\r\\n * *\\r\\n********\\r\\n * \\r\\n * \"], [\" * \\r\\n * \\r\\n * \\r\\n*******\\r\\n * \\r\\n * \\r\\n * \\r\\n * \\r\\n * \"], [\" * \\r\\n * \\r\\n * \\r\\n*******\\r\\n * \\r\\n * \\r\\n * \\r\\n * \\r\\n * \"], [\" * \\r\\n * \\r\\n * \\r\\n*******\\r\\n * \\r\\n * \\r\\n * \\r\\n * \\r\\n * \"], [\"********* \\r\\n* * \\r\\n* ***** * \\r\\n* * * * \\r\\n* * * * \\r\\n* * *** * \\r\\n* * * \\r\\n* ******* \\r\\n* \\r\\n***********\"], [\"********* \\r\\n* * \\r\\n* ***** * \\r\\n* * * * \\r\\n* * * * \\r\\n* * *** * \\r\\n* * * \\r\\n* ******* \\r\\n* \\r\\n***********\"], [\" ***** ***** *****\\r\\n * * * * * *\\r\\n * * * * * *\\r\\n * * * * * *\\r\\n***** ***** ***** *\"], [\" ***** ***** *****\\r\\n * * * * * *\\r\\n * * * * * *\\r\\n * * * * * *\\r\\n***** ***** ***** *\"]]}", "source": "taco"}
|
# RoboScript #2 - Implement the RS1 Specification
## Disclaimer
The story presented in this Kata Series is purely fictional; any resemblance to actual programming languages, products, organisations or people should be treated as purely coincidental.
## About this Kata Series
This Kata Series is based on a fictional story about a computer scientist and engineer who owns a firm that sells a toy robot called MyRobot which can interpret its own (esoteric) programming language called RoboScript. Naturally, this Kata Series deals with the software side of things (I'm afraid Codewars cannot test your ability to build a physical robot!).
## Story
Now that you've built your own code editor for RoboScript with appropriate syntax highlighting to make it look like serious code, it's time to properly implement RoboScript so that our MyRobots can execute any RoboScript provided and move according to the will of our customers. Since this is the first version of RoboScript, let's call our specification RS1 (like how the newest specification for JavaScript is called ES6 :p)
## Task
Write an interpreter for RS1 called `execute()` which accepts 1 required argument `code`, the RS1 program to be executed. The interpreter should return a string representation of the smallest 2D grid containing the full path that the MyRobot has walked on (explained in more detail later).
Initially, the robot starts at the middle of a 1x1 grid. Everywhere the robot walks it will leave a path `"*"`. If the robot has not been at a particular point on the grid then that point will be represented by a whitespace character `" "`. So if the RS1 program passed in to `execute()` is empty, then:
```
"" --> "*"
```
The robot understands 3 major commands:
- `F` - Move forward by 1 step in the direction that it is currently pointing. Initially, the robot faces to the right.
- `L` - Turn "left" (i.e. **rotate** 90 degrees **anticlockwise**)
- `R` - Turn "right" (i.e. **rotate** 90 degrees **clockwise**)
As the robot moves forward, if there is not enough space in the grid, the grid should expand accordingly. So:
```
"FFFFF" --> "******"
```
As you will notice, 5 `F` commands in a row should cause your interpreter to return a string containing 6 `"*"`s in a row. This is because initially, your robot is standing at the middle of the 1x1 grid facing right. It leaves a mark on the spot it is standing on, hence the first `"*"`. Upon the first command, the robot moves 1 unit to the right. Since the 1x1 grid is not large enough, your interpreter should expand the grid 1 unit to the right. The robot then leaves a mark on its newly arrived destination hence the second `"*"`. As this process is repeated 4 more times, the grid expands 4 more units to the right and the robot keeps leaving a mark on its newly arrived destination so by the time the entire program is executed, 6 "squares" have been marked `"*"` from left to right.
Each row in your grid must be separated from the next by a CRLF (`\r\n`). Let's look at another example:
```
"FFFFFLFFFFFLFFFFFLFFFFFL" --> "******\r\n* *\r\n* *\r\n* *\r\n* *\r\n******"
```
So the grid will look like this:
```
******
* *
* *
* *
* *
******
```
The robot moves 5 units to the right, then turns left, then moves 5 units upwards, then turns left again, then moves 5 units to the left, then turns left again and moves 5 units downwards, returning to the starting point before turning left one final time. Note that the marks do **not** disappear no matter how many times the robot steps on them, e.g. the starting point is still marked `"*"` despite the robot having stepped on it twice (initially and on the last step).
Another example:
```
"LFFFFFRFFFRFFFRFFFFFFF" --> " ****\r\n * *\r\n * *\r\n********\r\n * \r\n * "
```
So the grid will look like this:
```
****
* *
* *
********
*
*
```
Initially the robot turns left to face upwards, then moves upwards 5 squares, then turns right and moves 3 squares, then turns right again (to face downwards) and move 3 squares, then finally turns right again and moves 7 squares.
Since you've realised that it is probably quite inefficient to repeat certain commands over and over again by repeating the characters (especially the `F` command - what if you want to move forwards 20 steps?), you decide to allow a shorthand notation in the RS1 specification which allows your customers to postfix a non-negative integer onto a command to specify how many times an instruction is to be executed:
- `Fn` - Execute the `F` command `n` times (NOTE: `n` *may* be more than 1 digit long!)
- `Ln` - Execute `L` n times
- `Rn` - Execute `R` n times
So the example directly above can also be written as:
```
"LF5RF3RF3RF7"
```
These 5 example test cases have been included for you :)
## Kata in this Series
1. [RoboScript #1 - Implement Syntax Highlighting](https://www.codewars.com/kata/roboscript-number-1-implement-syntax-highlighting)
2. **RoboScript #2 - Implement the RS1 Specification**
3. [RoboScript #3 - Implement the RS2 Specification](https://www.codewars.com/kata/58738d518ec3b4bf95000192)
4. [RoboScript #4 - RS3 Patterns to the Rescue](https://www.codewars.com/kata/594b898169c1d644f900002e)
5. [RoboScript #5 - The Final Obstacle (Implement RSU)](https://www.codewars.com/kata/5a12755832b8b956a9000133)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 3\\n\", \"1 2\\n\", \"1 1\\n\", \"2 1\\n\", \"1 3\\n\", \"3 1\\n\", \"2 5\\n\", \"3 6\\n\", \"2 2\\n\", \"1 100000\\n\", \"100000 1\\n\", \"91697 91697\\n\", \"86821 24538\\n\", \"100000 100000\\n\", \"99999 1\\n\", \"1 99999\\n\", \"1 99998\\n\", \"99998 1\\n\", \"1 88588\\n\", \"68869 1\\n\", \"91248 82914\\n\", \"99999 100000\\n\", \"100000 99999\\n\", \"99999 99999\\n\", \"13771 94814\\n\", \"99411 90913\\n\", \"52702 64157\\n\", \"24538 86821\\n\", \"2 1\\n\", \"3 6\\n\", \"2 5\\n\", \"1 2\\n\", \"100000 100000\\n\", \"1 3\\n\", \"1 100000\\n\", \"91697 91697\\n\", \"1 99999\\n\", \"100000 1\\n\", \"91248 82914\\n\", \"1 1\\n\", \"52702 64157\\n\", \"99998 1\\n\", \"99411 90913\\n\", \"99999 1\\n\", \"3 1\\n\", \"1 99998\\n\", \"24538 86821\\n\", \"99999 100000\\n\", \"2 2\\n\", \"99999 99999\\n\", \"1 88588\\n\", \"86821 24538\\n\", \"100000 99999\\n\", \"68869 1\\n\", \"13771 94814\\n\", \"3 5\\n\", \"1 4\\n\", \"707 91697\\n\", \"1 14401\\n\", \"97883 64157\\n\", \"99998 2\\n\", \"56892 90913\\n\", \"74780 1\\n\", \"6 1\\n\", \"24538 88245\\n\", \"2 6\\n\", \"12647 99999\\n\", \"86821 25239\\n\", \"13126 1\\n\", \"25085 94814\\n\", \"6 5\\n\", \"186 91697\\n\", \"1 8126\\n\", \"5 1\\n\", \"64677 64157\\n\", \"99998 3\\n\", \"21596 90913\\n\", \"24538 64920\\n\", \"2 7\\n\", \"86821 42496\\n\", \"18055 1\\n\", \"25085 77471\\n\", \"6 4\\n\", \"204 91697\\n\", \"1 15169\\n\", \"5 2\\n\", \"12176 64157\\n\", \"99998 5\\n\", \"40893 90913\\n\", \"10 2\\n\", \"3 8873\\n\", \"27158 64920\\n\", \"1 7\\n\", \"86821 35804\\n\", \"23084 1\\n\", \"25085 97137\\n\", \"74 91697\\n\", \"1 22677\\n\", \"16536 64157\\n\", \"40825 90913\\n\", \"9 2\\n\", \"2 8873\\n\", \"27158 73373\\n\", \"2 12\\n\", \"104 91697\\n\", \"1 14856\\n\", \"12503 64157\\n\", \"14398 90913\\n\", \"4 8873\\n\", \"17028 73373\\n\", \"2 20\\n\", \"1 27816\\n\", \"7258 64157\\n\", \"14398 19509\\n\", \"6 8873\\n\", \"17028 74854\\n\", \"2 25\\n\", \"7258 37828\\n\", \"14398 33475\\n\", \"11 8873\\n\", \"9261 74854\\n\", \"3186 37828\\n\", \"14398 16144\\n\", \"6630 74854\\n\", \"3186 65732\\n\", \"17290 16144\\n\", \"1452 74854\\n\", \"4546 65732\\n\", \"17290 9243\\n\", \"1452 95660\\n\", \"4546 94609\\n\", \"17290 11338\\n\", \"129 95660\\n\", \"3301 94609\\n\", \"17290 3403\\n\", \"134 95660\\n\", \"2131 3403\\n\", \"2131 1463\\n\", \"2710 1463\\n\", \"2710 1269\\n\", \"2710 1179\\n\", \"2710 2023\\n\", \"2710 1874\\n\", \"2320 1874\\n\", \"1530 1874\\n\", \"1530 3192\\n\", \"1284 3192\\n\", \"635 3192\\n\", \"1169 3192\\n\", \"1169 4564\\n\", \"1169 4529\\n\", \"883 4529\\n\", \"1172 4529\\n\", \"1525 4529\\n\", \"1525 3259\\n\", \"2 3\\n\"], \"outputs\": [\"8\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"18\\n\", \"30\\n\", \"6\\n\", \"935236457\\n\", \"935236457\\n\", \"999949469\\n\", \"1000000005\\n\", \"870472905\\n\", \"822870997\\n\", \"822870997\\n\", \"112365460\\n\", \"112365460\\n\", \"153641669\\n\", \"840775285\\n\", \"542035391\\n\", \"758107445\\n\", \"758107445\\n\", \"645741985\\n\", \"581579207\\n\", \"189215541\\n\", \"1000000005\\n\", \"1000000005\\n\", \"4\\n\", \"30\\n\", \"18\\n\", \"4\\n\", \"870472905\\n\", \"6\\n\", \"935236457\\n\", \"999949469\\n\", \"822870997\\n\", \"935236457\\n\", \"542035391\\n\", \"2\\n\", \"1000000005\\n\", \"112365460\\n\", \"189215541\\n\", \"822870997\\n\", \"6\\n\", \"112365460\\n\", \"1000000005\\n\", \"758107445\\n\", \"6\\n\", \"645741985\\n\", \"153641669\\n\", \"1000000005\\n\", \"758107445\\n\", \"840775285\\n\", \"581579207\\n\", \"20\\n\", \"10\\n\", \"522450300\\n\", \"320306147\\n\", \"218236626\\n\", \"112365462\\n\", \"915119763\\n\", \"493700786\\n\", \"26\\n\", \"96405655\\n\", \"28\\n\", \"620269507\\n\", \"874436040\\n\", \"462274472\\n\", \"977120009\\n\", \"40\\n\", \"239619845\\n\", \"532737860\\n\", \"16\\n\", \"285816347\\n\", \"112365464\\n\", \"424970023\\n\", \"33102532\\n\", \"44\\n\", \"596627610\\n\", \"21629559\\n\", \"722225689\\n\", \"34\\n\", \"389241661\\n\", \"236197972\\n\", \"18\\n\", \"788477312\\n\", \"112365474\\n\", \"21814862\\n\", \"180\\n\", \"494003147\\n\", \"342368205\\n\", \"42\\n\", \"753691657\\n\", \"531625893\\n\", \"996667700\\n\", \"126370040\\n\", \"765858765\\n\", \"908489524\\n\", \"275694116\\n\", \"112\\n\", \"494003145\\n\", \"96856440\\n\", \"468\\n\", \"949986685\\n\", \"449741613\\n\", \"908653453\\n\", \"611812489\\n\", \"494003151\\n\", \"367786795\\n\", \"21894\\n\", \"258569881\\n\", \"481619627\\n\", \"919460675\\n\", \"494003167\\n\", \"94085153\\n\", \"242788\\n\", \"653952363\\n\", \"934838947\\n\", \"494003429\\n\", \"777600909\\n\", \"474970359\\n\", \"28862110\\n\", \"23643286\\n\", \"141181170\\n\", \"751882941\\n\", \"434417640\\n\", \"436282448\\n\", \"523076649\\n\", \"470206636\\n\", \"374902158\\n\", \"279829896\\n\", \"509089974\\n\", \"772717210\\n\", \"609014176\\n\", \"389007481\\n\", \"434018964\\n\", \"428719577\\n\", \"527646690\\n\", \"630885735\\n\", \"350226567\\n\", \"212577904\\n\", \"399880216\\n\", \"576197175\\n\", \"676660731\\n\", \"540037584\\n\", \"211452380\\n\", \"290549063\\n\", \"541185512\\n\", \"719146028\\n\", \"355294274\\n\", \"57637150\\n\", \"861374865\\n\", \"701355269\\n\", \"182802806\\n\", \"8\\n\"]}", "source": "taco"}
|
Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area.
To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of $n$ rows and $m$ columns, where each cell is either black or white. Ivan calls the picture random if for every cell it has at most one adjacent cell of the same color. Two cells are considered adjacent if they share a side.
Ivan's brothers spent some time trying to explain that it's not how the randomness usually works. Trying to convince Ivan, they want to count the number of different random (according to Ivan) pictures. Two pictures are considered different if at least one cell on those two picture is colored differently. Since the number of such pictures may be quite large, print it modulo $10^9 + 7$.
-----Input-----
The only line contains two integers $n$ and $m$ ($1 \le n, m \le 100\,000$), the number of rows and the number of columns of the field.
-----Output-----
Print one integer, the number of random pictures modulo $10^9 + 7$.
-----Example-----
Input
2 3
Output
8
-----Note-----
The picture below shows all possible random pictures of size $2$ by $3$. [Image]
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [[[]], [[\"cw\"]], [[\"CW\"]], [[\"cw\", \"CAT\"]], [[\"cw\", \"CAT\", \"DOG\"]], [[\"cw\", \"CAT\", \"cw=others\"]]], \"outputs\": [[0], [1], [2], [3], [\"You need extra sleep\"], [3]]}", "source": "taco"}
|
Everybody know that you passed to much time awake during night time...
Your task here is to define how much coffee you need to stay awake after your night.
You will have to complete a function that take an array of events in arguments, according to this list you will return the number of coffee you need to stay awake during day time. **Note**: If the count exceed 3 please return 'You need extra sleep'.
The list of events can contain the following:
- You come here, to solve some kata ('cw').
- You have a dog or a cat that just decide to wake up too early ('dog' | 'cat').
- You just watch a movie ('movie').
- Other events can be present and it will be represent by arbitrary string, just ignore this one.
Each event can be downcase/lowercase, or uppercase. If it is downcase/lowercase you need 1 coffee by events and if it is uppercase you need 2 coffees.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
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