info
large_stringlengths 120
50k
| question
large_stringlengths 504
10.4k
| avg@8_qwen3_4b_instruct_2507
float64 0
0.88
|
|---|---|---|
{"tests": "{\"inputs\": [\"4\\n1 2\\n2 3\\n2 3\", \"4\\n1 2\\n1 3\\n2 4\", \"3\\n1 2\\n1 3\", \"4\\n1 2\\n2 3\\n2 2\", \"4\\n1 2\\n2 3\\n2 0\", \"4\\n0 2\\n2 3\\n2 2\", \"4\\n1 2\\n2 3\\n0 0\", \"3\\n0 2\\n2 3\", \"6\\n2 2\\n2 3\\n3 4\\n2 5\\n5 6\", \"4\\n1 2\\n2 3\\n0 2\", \"4\\n1 1\\n2 3\\n2 0\", \"4\\n0 2\\n2 4\\n2 2\", \"4\\n0 2\\n2 3\\n0 2\", \"3\\n1 1\\n2 3\", \"6\\n1 2\\n2 3\\n3 4\\n2 5\\n4 6\", \"4\\n1 2\\n2 0\\n2 4\", \"4\\n0 2\\n2 3\\n2 3\", \"4\\n0 2\\n2 3\\n3 2\", \"4\\n0 2\\n2 3\\n2 1\", \"6\\n2 1\\n2 3\\n3 4\\n2 5\\n5 6\", \"4\\n0 2\\n2 4\\n0 2\", \"4\\n0 2\\n2 1\\n2 3\", \"4\\n1 2\\n2 3\\n3 2\", \"6\\n1 1\\n2 3\\n3 4\\n2 5\\n5 6\", \"4\\n1 3\\n2 3\\n2 4\", \"4\\n1 2\\n4 3\\n2 3\", \"4\\n0 2\\n3 3\\n2 2\", \"4\\n1 1\\n2 3\\n2 1\", \"4\\n1 1\\n2 0\\n2 4\", \"4\\n0 2\\n2 0\\n2 3\", \"4\\n1 2\\n2 4\\n3 2\", \"6\\n1 1\\n2 3\\n6 4\\n2 5\\n5 6\", \"4\\n0 2\\n0 3\\n2 2\", \"4\\n2 1\\n2 0\\n2 4\", \"4\\n0 2\\n2 0\\n2 4\", \"4\\n0 1\\n0 3\\n2 2\", \"4\\n1 2\\n1 3\\n1 4\", \"4\\n0 2\\n2 3\\n2 0\", \"6\\n2 2\\n1 3\\n3 4\\n2 5\\n5 6\", \"4\\n0 2\\n2 0\\n0 2\", \"3\\n1 1\\n2 2\", \"6\\n1 2\\n2 5\\n3 4\\n2 5\\n4 6\", \"4\\n1 1\\n2 3\\n2 2\", \"6\\n2 1\\n2 3\\n6 4\\n2 5\\n5 6\", \"4\\n1 3\\n2 3\\n4 4\", \"4\\n1 2\\n4 4\\n2 3\", \"4\\n1 2\\n2 0\\n2 3\", \"4\\n1 2\\n2 4\\n2 2\", \"6\\n1 2\\n2 3\\n6 4\\n2 5\\n5 6\", \"4\\n1 2\\n1 3\\n1 2\", \"4\\n1 1\\n2 3\\n2 4\", \"6\\n2 1\\n2 3\\n6 4\\n2 5\\n5 5\", \"4\\n1 2\\n4 4\\n1 3\", \"4\\n1 2\\n1 4\\n2 2\", \"6\\n1 2\\n2 3\\n6 4\\n1 5\\n5 6\", \"4\\n1 1\\n3 3\\n2 4\", \"4\\n1 1\\n3 3\\n3 4\", \"4\\n1 1\\n3 3\\n3 3\", \"4\\n1 2\\n3 3\\n2 4\", \"4\\n1 3\\n2 3\\n2 3\", \"4\\n1 2\\n2 4\\n2 0\", \"6\\n2 2\\n2 3\\n3 4\\n1 5\\n5 6\", \"4\\n1 1\\n2 4\\n2 0\", \"4\\n1 2\\n2 4\\n0 2\", \"6\\n1 4\\n2 3\\n3 4\\n2 5\\n4 6\", \"4\\n0 2\\n2 2\\n3 2\", \"4\\n1 2\\n2 3\\n3 3\", \"4\\n2 3\\n2 3\\n2 4\", \"4\\n1 1\\n2 1\\n2 4\", \"4\\n0 2\\n2 0\\n3 3\", \"4\\n0 2\\n0 3\\n2 0\", \"4\\n2 2\\n1 3\\n1 4\", \"4\\n0 2\\n2 3\\n0 0\", \"6\\n1 2\\n2 3\\n6 5\\n1 5\\n5 6\", \"6\\n1 2\\n1 3\\n6 4\\n1 5\\n5 6\", \"4\\n1 1\\n3 3\\n2 3\", \"4\\n2 1\\n2 4\\n2 0\", \"6\\n1 4\\n2 4\\n3 4\\n2 5\\n4 6\", \"4\\n1 2\\n2 0\\n3 0\", \"6\\n1 2\\n1 3\\n4 4\\n1 5\\n5 6\", \"6\\n1 4\\n2 4\\n4 4\\n2 5\\n4 6\", \"4\\n1 1\\n2 0\\n3 0\", \"6\\n1 2\\n1 3\\n1 4\\n1 5\\n5 6\", \"6\\n1 2\\n1 3\\n2 4\\n1 5\\n5 6\", \"4\\n1 2\\n1 3\\n4 4\", \"4\\n2 2\\n2 3\\n2 0\", \"4\\n2 2\\n2 4\\n0 2\", \"6\\n1 2\\n2 1\\n3 4\\n2 5\\n4 6\", \"4\\n0 2\\n2 0\\n2 2\", \"6\\n2 1\\n2 3\\n1 4\\n2 5\\n5 6\", \"4\\n1 2\\n2 3\\n3 4\", \"6\\n1 1\\n4 3\\n3 4\\n2 5\\n5 6\", \"4\\n1 4\\n2 3\\n2 4\", \"4\\n0 2\\n3 2\\n2 2\", \"4\\n1 2\\n3 4\\n3 2\", \"6\\n1 1\\n2 3\\n1 4\\n2 5\\n5 6\", \"4\\n0 2\\n0 1\\n2 2\", \"4\\n1 1\\n4 3\\n2 2\", \"4\\n2 3\\n2 3\\n4 4\", \"4\\n1 2\\n2 4\\n2 4\", \"3\\n1 2\\n2 3\", \"6\\n1 2\\n2 3\\n3 4\\n2 5\\n5 6\", \"4\\n1 2\\n2 3\\n2 4\"], \"outputs\": [\"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\", \"Second\", \"First\"]}", "source": "taco"}
|
There is a tree with N vertices numbered 1 through N. The i-th of the N-1 edges connects vertices a_i and b_i.
Initially, each vertex is uncolored.
Takahashi and Aoki is playing a game by painting the vertices. In this game, they alternately perform the following operation, starting from Takahashi:
* Select a vertex that is not painted yet.
* If it is Takahashi who is performing this operation, paint the vertex white; paint it black if it is Aoki.
Then, after all the vertices are colored, the following procedure takes place:
* Repaint every white vertex that is adjacent to a black vertex, in black.
Note that all such white vertices are repainted simultaneously, not one at a time.
If there are still one or more white vertices remaining, Takahashi wins; if all the vertices are now black, Aoki wins. Determine the winner of the game, assuming that both persons play optimally.
Constraints
* 2 ≤ N ≤ 10^5
* 1 ≤ a_i,b_i ≤ N
* a_i ≠ b_i
* The input graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_1 b_1
:
a_{N-1} b_{N-1}
Output
Print `First` if Takahashi wins; print `Second` if Aoki wins.
Examples
Input
3
1 2
2 3
Output
First
Input
4
1 2
2 3
2 4
Output
First
Input
6
1 2
2 3
3 4
2 5
5 6
Output
Second
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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N\\n.NNNNNNNNNN\\n.NNNNNNNNNN\\n........RRR\\n........RRR\\n........RRR\\n..MMMMMMRRS\\n..MMMMMMRRR\\n..MMMMMMRRR\\n..MMMMMM...\\n....XXXXXXX\\n...........\\n..-..CCCCCC\\n.....CCCCCC\\n.HHHHHHHHHH\\n..VVVVV....\\n..VVVVV....\\n....VVVVV./\\n..VVVVV.I..\\n..VVVVV.I..\\n..UVVVV.I..\\n..I.VVVVV..\\n..VVVVV....\\n..VVVVV....\\n..VVVVV....\\n\", \"20 5 O\\n.....\\n.....\\n.....\\n.....\\n.....\\n/....\\n.....\\n.....\\n..-..\\n.....\\n.....\\n.....\\n../..\\n.....\\n..[.-\\n..A..\\n....Y\\n.OO.Y\\n.OO..\\nR....\\n\", \"20 5 O\\n.....\\n.....\\n.....\\n.....\\n.....\\n/....\\n.....\\n.....\\n..-..\\n.....\\n.....\\n..-..\\n.....\\n.....\\n..Z..\\n..A..\\n...-Y\\n.OO.Y\\n.OO..\\nR....\\n\", \"20 5 O\\n.....\\n../..\\n.....\\n....-\\n.....\\n/....\\n/....\\n.....\\n..-..\\n.....\\n.....\\n..-..\\n.....\\n.....\\n..Z.-\\n..A..\\n....Y\\n.OO.Y\\n.OO..\\nR....\\n\", \"8 10 B\\n..BBBBEEEE\\n..BBBBEEEE\\n..BBBBEEEE\\n..BBBBEEEE\\nJJJJYYXY..\\nKJJJYYYY..\\nJJJJYYYY..\\nJJJYYJYY..\\n\", \"3 3 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|
President of Berland has a very vast office-room, where, apart from him, work his subordinates. Each subordinate, as well as President himself, has his own desk of a unique colour. Each desk is rectangular, and its sides are parallel to the office walls. One day President decided to establish an assembly, of which all his deputies will be members. Unfortunately, he does not remember the exact amount of his deputies, but he remembers that the desk of each his deputy is adjacent to his own desk, that is to say, the two desks (President's and each deputy's) have a common side of a positive length.
The office-room plan can be viewed as a matrix with n rows and m columns. Each cell of this matrix is either empty, or contains a part of a desk. An uppercase Latin letter stands for each desk colour. The «period» character («.») stands for an empty cell.
Input
The first line contains two separated by a space integer numbers n, m (1 ≤ n, m ≤ 100) — the length and the width of the office-room, and c character — the President's desk colour. The following n lines contain m characters each — the office-room description. It is guaranteed that the colour of each desk is unique, and each desk represents a continuous subrectangle of the given matrix. All colours are marked by uppercase Latin letters.
Output
Print the only number — the amount of President's deputies.
Examples
Input
3 4 R
G.B.
.RR.
TTT.
Output
2
Input
3 3 Z
...
.H.
..Z
Output
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\": [\"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n4 6 22645\\n0 2 30739\\n1 4 68417\\n1 5 78537\", \"6 2 2\\n2 2 2\\n1 1 8\\n1 1 5\\n1 2 9\\n1 2 2\\n2 1 4\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"6 2 2\\n2 2 4\\n1 1 12\\n1 1 5\\n1 2 9\\n1 2 2\\n2 1 4\", \"6 2 2\\n2 2 4\\n1 1 3\\n1 1 5\\n1 2 9\\n1 2 2\\n2 1 4\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 84109\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 35902\\n8 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 84109\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 35902\\n8 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 84109\\n3 6 39083\\n0 2 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1 36357\\n2 0 24830\\n5 6 50219\\n1 6 39083\\n0 2 30739\\n1 4 25853\\n0 5 78537\", \"13 5 6\\n1 3 35902\\n8 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 157051\\n4 6 39083\\n0 2 7882\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 33001\\n2 1 24830\\n2 6 84109\\n4 6 55665\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 35902\\n8 6 19698\\n4 6 46661\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 71541\\n2 0 3047\\n5 6 84109\\n3 6 71839\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 0 6\\n1 3 8624\\n4 6 19698\\n4 6 73389\\n3 6 5591\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n6 6 22645\\n1 2 30739\\n2 4 68417\\n1 5 78537\", \"6 2 2\\n2 2 4\\n1 1 8\\n1 0 2\\n1 2 9\\n1 2 7\\n2 1 1\", \"2 5 9\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n3 1 36357\\n2 1 24830\\n5 6 44132\\n4 5 22645\\n0 2 30739\\n2 4 68417\\n1 5 78537\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 6 4784\\n2 1 36357\\n4 0 24830\\n9 6 66923\\n4 6 41235\\n1 2 30739\\n1 4 68417\\n0 5 83493\", \"13 5 9\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n4 6 50219\\n4 9 22645\\n0 2 42757\\n1 5 68417\\n1 5 78537\", \"13 5 6\\n1 3 50810\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 2 30739\\n1 4 68417\\n0 5 67805\", \"6 3 2\\n2 2 0\\n2 1 8\\n2 0 2\\n1 2 9\\n1 0 7\\n2 1 5\", \"13 5 6\\n1 3 35902\\n4 3 19698\\n4 6 73389\\n3 6 3031\\n3 2 4771\\n1 4 4784\\n2 1 36357\\n5 0 8354\\n9 6 66923\\n4 2 39083\\n1 2 30739\\n1 4 68417\\n0 5 67805\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 2 34293\\n5 6 50219\\n4 6 22645\\n1 2 30739\\n1 4 29225\\n1 5 78537\", \"13 5 6\\n1 3 35902\\n4 1 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 50219\\n1 6 39083\\n0 2 42596\\n1 4 25853\\n0 5 78537\", \"13 5 6\\n1 3 36945\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 -1 24830\\n5 6 84109\\n4 6 36941\\n0 2 30739\\n1 4 68417\\n-1 5 78537\", \"13 5 11\\n1 3 35902\\n6 6 19698\\n4 6 73389\\n3 9 3031\\n4 1 4771\\n1 5 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 56904\\n4 6 33804\\n4 3 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n4 0 24830\\n5 6 66923\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 50810\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 4784\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 2 30739\\n1 4 68417\\n0 5 67805\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 2 34293\\n5 6 50219\\n4 6 22645\\n1 4 30739\\n1 4 29225\\n1 5 78537\", \"13 5 6\\n1 3 35902\\n4 1 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 0 24830\\n5 6 43993\\n1 6 39083\\n0 2 42596\\n1 4 25853\\n0 5 78537\", \"13 5 6\\n1 3 36945\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 -1 24830\\n5 6 160809\\n4 6 36941\\n0 2 30739\\n1 4 68417\\n-1 5 78537\", \"13 5 6\\n1 3 68321\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 4784\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 2 30739\\n1 4 68417\\n0 5 67805\", \"3 2 2\\n2 2 4\\n1 1 7\\n1 1 5\\n1 0 15\\n1 2 2\\n2 0 4\", \"2 5 9\\n1 3 23815\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n5 5 44132\\n4 5 22645\\n0 2 30739\\n2 4 68417\\n1 5 78537\", \"13 10 9\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n8 6 50219\\n8 9 22645\\n0 2 42757\\n1 5 68417\\n1 5 78537\", \"13 5 6\\n1 3 68321\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 4784\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 0 30739\\n1 4 68417\\n0 5 67805\", \"6 3 2\\n2 2 1\\n2 1 8\\n2 0 2\\n1 2 15\\n1 -1 7\\n2 1 5\", \"13 5 17\\n1 3 35902\\n6 6 19698\\n4 6 61475\\n3 9 3031\\n4 0 4771\\n1 5 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n4 6 39083\\n0 2 30739\\n1 4 68417\\n0 5 78537\", \"13 5 6\\n1 3 68321\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 4784\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 0 30739\\n1 4 106674\\n0 5 67805\", \"13 5 6\\n1 3 35902\\n1 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 2 36357\\n2 2 34293\\n5 6 17175\\n4 6 22645\\n1 4 30739\\n1 4 29225\\n1 5 78537\", \"3 2 2\\n2 2 4\\n1 1 4\\n1 1 5\\n1 0 15\\n1 2 2\\n2 0 3\", \"13 10 9\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 5134\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n8 6 50219\\n9 6 22645\\n0 2 42757\\n1 5 68417\\n1 5 78537\", \"13 5 6\\n1 3 33043\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 529\\n2 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 0 30739\\n1 4 106674\\n0 5 67805\", \"13 5 6\\n1 3 35902\\n1 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 5 1202\\n2 2 36357\\n2 2 34293\\n5 6 17175\\n4 6 22645\\n1 4 43212\\n1 4 29225\\n1 5 78537\", \"13 5 6\\n0 3 33043\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 0 4771\\n1 4 529\\n4 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 0 51538\\n1 4 106674\\n0 5 67805\", \"13 5 6\\n0 3 33043\\n4 6 19698\\n4 6 73389\\n2 6 3031\\n3 0 4771\\n1 4 529\\n4 1 36357\\n5 -1 41838\\n9 6 66923\\n4 6 39083\\n1 0 51538\\n1 4 106674\\n0 5 67805\", \"4 2 2\\n0 2 4\\n1 1 4\\n1 1 5\\n1 0 21\\n1 2 1\\n0 0 2\", \"1 100000 100000\\n1 1 1\", \"13 5 6\\n1 3 35902\\n4 6 19698\\n4 6 73389\\n3 6 3031\\n3 1 4771\\n1 4 4784\\n2 1 36357\\n2 1 24830\\n5 6 50219\\n4 6 22645\\n1 2 30739\\n1 4 68417\\n1 5 78537\", \"6 2 2\\n2 2 2\\n1 1 8\\n1 1 5\\n1 2 9\\n1 2 7\\n2 1 4\"], \"outputs\": [\"430590\\n\", \"26\\n\", \"447028\\n\", \"30\\n\", \"22\\n\", \"480918\\n\", \"495832\\n\", \"495845\\n\", \"431410\\n\", \"445504\\n\", \"24\\n\", \"425229\\n\", \"18\\n\", \"531029\\n\", \"404132\\n\", \"14\\n\", \"416116\\n\", \"441933\\n\", \"461979\\n\", \"520930\\n\", \"27\\n\", \"451247\\n\", \"1\\n\", \"15\\n\", \"416305\\n\", \"33\\n\", \"478776\\n\", \"472988\\n\", \"443764\\n\", \"23\\n\", \"450059\\n\", \"421875\\n\", \"477562\\n\", \"532586\\n\", \"510970\\n\", \"450288\\n\", \"420015\\n\", \"424449\\n\", \"439417\\n\", \"395184\\n\", \"462935\\n\", \"431178\\n\", \"464836\\n\", \"407945\\n\", \"29\\n\", \"434771\\n\", \"381433\\n\", \"486920\\n\", \"404464\\n\", \"472975\\n\", \"446324\\n\", \"21\\n\", \"4\\n\", \"494144\\n\", \"484242\\n\", \"439430\\n\", \"390400\\n\", \"482981\\n\", \"462347\\n\", \"464131\\n\", \"468255\\n\", \"390896\\n\", \"476532\\n\", \"419378\\n\", \"545917\\n\", \"469314\\n\", \"516998\\n\", \"315543\\n\", \"28\\n\", \"55600\\n\", \"469087\\n\", \"442608\\n\", \"483163\\n\", \"31\\n\", \"431740\\n\", \"400861\\n\", \"431235\\n\", \"479819\\n\", \"445288\\n\", \"491955\\n\", \"480132\\n\", \"399108\\n\", \"425009\\n\", \"556519\\n\", \"497643\\n\", \"16\\n\", \"43513\\n\", \"462306\\n\", \"466904\\n\", \"37\\n\", \"433374\\n\", \"505161\\n\", \"366064\\n\", \"13\\n\", \"462669\\n\", \"469883\\n\", \"378537\\n\", \"482338\\n\", \"485369\\n\", \"34\\n\", \"1\", \"430590\", \"28\"]}", "source": "taco"}
|
There are N cards placed on a grid with H rows and W columns of squares.
The i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.
Multiple cards may be placed on the same square.
You will first pick up at most one card from each row.
Then, you will pick up at most one card from each column.
Find the maximum possible sum of the integers written on the picked cards.
Constraints
* All values are integers.
* 1 \leq N \leq 10^5
* 1 \leq H, W \leq 10^5
* 1 \leq A_i \leq 10^5
* 1 \leq R_i \leq H
* 1 \leq C_i \leq W
Input
Input is given from Standard Input in the following format:
N H W
R_1 C_1 A_1
R_2 C_2 A_2
\vdots
R_N C_N A_N
Output
Print the maximum possible sum of the integers written on the picked cards.
Examples
Input
6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4
Output
28
Input
13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537
Output
430590
Input
1 100000 100000
1 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
|
{"tests": "{\"inputs\": [\"3\\n1 2 0\", \"3\\n3 2 1\", \"4\\n1 2 4 11\", \"3\\n0 2 0\", \"4\\n0 2 4 11\", \"3\\n0 1 0\", \"4\\n0 4 4 11\", \"3\\n0 1 -1\", \"4\\n0 4 4 20\", \"3\\n1 2 1\", \"4\\n0 4 1 20\", \"3\\n2 2 1\", \"4\\n0 4 1 33\", \"4\\n0 4 1 63\", \"3\\n3 4 1\", \"4\\n0 4 1 39\", \"3\\n3 7 1\", \"4\\n0 4 1 0\", \"3\\n6 7 1\", \"4\\n1 4 1 0\", \"3\\n5 7 1\", \"4\\n1 4 1 1\", \"3\\n9 7 1\", \"4\\n2 4 1 0\", \"3\\n2 7 1\", \"4\\n2 4 1 -1\", \"3\\n0 7 1\", \"4\\n1 4 1 -1\", \"3\\n0 13 1\", \"4\\n1 4 1 -2\", \"3\\n0 13 2\", \"4\\n0 4 1 -2\", \"3\\n1 13 2\", \"4\\n0 4 1 -3\", \"3\\n0 25 2\", \"4\\n1 4 1 -3\", \"3\\n0 25 0\", \"4\\n1 4 1 -4\", \"3\\n-1 25 0\", \"4\\n1 4 2 -1\", \"3\\n-1 49 0\", \"4\\n0 4 2 -1\", \"3\\n-1 49 -1\", \"4\\n0 4 1 -1\", \"3\\n0 49 -1\", \"4\\n0 7 1 -1\", \"3\\n1 49 -1\", \"4\\n0 7 1 0\", \"3\\n1 49 -2\", \"4\\n0 7 1 1\", \"3\\n1 13 -2\", \"4\\n0 7 1 2\", \"3\\n0 13 -2\", \"4\\n0 7 0 2\", \"3\\n0 13 -1\", \"4\\n0 7 0 1\", \"3\\n1 1 -1\", \"4\\n0 2 0 1\", \"3\\n0 0 -1\", \"4\\n0 2 0 0\", \"3\\n0 0 0\", \"4\\n1 2 0 0\", \"3\\n1 0 0\", \"4\\n1 2 1 0\", \"3\\n1 0 1\", \"4\\n1 2 1 1\", \"3\\n2 0 1\", \"4\\n1 0 1 1\", \"3\\n2 1 1\", \"4\\n1 0 1 2\", \"3\\n2 1 0\", \"4\\n0 0 1 2\", \"3\\n2 2 0\", \"4\\n0 -1 1 2\", \"3\\n1 2 2\", \"4\\n0 -1 0 2\", \"3\\n0 2 2\", \"4\\n0 -2 0 2\", \"3\\n-1 2 2\", \"4\\n0 -2 0 0\", \"3\\n-1 0 2\", \"4\\n0 -3 0 0\", \"3\\n-1 -1 2\", \"4\\n0 -3 0 1\", \"3\\n0 -1 2\", \"4\\n0 -3 0 2\", \"3\\n0 0 2\", \"4\\n1 -3 0 2\", \"3\\n0 0 1\", \"4\\n1 -3 1 2\", \"3\\n0 1 1\", \"4\\n1 -5 1 2\", \"3\\n0 2 1\", \"4\\n1 -5 2 2\", \"3\\n0 3 0\", \"4\\n2 -5 2 2\", \"3\\n1 3 0\", \"4\\n2 -5 0 2\", \"3\\n1 3 1\", \"4\\n2 -5 -1 2\", \"3\\n1 2 3\", \"4\\n1 2 4 8\"], \"outputs\": [\"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"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\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"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\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\", \"No\"]}", "source": "taco"}
|
Snuke has N hats. The i-th hat has an integer a_i written on it.
There are N camels standing in a circle. Snuke will put one of his hats on each of these camels.
If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print `Yes`; otherwise, print `No`.
* The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.
What is XOR? The bitwise XOR x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows: - When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. For example, 3 \oplus 5 = 6.
Constraints
* All values in input are integers.
* 3 \leq N \leq 10^{5}
* 0 \leq a_i \leq 10^{9}
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
Yes
Input
4
1 2 4 8
Output
No
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\": [[[6, 6]], [[5, 6, 4]], [[3, 15, 8, 20]], [[6]], [[3, 3]], [[20]], [[3, 6]]], \"outputs\": [[3], [5], [44], [0], [0], [1], [0]]}", "source": "taco"}
|
With one die of 6 sides we will have six different possible results:``` 1, 2, 3, 4, 5, 6``` .
With 2 dice of six sides, we will have 36 different possible results:
```
(1,1),(1,2),(2,1),(1,3),(3,1),(1,4),(4,1),(1,5),
(5,1), (1,6),(6,1),(2,2),(2,3),(3,2),(2,4),(4,2),
(2,5),(5,2)(2,6),(6,2),(3,3),(3,4),(4,3),(3,5),(5,3),
(3,6),(6,3),(4,4),(4,5),(5,4),(4,6),(6,4),(5,5),
(5,6),(6,5),(6,6)
```
So, with 2 dice of 6 sides we get 36 different events.
```
([6,6] ---> 36)
```
But with 2 different dice we can get for this case, the same number of events.
One die of ```4 sides``` and another of ```9 sides``` will produce the exact amount of events.
```
([4,9] ---> 36)
```
We say that the dice set ```[4,9]``` is equivalent to ```[6,6]``` because both produce the same number of events.
Also we may have an amount of three dice producing the same amount of events. It will be for:
```
[4,3,3] ---> 36
```
(One die of 4 sides and two dice of 3 sides each)
Perhaps you may think that the following set is equivalent: ```[6,3,2]``` but unfortunately dice have a **minimum of three sides** (well, really a
tetrahedron with one empty side)
The task for this kata is to get the amount of equivalent dice sets, having **2 dice at least**,for a given set.
For example, for the previous case: [6,6] we will have 3 equivalent sets that are: ``` [4, 3, 3], [12, 3], [9, 4]``` .
You may assume that dice are available from 3 and above for any value up to an icosahedral die (20 sides).
```
[5,6,4] ---> 5 (they are [10, 4, 3], [8, 5, 3], [20, 6], [15, 8], [12, 10])
```
For the cases we cannot get any equivalent set the result will be `0`.
For example for the set `[3,3]` we will not have equivalent dice.
Range of inputs for Random Tests:
```
3 <= sides <= 15
2 <= dices <= 7
```
See examples in the corresponding box.
Enjoy 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
|
{"tests": "{\"inputs\": [\"1000000\\n\", \"100\\n\", \"300000\\n\", \"300\\n\", \"9\\n\", \"1\\n\", \"3\\n\", \"3000\\n\", \"6\\n\", \"8\\n\", \"1500\\n\", \"10000\\n\", \"15\\n\", \"900\\n\", \"30\\n\", \"31\\n\", \"99999\\n\", \"100000\\n\", \"4000000\\n\", \"10000000\\n\", \"10\\n\", \"9999999\\n\", \"800000\\n\", \"9999998\\n\", \"50000\\n\", \"9000000\\n\", \"7\\n\", \"5\\n\", \"90000\\n\", \"5000\\n\", \"1000010\\n\", \"101\\n\", \"500019\\n\", \"326\\n\", \"17\\n\", \"1358\\n\", \"1256\\n\", \"11000\\n\", \"25\\n\", \"43\\n\", \"34\\n\", \"54\\n\", \"135287\\n\", \"101000\\n\", \"2406724\\n\", \"12\\n\", \"97481\\n\", \"2629500\\n\", \"75867\\n\", \"74780\\n\", \"8387\\n\", \"18\\n\", \"0000010\\n\", \"001\\n\", \"291626\\n\", \"492\\n\", \"19\\n\", \"11\\n\", \"1889\\n\", \"10001\\n\", \"27\\n\", \"65\\n\", \"63\\n\", \"67010\\n\", \"111000\\n\", \"3718008\\n\", \"21\\n\", \"108883\\n\", \"3753500\\n\", \"120271\\n\", \"117931\\n\", \"12883\\n\", \"24\\n\", \"444218\\n\", \"875\\n\", \"28\\n\", \"14\\n\", \"3054\\n\", \"11001\\n\", \"36\\n\", \"114\\n\", \"13\\n\", \"96738\\n\", \"111010\\n\", \"6023433\\n\", \"158444\\n\", \"1645671\\n\", \"164670\\n\", \"35678\\n\", \"12924\\n\", \"0000110\\n\", \"111\\n\", \"606449\\n\", \"1181\\n\", \"52\\n\", \"1598\\n\", \"11011\\n\", \"70\\n\", \"16\\n\", \"192461\\n\", \"110010\\n\", \"708464\\n\", \"308192\\n\", \"3068607\\n\", \"122204\\n\", \"67962\\n\", \"4936\\n\", \"1010010\\n\", \"609811\\n\", \"253\\n\", \"33\\n\", \"658\\n\", \"01001\\n\", \"22\\n\", \"9678\\n\", \"111110\\n\", \"359779\\n\", \"543749\\n\", \"0000011\\n\", \"011\\n\", \"110\\n\", \"2\\n\", \"4\\n\"], \"outputs\": [\"266233856\\n\", \"721510432\\n\", \"93822635\\n\", \"327873818\\n\", \"4920\\n\", \"0\\n\", \"6\\n\", \"645417275\\n\", \"183\\n\", \"1641\\n\", \"451187545\\n\", \"723907367\\n\", \"3587226\\n\", \"295068084\\n\", \"782663359\\n\", \"347990060\\n\", \"909741855\\n\", \"729225554\\n\", \"882155933\\n\", \"192336614\\n\", \"14763\\n\", \"730778875\\n\", \"178940616\\n\", \"576926295\\n\", \"969527595\\n\", \"295060537\\n\", \"546\\n\", \"60\\n\", \"548978368\\n\", \"755610910\\n\", \"842808618\\n\", \"164531279\\n\", \"964851839\\n\", \"683695217\\n\", \"32285040\\n\", \"997214452\\n\", \"445825152\\n\", \"677079220\\n\", \"822150883\\n\", \"184580488\\n\", \"395731578\\n\", \"879611718\\n\", \"135463628\\n\", \"723427517\\n\", \"457157881\\n\", \"132861\\n\", \"180769274\\n\", \"581087767\\n\", \"534526341\\n\", \"244295350\\n\", \"285886002\\n\", \"96855123\\n\", \"14763\\n\", \"0\\n\", \"444070460\\n\", \"57278800\\n\", \"290565366\\n\", \"44286\\n\", \"133053061\\n\", \"171722084\\n\", \"399357904\\n\", \"575784945\\n\", \"397309440\\n\", \"926920140\\n\", \"181820188\\n\", \"442151010\\n\", \"615088286\\n\", \"996042442\\n\", \"954184169\\n\", \"437784050\\n\", \"851999002\\n\", \"300619479\\n\", \"607383631\\n\", \"20551681\\n\", \"397568467\\n\", \"198073708\\n\", \"1195743\\n\", \"887362227\\n\", \"31237643\\n\", \"561584175\\n\", \"1688648\\n\", \"398580\\n\", \"431946095\\n\", \"300161774\\n\", \"339077305\\n\", \"521034813\\n\", \"73718715\\n\", \"581917459\\n\", \"597151800\\n\", \"827380583\\n\", \"469156654\\n\", \"407469952\\n\", \"729875053\\n\", \"815322385\\n\", \"97734636\\n\", \"376751264\\n\", \"551612885\\n\", \"915740845\\n\", \"10761681\\n\", \"719653349\\n\", \"992061160\\n\", \"834848952\\n\", \"892756033\\n\", \"151266759\\n\", \"956575794\\n\", \"838211016\\n\", \"502528390\\n\", \"381777136\\n\", \"535501844\\n\", \"122889822\\n\", \"131910525\\n\", \"291677062\\n\", \"42666144\\n\", \"845264854\\n\", \"173297168\\n\", \"785533092\\n\", \"883283430\\n\", \"721411677\\n\", \"44286\\n\", \"44286\\n\", \"469156654\\n\", \"3\\n\", \"21\\n\"]}", "source": "taco"}
|
You are given a tetrahedron. Let's mark its vertices with letters A, B, C and D correspondingly.
<image>
An ant is standing in the vertex D of the tetrahedron. The ant is quite active and he wouldn't stay idle. At each moment of time he makes a step from one vertex to another one along some edge of the tetrahedron. The ant just can't stand on one place.
You do not have to do much to solve the problem: your task is to count the number of ways in which the ant can go from the initial vertex D to itself in exactly n steps. In other words, you are asked to find out the number of different cyclic paths with the length of n from vertex D to itself. As the number can be quite large, you should print it modulo 1000000007 (109 + 7).
Input
The first line contains the only integer n (1 ≤ n ≤ 107) — the required length of the cyclic path.
Output
Print the only integer — the required number of ways modulo 1000000007 (109 + 7).
Examples
Input
2
Output
3
Input
4
Output
21
Note
The required paths in the first sample are:
* D - A - D
* D - B - D
* D - C - D
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\": [\"3\\n2 2 2\\n\", \"2\\n2 3\\n\", \"3\\n1 1 1\\n\", \"1\\n1000000000\\n\", \"10\\n10 10 7 9 8 3 3 10 7 3\\n\", \"100\\n23 39 85 46 97 72 41 70 37 18 8 40 33 61 12 79 51 78 61 66 85 97 78 14 70 47 100 40 15 40 61 52 19 30 14 91 82 56 10 6 68 24 97 61 31 78 18 45 88 6 37 38 51 86 37 42 58 30 79 56 50 14 61 18 13 20 57 3 93 15 24 74 32 21 71 93 2 66 25 75 75 10 86 82 30 31 6 49 15 33 100 35 1 96 87 83 29 21 41 22\\n\"], \"outputs\": [\"2\", \"4\", \"0\", \"1755647\", \"24763644\", \"558513243\"]}", "source": "taco"}
|
You are given an array of $n$ positive integers $a_1, a_2, \ldots, a_n$. Your task is to calculate the number of arrays of $n$ positive integers $b_1, b_2, \ldots, b_n$ such that:
$1 \le b_i \le a_i$ for every $i$ ($1 \le i \le n$), and
$b_i \neq b_{i+1}$ for every $i$ ($1 \le i \le n - 1$).
The number of such arrays can be very large, so print it modulo $998\,244\,353$.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array $a$.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).
-----Output-----
Print the answer modulo $998\,244\,353$ in a single line.
-----Examples-----
Input
3
2 2 2
Output
2
Input
2
2 3
Output
4
Input
3
1 1 1
Output
0
-----Note-----
In the first test case possible arrays are $[1, 2, 1]$ and $[2, 1, 2]$.
In the second test case possible arrays are $[1, 2]$, $[1, 3]$, $[2, 1]$ and $[2, 3]$.
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\": [\"2\\n1 2 3 6\\n3 4 7 8\\n\", \"3\\n1 3 2 4\\n4 5 6 7\\n3 4 5 5\\n\", \"6\\n1 5 2 9\\n2 4 5 8\\n3 6 7 11\\n7 10 12 16\\n8 11 13 17\\n9 12 14 18\\n\", \"1\\n21044762 968128997 570202182 610619156\\n\", \"2\\n4 4 4 5\\n4 5 1 2\\n\", \"2\\n311374951 311375694 79710796 79710890\\n311374081 311374676 79712235 79712404\\n\", \"4\\n544431836 544432042 793496989 793497079\\n544429970 544430041 793496343 793496350\\n544432412 544432541 793497670 793498269\\n544431029 544431033 793494552 793494859\\n\", \"4\\n922033367 922033530 246113700 246113747\\n922034178 922034457 246112224 246112584\\n922032889 922035756 246111602 246114286\\n922032155 922035184 246111686 246114644\\n\", \"3\\n1 4 1 2\\n2 5 2 3\\n3 6 3 4\\n\", \"4\\n1 5 1 3\\n2 6 2 4\\n3 7 3 5\\n4 8 4 6\\n\", \"3\\n1 3 1 4\\n3 5 2 5\\n5 7 3 6\\n\", \"5\\n1 6 1 4\\n2 7 2 5\\n3 8 3 6\\n4 9 4 7\\n5 10 5 8\\n\", \"4\\n1 2 1 2\\n3 4 3 4\\n1 2 3 4\\n3 4 1 2\\n\", \"5\\n5 15 5 15\\n3 4 3 5\\n6 7 6 7\\n4 5 8 16\\n8 9 16 17\\n\", \"4\\n1 4 5 8\\n2 3 2 3\\n6 7 6 7\\n5 8 1 4\\n\", \"4\\n1 1 1 1\\n1 1 2 2\\n2 2 1 1\\n2 2 2 2\\n\", \"4\\n1 2 5 6\\n2 3 1 2\\n5 6 2 3\\n6 7 6 7\\n\", \"5\\n1 10 1 10\\n2 20 11 30\\n11 30 2 20\\n21 40 21 40\\n31 50 31 50\\n\", \"4\\n1 5 1 5\\n2 8 7 10\\n7 10 2 8\\n9 20 9 20\\n\", \"5\\n1 4 1 4\\n2 6 5 8\\n5 8 2 6\\n7 10 7 10\\n9 11 9 11\\n\", \"4\\n1 1 1 1\\n2 2 2 2\\n3 3 1 1\\n4 4 4 4\\n\", \"6\\n1 4 11 14\\n2 5 2 5\\n3 6 3 6\\n11 14 1 4\\n12 15 12 15\\n13 16 13 16\\n\", \"4\\n1 3 5 7\\n2 4 1 3\\n5 7 6 8\\n6 8 2 4\\n\", \"4\\n1 2 1 2\\n2 3 3 4\\n3 4 2 3\\n4 5 4 5\\n\", \"6\\n1 6 7 12\\n2 3 2 3\\n4 5 4 5\\n7 12 1 6\\n8 9 8 9\\n10 11 10 11\\n\", \"4\\n1 5 1 5\\n2 3 2 3\\n4 6 6 8\\n100 200 100 200\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n\", \"4\\n1 5 1 3\\n2 6 2 4\\n3 7 3 5\\n4 8 4 6\\n\", \"4\\n1 5 1 5\\n2 3 2 3\\n4 6 6 8\\n100 200 100 200\\n\", \"4\\n1 2 5 6\\n2 3 1 2\\n5 6 2 3\\n6 7 6 7\\n\", \"4\\n1 3 5 7\\n2 4 1 3\\n5 7 6 8\\n6 8 2 4\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n\", \"2\\n311374951 311375694 79710796 79710890\\n311374081 311374676 79712235 79712404\\n\", \"6\\n1 6 7 12\\n2 3 2 3\\n4 5 4 5\\n7 12 1 6\\n8 9 8 9\\n10 11 10 11\\n\", \"4\\n1 4 5 8\\n2 3 2 3\\n6 7 6 7\\n5 8 1 4\\n\", \"4\\n1 2 1 2\\n2 3 3 4\\n3 4 2 3\\n4 5 4 5\\n\", \"2\\n4 4 4 5\\n4 5 1 2\\n\", \"4\\n1 1 1 1\\n2 2 2 2\\n3 3 1 1\\n4 4 4 4\\n\", \"3\\n1 4 1 2\\n2 5 2 3\\n3 6 3 4\\n\", \"4\\n1 1 1 1\\n1 1 2 2\\n2 2 1 1\\n2 2 2 2\\n\", \"5\\n5 15 5 15\\n3 4 3 5\\n6 7 6 7\\n4 5 8 16\\n8 9 16 17\\n\", \"4\\n1 5 1 5\\n2 8 7 10\\n7 10 2 8\\n9 20 9 20\\n\", \"6\\n1 4 11 14\\n2 5 2 5\\n3 6 3 6\\n11 14 1 4\\n12 15 12 15\\n13 16 13 16\\n\", \"4\\n1 2 1 2\\n3 4 3 4\\n1 2 3 4\\n3 4 1 2\\n\", \"4\\n544431836 544432042 793496989 793497079\\n544429970 544430041 793496343 793496350\\n544432412 544432541 793497670 793498269\\n544431029 544431033 793494552 793494859\\n\", \"5\\n1 4 1 4\\n2 6 5 8\\n5 8 2 6\\n7 10 7 10\\n9 11 9 11\\n\", \"5\\n1 6 1 4\\n2 7 2 5\\n3 8 3 6\\n4 9 4 7\\n5 10 5 8\\n\", \"3\\n1 3 1 4\\n3 5 2 5\\n5 7 3 6\\n\", \"1\\n21044762 968128997 570202182 610619156\\n\", \"5\\n1 10 1 10\\n2 20 11 30\\n11 30 2 20\\n21 40 21 40\\n31 50 31 50\\n\", \"4\\n922033367 922033530 246113700 246113747\\n922034178 922034457 246112224 246112584\\n922032889 922035756 246111602 246114286\\n922032155 922035184 246111686 246114644\\n\", \"4\\n1 5 1 1\\n2 6 2 4\\n3 7 3 5\\n4 8 4 6\\n\", \"1\\n21044762 537546491 570202182 610619156\\n\", \"4\\n1 2 5 6\\n2 2 1 2\\n5 6 2 3\\n6 7 6 7\\n\", \"4\\n1 3 5 6\\n2 4 1 3\\n5 7 6 8\\n6 8 2 4\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 3\\n\", \"4\\n1 4 5 8\\n2 3 2 4\\n6 7 6 7\\n5 8 1 4\\n\", \"3\\n1 4 1 2\\n2 5 3 3\\n3 6 3 4\\n\", \"4\\n1 6 1 5\\n2 8 7 10\\n7 10 2 8\\n9 20 9 20\\n\", \"4\\n1 2 1 4\\n3 4 3 4\\n1 2 3 4\\n3 4 1 2\\n\", \"5\\n1 4 1 4\\n2 6 5 8\\n5 8 2 6\\n7 10 7 15\\n9 11 9 11\\n\", \"5\\n1 6 1 4\\n2 7 2 5\\n3 8 3 6\\n4 9 4 7\\n6 10 5 8\\n\", \"3\\n1 3 1 4\\n3 5 2 5\\n5 7 3 8\\n\", \"5\\n1 10 1 10\\n2 20 11 30\\n11 30 3 20\\n21 40 21 40\\n31 50 31 50\\n\", \"3\\n1 3 3 4\\n4 5 6 7\\n3 4 5 5\\n\", \"4\\n1 5 1 1\\n2 9 2 4\\n3 7 3 5\\n4 8 4 6\\n\", \"4\\n1 2 5 6\\n2 2 1 2\\n5 6 2 6\\n6 7 6 7\\n\", \"4\\n1 3 5 6\\n2 4 1 3\\n5 7 8 8\\n6 8 2 4\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 2 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 3\\n\", \"4\\n1 4 5 8\\n2 3 2 4\\n6 7 2 7\\n5 8 1 4\\n\", \"3\\n1 5 1 2\\n2 5 3 3\\n3 6 3 4\\n\", \"4\\n1 6 1 5\\n2 8 7 13\\n7 10 2 8\\n9 20 9 20\\n\", \"5\\n1 6 1 4\\n2 2 2 5\\n3 8 3 6\\n4 9 4 7\\n6 10 5 8\\n\", \"3\\n1 3 1 4\\n3 5 2 5\\n5 7 3 9\\n\", \"5\\n1 10 1 10\\n2 20 11 12\\n11 30 3 20\\n21 40 21 40\\n31 50 31 50\\n\", \"3\\n1 3 3 4\\n4 5 6 7\\n3 5 5 5\\n\", \"4\\n1 5 0 1\\n2 9 2 4\\n3 7 3 5\\n4 8 4 6\\n\", \"4\\n1 2 5 8\\n2 2 1 2\\n5 6 2 3\\n6 7 6 7\\n\", \"4\\n1 3 0 6\\n2 4 1 3\\n5 7 6 8\\n6 8 2 4\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 3 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 2 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 3\\n\", \"4\\n2 4 5 8\\n2 3 2 4\\n6 7 2 7\\n5 8 1 4\\n\", \"4\\n1 6 1 5\\n3 8 7 13\\n7 10 2 8\\n9 20 9 20\\n\", \"5\\n1 6 1 4\\n2 2 2 5\\n3 8 3 6\\n4 8 4 7\\n6 10 5 8\\n\", \"3\\n1 3 1 4\\n3 5 4 5\\n5 7 3 9\\n\", \"5\\n1 10 1 3\\n2 20 11 12\\n11 30 3 20\\n21 40 21 40\\n31 50 31 50\\n\", \"3\\n1 3 3 7\\n4 5 6 7\\n3 5 5 5\\n\", \"4\\n1 5 0 1\\n2 9 2 4\\n3 7 3 5\\n4 8 0 6\\n\", \"4\\n1 1 5 8\\n2 2 1 2\\n5 6 2 3\\n6 7 6 7\\n\", \"4\\n1 3 0 6\\n2 4 1 3\\n5 7 6 12\\n6 8 2 4\\n\", \"16\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 3 1 2\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 3 4\\n1 2 1 2\\n1 2 3 4\\n3 4 1 2\\n3 4 4 4\\n3 4 3 4\\n3 4 1 2\\n1 2 3 4\\n1 2 1 3\\n\", \"4\\n2 4 5 16\\n2 3 2 4\\n6 7 2 7\\n5 8 1 4\\n\", \"4\\n1 6 1 5\\n3 8 7 13\\n7 10 3 8\\n9 20 9 20\\n\", \"3\\n1 3 1 4\\n3 5 3 5\\n5 7 3 9\\n\", \"5\\n1 10 1 3\\n2 20 11 12\\n11 30 3 20\\n21 40 25 40\\n31 50 31 50\\n\", \"3\\n1 3 3 7\\n4 5 6 7\\n3 6 5 5\\n\", \"4\\n1 5 0 1\\n2 9 1 4\\n3 7 3 5\\n4 8 0 6\\n\", \"3\\n1 3 2 4\\n4 5 6 7\\n3 4 5 5\\n\", \"6\\n1 5 2 9\\n2 4 5 8\\n3 6 7 11\\n7 10 12 16\\n8 11 13 17\\n9 12 14 18\\n\", \"2\\n1 2 3 6\\n3 4 7 8\\n\"], \"outputs\": [\"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\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\", \"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\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"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\", \"YES\\n\", \"YES\\n\"]}", "source": "taco"}
|
Filled with optimism, Hyunuk will host a conference about how great this new year will be!
The conference will have $n$ lectures. Hyunuk has two candidate venues $a$ and $b$. For each of the $n$ lectures, the speaker specified two time intervals $[sa_i, ea_i]$ ($sa_i \le ea_i$) and $[sb_i, eb_i]$ ($sb_i \le eb_i$). If the conference is situated in venue $a$, the lecture will be held from $sa_i$ to $ea_i$, and if the conference is situated in venue $b$, the lecture will be held from $sb_i$ to $eb_i$. Hyunuk will choose one of these venues and all lectures will be held at that venue.
Two lectures are said to overlap if they share any point in time in common. Formally, a lecture held in interval $[x, y]$ overlaps with a lecture held in interval $[u, v]$ if and only if $\max(x, u) \le \min(y, v)$.
We say that a participant can attend a subset $s$ of the lectures if the lectures in $s$ do not pairwise overlap (i.e. no two lectures overlap). Note that the possibility of attending may depend on whether Hyunuk selected venue $a$ or venue $b$ to hold the conference.
A subset of lectures $s$ is said to be venue-sensitive if, for one of the venues, the participant can attend $s$, but for the other venue, the participant cannot attend $s$.
A venue-sensitive set is problematic for a participant who is interested in attending the lectures in $s$ because the participant cannot be sure whether the lecture times will overlap. Hyunuk will be happy if and only if there are no venue-sensitive sets. Determine whether Hyunuk will be happy.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 100000$), the number of lectures held in the conference.
Each of the next $n$ lines contains four integers $sa_i$, $ea_i$, $sb_i$, $eb_i$ ($1 \le sa_i, ea_i, sb_i, eb_i \le 10^9$, $sa_i \le ea_i, sb_i \le eb_i$).
-----Output-----
Print "YES" if Hyunuk will be happy. Print "NO" otherwise.
You can print each letter in any case (upper or lower).
-----Examples-----
Input
2
1 2 3 6
3 4 7 8
Output
YES
Input
3
1 3 2 4
4 5 6 7
3 4 5 5
Output
NO
Input
6
1 5 2 9
2 4 5 8
3 6 7 11
7 10 12 16
8 11 13 17
9 12 14 18
Output
YES
-----Note-----
In second example, lecture set $\{1, 3\}$ is venue-sensitive. Because participant can't attend this lectures in venue $a$, but can attend in venue $b$.
In first and third example, venue-sensitive set does not exist.
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 31\\n\", \"2\\n1 0\\n\", \"10\\n450661 128600 993228 725823 293549 33490 843121 903634 556169 448234\\n\", \"1\\n1\\n\", \"5\\n1 3 5 7 9\\n\", \"6\\n524 529 5249 524 529 529\\n\", \"3\\n1 2 3\\n\", \"2\\n0 1\\n\", \"55\\n0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9 4 5 6 7 8 9 5 6 7 8 9 6 7 8 9 7 8 9 8 9 9\\n\", \"16\\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15\\n\", \"3\\n128 1024 2048\\n\", \"10\\n3 3 3 5 5 3 3 3 3 5\\n\", \"1\\n0\\n\", \"2\\n1 2\\n\", \"2\\n0 0\\n\", \"2\\n1 1\\n\", \"2\\n1 20\\n\", \"10\\n450661 128600 993228 725823 293549 33490 843121 528432 556169 448234\\n\", \"1\\n2\\n\", \"5\\n1 6 5 7 9\\n\", \"6\\n524 529 5249 867 529 529\\n\", \"3\\n1 4 3\\n\", \"55\\n0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 3 4 10 6 7 8 9 3 4 5 6 7 8 9 4 5 6 7 8 9 5 6 7 8 9 6 7 8 9 7 8 9 8 9 9\\n\", \"16\\n0 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15\\n\", \"3\\n20 1024 2048\\n\", \"10\\n3 3 3 10 5 3 3 3 3 5\\n\", \"4\\n0 1 4 3\\n\", \"6\\n5 3 0 5 2 1\\n\", \"10\\n450661 104230 993228 725823 293549 33490 843121 528432 556169 448234\\n\", \"5\\n1 6 5 7 13\\n\", \"6\\n524 529 5249 867 231 529\\n\", \"3\\n0 4 3\\n\", \"55\\n0 1 2 3 4 5 6 7 8 9 1 2 4 4 5 6 7 8 9 2 3 4 10 6 7 8 9 3 4 5 6 7 8 9 4 5 6 7 8 9 5 6 7 8 9 6 7 8 9 7 8 9 8 9 9\\n\", \"16\\n0 2 2 3 4 5 6 7 8 11 10 11 12 13 14 15\\n\", \"10\\n3 3 3 10 5 4 3 3 3 5\\n\", \"2\\n0 2\\n\", \"6\\n5 3 0 2 2 1\\n\", \"10\\n450661 104230 993228 725823 293549 33490 843121 528432 556169 148241\\n\", \"5\\n1 6 5 0 13\\n\", \"55\\n0 1 2 3 4 5 6 7 8 9 1 2 4 4 5 6 7 8 9 2 3 4 10 6 7 8 9 3 4 5 6 7 8 9 4 5 5 7 8 9 5 6 7 8 9 6 7 8 9 7 8 9 8 9 9\\n\", \"16\\n0 2 2 3 4 5 6 7 8 11 10 11 12 10 14 15\\n\", \"10\\n3 3 3 10 5 4 3 3 3 7\\n\", \"6\\n5 3 1 2 2 1\\n\", \"10\\n755545 104230 993228 725823 293549 33490 843121 528432 556169 148241\\n\", \"5\\n1 6 5 0 2\\n\", \"6\\n524 529 5249 867 390 835\\n\", \"55\\n0 1 2 3 4 5 6 7 8 9 1 2 4 4 5 6 4 8 9 2 3 4 10 6 7 8 9 3 4 5 6 7 8 9 4 5 5 7 8 9 5 6 7 8 9 6 7 8 9 7 8 9 8 9 9\\n\", \"16\\n0 2 2 3 4 5 6 5 8 11 10 11 12 10 14 15\\n\", \"2\\n2 2\\n\", \"2\\n1 4\\n\", \"3\\n1 3 3\\n\", \"2\\n1 35\\n\", \"1\\n4\\n\", \"3\\n20 1750 2048\\n\", \"2\\n2 1\\n\", \"3\\n0 3 3\\n\", \"4\\n0 1 0 3\\n\", \"2\\n0 35\\n\", \"1\\n8\\n\", \"6\\n524 529 5249 867 231 835\\n\", \"3\\n0 7 3\\n\", \"3\\n9 1750 2048\\n\", \"2\\n0 3\\n\", \"3\\n0 5 3\\n\", \"4\\n0 2 0 3\\n\", \"2\\n1 58\\n\", \"1\\n14\\n\", \"3\\n2 3 3\\n\", \"4\\n0 1 2 3\\n\", \"6\\n5 2 0 5 2 1\\n\"], \"outputs\": [\"0\\n\", \"2\\n\", \"632\\n\", \"0\\n\", \"0\\n\", \"24\\n\", \"2\\n\", \"2\\n\", \"621247139\\n\", \"64594\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"1\", \"690\", \"0\", \"12\", \"16\", \"3\", \"186945693\", \"64466\", \"4\", \"384\", \"11\", \"46\", \"693\", \"8\", \"23\", \"5\", \"426018973\", \"63982\", \"700\", \"2\", \"50\", \"767\", \"20\", \"159672477\", \"63160\", \"636\", \"42\", \"699\", \"24\", \"34\", \"429139229\", \"64162\", \"0\", \"1\", \"0\", \"0\", \"0\", \"3\", \"1\", \"4\", \"12\", \"2\", \"0\", \"23\", \"4\", \"4\", \"2\", \"4\", \"12\", \"1\", \"0\", \"0\\n\", \"10\\n\", \"53\\n\"]}", "source": "taco"}
|
Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k.
Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers.
Input
The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).
Examples
Input
3
2 3 3
Output
0
Input
4
0 1 2 3
Output
10
Input
6
5 2 0 5 2 1
Output
53
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\": [\"4 3\\n2\\n6\\n8\\n1\\n2\\n9\\n3\", \"2 2\\n3\\n6\\n2\\n7\", \"0 3\\n2\\n6\\n8\\n1\\n2\\n9\\n3\", \"2 2\\n3\\n9\\n2\\n7\", \"0 3\\n2\\n6\\n13\\n1\\n2\\n9\\n3\", \"2 2\\n3\\n16\\n2\\n7\", \"2 2\\n3\\n32\\n2\\n7\", \"2 2\\n0\\n32\\n2\\n7\", \"0 3\\n1\\n6\\n8\\n1\\n2\\n9\\n0\", \"2 2\\n-1\\n32\\n2\\n7\", \"0 3\\n0\\n6\\n8\\n1\\n2\\n9\\n0\", \"2 2\\n-1\\n32\\n2\\n9\", \"2 2\\n-1\\n32\\n2\\n3\", \"0 4\\n0\\n6\\n15\\n1\\n3\\n5\\n1\", \"0 4\\n0\\n6\\n0\\n1\\n4\\n5\\n1\", \"0 4\\n0\\n6\\n-1\\n1\\n4\\n5\\n1\", \"0 4\\n0\\n6\\n-1\\n4\\n4\\n5\\n1\", \"1 4\\n0\\n6\\n-1\\n4\\n4\\n5\\n1\", \"1 2\\n0\\n6\\n-1\\n4\\n4\\n5\\n1\", \"1 3\\n0\\n6\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n0\\n6\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n1\\n6\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n1\\n3\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n1\\n2\\n0\\n6\\n3\\n1\\n1\", \"0 3\\n1\\n2\\n0\\n6\\n3\\n1\\n1\", \"1 3\\n1\\n2\\n0\\n6\\n3\\n1\\n1\", \"1 3\\n1\\n0\\n0\\n3\\n3\\n1\\n1\", \"1 3\\n1\\n0\\n-1\\n1\\n3\\n0\\n1\", \"1 1\\n2\\n0\\n-3\\n2\\n21\\n1\\n2\", \"1 1\\n0\\n0\\n-1\\n3\\n21\\n1\\n0\", \"1 1\\n1\\n-1\\n-1\\n3\\n21\\n1\\n0\", \"1 2\\n1\\n-1\\n-1\\n6\\n21\\n1\\n0\", \"1 2\\n1\\n-1\\n-2\\n0\\n21\\n1\\n0\", \"4 3\\n2\\n4\\n8\\n1\\n2\\n17\\n3\", \"4 3\\n2\\n6\\n8\\n0\\n2\\n9\\n3\", \"0 3\\n2\\n6\\n9\\n1\\n2\\n9\\n3\", \"2 2\\n3\\n9\\n0\\n7\", \"2 2\\n6\\n16\\n2\\n7\", \"2 2\\n3\\n32\\n0\\n7\", \"2 1\\n0\\n32\\n2\\n7\", \"0 3\\n-1\\n6\\n8\\n1\\n2\\n9\\n0\", \"2 2\\n0\\n10\\n2\\n3\", \"1 2\\n2\\n1\\n-6\\n3\\n21\\n1\\n2\", \"4 3\\n2\\n4\\n8\\n1\\n4\\n17\\n3\", \"4 3\\n2\\n6\\n8\\n0\\n2\\n6\\n3\", \"2 2\\n3\\n9\\n1\\n7\", \"2 0\\n-1\\n50\\n2\\n9\", \"2 1\\n-1\\n32\\n2\\n3\", \"2 1\\n2\\n1\\n-3\\n2\\n1\\n1\\n2\", \"1 1\\n0\\n-1\\n-6\\n2\\n21\\n1\\n2\", \"1 2\\n1\\n-1\\n-4\\n0\\n21\\n2\\n0\", \"4 3\\n2\\n7\\n8\\n0\\n2\\n6\\n3\", \"2 2\\n6\\n19\\n0\\n7\", \"2 2\\n3\\n32\\n0\\n8\", \"3 1\\n-1\\n32\\n2\\n3\", \"1 4\\n1\\n1\\n-1\\n1\\n4\\n0\\n0\", \"4 3\\n2\\n7\\n8\\n0\\n2\\n10\\n3\", \"0 3\\n2\\n6\\n16\\n1\\n4\\n13\\n1\", \"3 1\\n-1\\n32\\n2\\n6\", \"4 3\\n0\\n4\\n-1\\n6\\n5\\n5\\n1\", \"4 3\\n2\\n2\\n0\\n2\\n5\\n1\\n1\", \"2 1\\n1\\n1\\n-2\\n2\\n8\\n0\\n1\", \"4 3\\n2\\n7\\n8\\n0\\n3\\n10\\n3\", \"3 0\\n-1\\n32\\n2\\n6\", \"2 4\\n1\\n6\\n-2\\n4\\n4\\n4\\n1\", \"1 4\\n1\\n4\\n0\\n14\\n8\\n1\\n1\", \"2 1\\n2\\n0\\n-6\\n6\\n42\\n1\\n1\", \"1 2\\n0\\n-1\\n-4\\n0\\n7\\n3\\n0\", \"2 2\\n1\\n8\\n1\\n7\", \"2 1\\n2\\n1\\n-5\\n1\\n2\\n2\\n2\", \"2 1\\n0\\n0\\n-6\\n6\\n42\\n1\\n1\", \"4 2\\n0\\n0\\n0\\n3\\n31\\n2\\n0\", \"4 3\\n2\\n11\\n8\\n0\\n0\\n10\\n3\", \"0 4\\n3\\n28\\n-1\\n8\", \"2 1\\n2\\n2\\n-5\\n1\\n2\\n2\\n2\", \"4 3\\n0\\n0\\n0\\n3\\n62\\n2\\n0\", \"0 7\\n1\\n36\\n4\\n2\\n3\\n7\\n0\", \"2 3\\n1\\n6\\n0\\n15\\n8\\n1\\n2\", \"2 1\\n0\\n2\\n-5\\n1\\n2\\n1\\n0\", \"0 3\\n2\\n6\\n13\\n1\\n2\\n9\\n0\", \"0 3\\n2\\n6\\n8\\n1\\n2\\n9\\n0\", \"0 4\\n0\\n6\\n8\\n1\\n2\\n9\\n0\", \"0 4\\n0\\n6\\n8\\n1\\n3\\n9\\n0\", \"2 2\\n0\\n32\\n2\\n3\", \"0 4\\n0\\n6\\n8\\n1\\n3\\n9\\n1\", \"0 4\\n0\\n6\\n8\\n1\\n3\\n5\\n1\", \"0 4\\n0\\n6\\n9\\n1\\n3\\n5\\n1\", \"0 4\\n0\\n6\\n15\\n1\\n4\\n5\\n1\", \"0 4\\n0\\n6\\n-1\\n2\\n4\\n5\\n1\", \"1 2\\n0\\n6\\n-1\\n3\\n4\\n5\\n1\", \"1 2\\n0\\n6\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n1\\n2\\n-1\\n6\\n4\\n5\\n1\", \"2 3\\n1\\n2\\n-1\\n6\\n4\\n1\\n1\", \"2 3\\n1\\n2\\n-1\\n6\\n3\\n1\\n1\", \"1 3\\n1\\n2\\n0\\n7\\n3\\n1\\n1\", \"1 3\\n0\\n2\\n0\\n7\\n3\\n1\\n1\", \"1 3\\n1\\n0\\n0\\n7\\n3\\n1\\n1\", \"1 3\\n1\\n-1\\n0\\n3\\n3\\n1\\n1\", \"1 3\\n1\\n0\\n0\\n1\\n3\\n1\\n1\", \"1 3\\n1\\n0\\n0\\n1\\n3\\n0\\n1\", \"4 3\\n2\\n4\\n8\\n1\\n2\\n9\\n3\", \"2 2\\n3\\n5\\n2\\n7\"], \"outputs\": [\"64\\n\", \"31\\n\", \"16\\n\", \"35\\n\", \"21\\n\", \"42\\n\", \"58\\n\", \"50\\n\", \"15\\n\", \"47\\n\", \"14\\n\", \"51\\n\", \"39\\n\", \"22\\n\", \"7\\n\", \"6\\n\", \"9\\n\", \"12\\n\", \"4\\n\", \"10\\n\", \"23\\n\", \"26\\n\", \"19\\n\", \"18\\n\", \"3\\n\", \"11\\n\", \"5\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"-1\\n\", \"-3\\n\", \"-5\\n\", \"68\\n\", \"60\\n\", \"17\\n\", \"29\\n\", \"48\\n\", \"52\\n\", \"36\\n\", \"13\\n\", \"20\\n\", \"-8\\n\", \"74\\n\", \"55\\n\", \"32\\n\", \"49\\n\", \"34\\n\", \"-6\\n\", \"-2\\n\", \"-9\\n\", \"56\\n\", \"45\\n\", \"54\\n\", \"40\\n\", \"8\\n\", \"63\\n\", \"24\\n\", \"46\\n\", \"37\\n\", \"25\\n\", \"-4\\n\", \"66\\n\", \"33\\n\", \"28\\n\", \"30\\n\", \"-16\\n\", \"-10\\n\", \"27\\n\", \"-12\\n\", \"-18\\n\", \"41\\n\", \"62\\n\", \"38\\n\", \"-11\\n\", \"72\\n\", \"53\\n\", \"44\\n\", \"-13\\n\", \"21\\n\", \"16\\n\", \"15\\n\", \"15\\n\", \"42\\n\", \"15\\n\", \"15\\n\", \"16\\n\", \"22\\n\", \"7\\n\", \"4\\n\", \"4\\n\", \"16\\n\", \"16\\n\", \"15\\n\", \"12\\n\", \"9\\n\", \"9\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"60\", \"29\"]}", "source": "taco"}
|
On an xy plane, in an area satisfying 0 ≤ x ≤ W, 0 ≤ y ≤ H, there is one house at each and every point where both x and y are integers.
There are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.
The cost of paving a road between houses on coordinates (i,j) and (i+1,j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i,j) and (i,j+1) is q_j for any value of i.
Mr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.
Constraints
* 1 ≦ W,H ≦ 10^5
* 1 ≦ p_i ≦ 10^8(0 ≦ i ≦ W-1)
* 1 ≦ q_j ≦ 10^8(0 ≦ j ≦ H-1)
* p_i (0 ≦ i ≦ W−1) is an integer.
* q_j (0 ≦ j ≦ H−1) is an integer.
Input
Inputs are provided from Standard Input in the following form.
W H
p_0
:
p_{W-1}
q_0
:
q_{H-1}
Output
Output an integer representing the minimum total cost.
Examples
Input
2 2
3
5
2
7
Output
29
Input
4 3
2
4
8
1
2
9
3
Output
60
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\": [\"512 4\\n\", \"1000000000 9\\n\", \"131203 11\\n\", \"999999999 50\\n\", \"999999999 49\\n\", \"131203 9\\n\", \"900000000 16\\n\", \"909090909 50\\n\", \"1001 2\\n\", \"5 2\\n\", \"2 1\\n\", \"900000000 16\\n\", \"131203 11\\n\", \"131203 9\\n\", \"999999999 50\\n\", \"909090909 50\\n\", \"999999999 49\\n\", \"2 1\\n\", \"5 2\\n\", \"1001 2\\n\", \"1747026028 16\\n\", \"102926 11\\n\", \"131203 5\\n\", \"999999999 54\\n\", \"2 0\\n\", \"9 2\\n\", \"1000 2\\n\", \"537 4\\n\", \"1000000000 4\\n\", \"1559848638 16\\n\", \"102926 19\\n\", \"148893 5\\n\", \"999999999 10\\n\", \"3 2\\n\", \"537 7\\n\", \"1000000000 0\\n\", \"1559848638 5\\n\", \"148893 0\\n\", \"1263106103 10\\n\", \"537 11\\n\", \"1100000000 0\\n\", \"1703310190 5\\n\", \"1477 19\\n\", \"228718 0\\n\", \"1086932676 10\\n\", \"1000010000 0\\n\", \"1703310190 4\\n\", \"368965 0\\n\", \"1086932676 2\\n\", \"1001010000 0\\n\", \"167948 0\\n\", \"527523159 2\\n\", \"1001011000 0\\n\", \"256471 0\\n\", \"854684177 2\\n\", \"1001011001 0\\n\", \"256471 1\\n\", \"854684177 0\\n\", \"349125 1\\n\", \"449863133 0\\n\", \"349125 0\\n\", \"449863133 1\\n\", \"34347 0\\n\", \"493572780 0\\n\", \"43112 0\\n\", \"356048457 0\\n\", \"50670 0\\n\", \"315597190 0\\n\", \"248063397 0\\n\", \"182392276 0\\n\", \"363358023 0\\n\", \"363358023 1\\n\", \"605046573 1\\n\", \"605046573 0\\n\", \"275425459 0\\n\", \"433788887 0\\n\", \"393919788 0\\n\", \"131203 3\\n\", \"209408 9\\n\", \"999999999 22\\n\", \"999999999 13\\n\", \"1001 1\\n\", \"519 4\\n\", \"2009760740 16\\n\", \"102926 6\\n\", \"10516 5\\n\", \"1001 0\\n\", \"322 4\\n\", \"102926 8\\n\", \"52368 5\\n\", \"999999999 16\\n\", \"3 0\\n\", \"1047 7\\n\", \"2145180599 5\\n\", \"40066 0\\n\", \"1263106103 4\\n\", \"620 4\\n\", \"0100000000 0\\n\", \"600900476 5\\n\", \"1477 7\\n\", \"399020 0\\n\", \"987796534 10\\n\", \"1000010000 1\\n\", \"1458107387 4\\n\", \"1716008080 2\\n\", \"237726 0\\n\", \"891749335 2\\n\", \"1001011000 1\\n\", \"1118024550 2\\n\", \"7682 19\\n\", \"909090909 46\\n\", \"5 4\\n\", \"4 2\\n\", \"9550 19\\n\", \"512 4\\n\", \"1000000000 9\\n\"], \"outputs\": [\"50\\n\", \"1\\n\", \"12\\n\", \"9999\\n\", \"99990\\n\", \"130\\n\", \"1\\n\", \"3\\n\", \"100\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"130\\n\", \"9999\\n\", \"3\\n\", \"99990\\n\", \"1\\n\", \"3\\n\", \"100\\n\", \"1747023\\n\", \"1028\\n\", \"1312\\n\", \"9995\\n\", \"2\\n\", \"7\\n\", \"10\\n\", \"533\\n\", \"100000\\n\", \"15598483\\n\", \"1020\\n\", \"14888\\n\", \"99999999\\n\", \"1\\n\", \"530\\n\", \"1000000000\\n\", \"1559848633\\n\", \"148893\\n\", \"1263103\\n\", \"50\\n\", \"1100000000\\n\", \"170331015\\n\", \"11\\n\", \"228718\\n\", \"108693264\\n\", \"1000010000\\n\", \"170331016\\n\", \"368965\\n\", \"1086932674\\n\", \"1001010000\\n\", \"167948\\n\", \"527523157\\n\", \"1001011000\\n\", \"256471\\n\", \"854684175\\n\", \"1001011001\\n\", \"256470\\n\", \"854684177\\n\", \"349124\\n\", \"449863133\\n\", \"349125\\n\", \"449863132\\n\", \"34347\\n\", \"493572780\\n\", \"43112\\n\", \"356048457\\n\", \"50670\\n\", \"315597190\\n\", \"248063397\\n\", \"182392276\\n\", \"363358023\\n\", \"363358022\\n\", \"605046572\\n\", \"605046573\\n\", \"275425459\\n\", \"433788887\\n\", \"393919788\\n\", \"131200\\n\", \"20940\\n\", \"9999997\\n\", \"99999996\\n\", \"1000\\n\", \"515\\n\", \"200975\\n\", \"102920\\n\", \"10511\\n\", \"1001\\n\", \"31\\n\", \"10291\\n\", \"52363\\n\", \"99999993\\n\", \"3\\n\", \"1040\\n\", \"2145180594\\n\", \"40066\\n\", \"126310610\\n\", \"6\\n\", \"100000000\\n\", \"600900471\\n\", \"1470\\n\", \"399020\\n\", \"9877964\\n\", \"100001000\\n\", \"1458107383\\n\", \"171600807\\n\", \"237726\\n\", \"891749333\\n\", \"100101100\\n\", \"111802454\\n\", \"7\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"50\\n\", \"1\\n\"]}", "source": "taco"}
|
Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm: if the last digit of the number is non-zero, she decreases the number by one; if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit).
You are given an integer number $n$. Tanya will subtract one from it $k$ times. Your task is to print the result after all $k$ subtractions.
It is guaranteed that the result will be positive integer number.
-----Input-----
The first line of the input contains two integer numbers $n$ and $k$ ($2 \le n \le 10^9$, $1 \le k \le 50$) — the number from which Tanya will subtract and the number of subtractions correspondingly.
-----Output-----
Print one integer number — the result of the decreasing $n$ by one $k$ times.
It is guaranteed that the result will be positive integer number.
-----Examples-----
Input
512 4
Output
50
Input
1000000000 9
Output
1
-----Note-----
The first example corresponds to the following sequence: $512 \rightarrow 511 \rightarrow 510 \rightarrow 51 \rightarrow 50$.
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\": [\"10\\n1 1 0 0 0 0 1 1 1 0\", \"10\\n1 1 0 0 0 0 1 1 1 1\", \"10\\n1 1 0 0 0 0 1 2 1 1\", \"10\\n1 1 0 0 -1 0 1 2 1 1\", \"10\\n1 1 0 0 -1 1 1 2 1 1\", \"10\\n1 1 0 0 -1 2 1 2 1 2\", \"10\\n-1 1 1 1 1 -1 -21 1 1 15\", \"10\\n1 1 0 0 -1 1 1 2 1 2\", \"10\\n1 1 0 0 -1 2 1 4 1 2\", \"10\\n0 1 0 0 -1 2 1 4 1 2\", \"10\\n0 1 0 0 -1 2 1 5 1 2\", \"10\\n0 1 0 0 -1 2 1 5 2 2\", \"10\\n0 1 0 0 -1 1 1 5 2 2\", \"10\\n0 2 0 0 -1 1 1 5 2 2\", \"10\\n0 2 0 0 -1 1 1 5 1 2\", \"10\\n0 2 0 1 -1 1 1 5 1 2\", \"10\\n0 2 1 1 -1 1 1 5 1 2\", \"10\\n0 2 1 1 -1 1 0 5 1 2\", \"10\\n0 3 1 1 -1 1 0 5 1 2\", \"10\\n0 3 1 1 -1 1 0 5 1 4\", \"10\\n0 3 1 1 -1 1 0 5 2 4\", \"10\\n0 3 1 1 -1 1 1 5 2 4\", \"10\\n0 3 1 1 -1 1 2 5 2 4\", \"10\\n0 3 1 1 -1 0 2 5 2 4\", \"10\\n0 2 1 1 -1 0 2 5 2 4\", \"10\\n0 2 1 1 -2 0 2 5 2 4\", \"10\\n0 2 1 1 -2 0 2 7 2 4\", \"10\\n0 2 1 2 -2 0 2 7 2 4\", \"10\\n0 2 1 2 -2 0 2 9 2 4\", \"10\\n0 2 1 2 -2 0 2 3 2 4\", \"10\\n-1 2 1 2 -2 0 2 3 2 4\", \"10\\n-1 2 1 0 -2 0 2 3 2 4\", \"10\\n-1 2 1 0 -2 -1 2 3 2 4\", \"10\\n-1 2 1 0 -2 -1 2 5 2 4\", \"10\\n-1 2 1 0 0 -1 2 5 2 4\", \"10\\n-1 2 1 0 0 -1 2 5 0 4\", \"10\\n-1 2 1 0 0 -1 2 9 0 4\", \"10\\n-1 2 1 0 1 -1 2 9 0 4\", \"10\\n-1 2 1 0 1 -1 2 9 1 4\", \"10\\n-2 2 1 0 1 -1 2 9 1 4\", \"10\\n-2 2 1 0 1 -2 2 9 1 4\", \"10\\n-2 2 1 0 1 -4 2 9 1 4\", \"10\\n-2 1 1 0 1 -4 2 9 1 4\", \"10\\n-2 1 2 0 1 -4 2 9 1 4\", \"10\\n-2 1 2 0 1 -4 2 7 1 4\", \"10\\n-2 1 2 0 1 -4 2 7 1 8\", \"10\\n-2 1 4 0 1 -4 2 7 1 8\", \"10\\n-2 1 4 0 1 -4 2 1 1 8\", \"10\\n-2 1 4 0 2 -4 2 1 1 8\", \"10\\n0 1 4 0 2 -4 2 1 1 8\", \"10\\n0 1 4 0 2 -4 2 2 1 8\", \"10\\n0 1 4 0 2 -4 1 2 1 8\", \"10\\n0 1 4 0 2 -4 1 2 1 3\", \"10\\n0 1 4 1 2 -4 1 2 1 3\", \"10\\n-1 1 4 1 2 -4 1 2 1 3\", \"10\\n-1 1 4 1 3 -4 1 2 1 3\", \"10\\n-1 1 3 1 3 -4 1 2 1 3\", \"10\\n-1 1 3 0 3 -4 1 2 1 3\", \"10\\n-1 1 3 1 6 -4 1 2 1 3\", \"10\\n-1 2 3 1 6 -4 1 2 1 3\", \"10\\n-1 2 3 1 6 -4 1 2 1 4\", \"10\\n-1 2 3 1 6 -4 1 2 1 0\", \"10\\n-1 2 3 1 6 -4 1 2 1 1\", \"10\\n0 2 3 1 6 -4 1 2 1 1\", \"10\\n0 2 3 1 6 -4 1 2 1 2\", \"10\\n0 2 3 1 6 -4 1 2 2 2\", \"10\\n0 2 3 1 6 -6 1 2 2 2\", \"10\\n-1 2 3 1 6 -6 1 2 2 2\", \"10\\n-1 2 3 1 6 -6 1 3 2 2\", \"10\\n-1 2 3 1 4 -6 1 3 2 2\", \"10\\n-1 2 3 1 4 -6 1 3 2 3\", \"10\\n-1 4 3 1 4 -6 1 3 2 3\", \"10\\n-1 4 3 1 4 -6 1 3 4 3\", \"10\\n-1 4 3 1 4 -6 1 1 4 3\", \"10\\n-1 4 3 1 4 -6 1 2 4 3\", \"10\\n-1 4 3 1 4 -12 1 2 4 3\", \"10\\n-1 4 2 1 4 -12 1 2 4 3\", \"10\\n-1 4 2 1 4 -12 2 2 4 3\", \"10\\n-1 4 2 0 4 -12 2 2 4 3\", \"10\\n-1 4 2 0 7 -12 2 2 4 3\", \"10\\n-1 4 2 0 7 -12 2 0 4 3\", \"10\\n-1 4 2 0 7 -12 2 0 4 5\", \"10\\n-1 4 2 0 9 -12 2 0 4 5\", \"10\\n-1 4 2 0 9 -12 2 1 4 5\", \"10\\n-1 4 2 0 9 -12 0 0 4 5\", \"10\\n-1 4 2 0 9 -6 0 0 4 5\", \"10\\n-1 4 2 0 9 -6 -1 0 4 5\", \"10\\n-1 4 2 0 18 -6 -1 0 4 5\", \"10\\n0 4 2 0 18 -6 -1 0 4 5\", \"10\\n0 4 2 -1 18 -6 -1 0 4 5\", \"10\\n0 4 2 -1 18 -6 -1 -1 4 5\", \"10\\n0 4 2 -2 18 -6 -1 -1 4 5\", \"10\\n0 4 2 -2 18 -2 -1 -1 4 5\", \"10\\n0 4 2 -2 18 -2 -1 -1 5 5\", \"10\\n0 4 2 -2 18 -4 -1 -1 5 5\", \"10\\n0 4 2 -2 18 -5 -1 -1 5 5\", \"10\\n0 4 4 -2 18 -5 -1 -1 5 5\", \"10\\n0 4 4 -2 18 -5 -1 -2 5 5\", \"10\\n0 6 4 -2 18 -5 -1 -2 5 5\", \"10\\n0 6 4 -2 18 -5 -1 -2 3 5\", \"10\\n1 1 0 0 1 0 1 1 1 0\"], \"outputs\": [\"5\\n\", \"4\\n\", \"6\\n\", \"9\\n\", \"8\\n\", \"10\\n\", \"7\\n\", \"9\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"9\\n\", \"9\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"9\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"7\"]}", "source": "taco"}
|
Illumination
Illuminations are displayed in the corridors every year at the JOI High School Cultural Festival. The illuminations consist of N light bulbs, which are lined up in a row from the west side to the east side of the corridor. Each light bulb is either on or off.
A machine that operates a light bulb is sleeping in the warehouse of JOI High School. When a continuous light bulb is specified in the illumination, this machine turns all the specified light bulbs with the light on and all the light bulbs without the light on. However, the machine is aging and can only be used once.
JOI high school students like alternating rows of light bulbs with and without lights (such rows of light bulbs are called alternating rows). Therefore, I decided to use this machine only once if necessary to make illuminations containing alternating rows as long as possible.
Example
For example, the arrangement of illuminations is from west to east
<image>
(○ indicates a light bulb with a light, ● indicates a light bulb without a light). At this time, if you operate the machine for the four light bulbs from the 4th to the 7th,
<image>
The second to eighth bulbs form an alternating row of length 7.
<image>
Also, if you operate the machine only for the 8th light bulb,
<image>
The 4th to 10th light bulbs form an alternating row of length 7.
<image>
It is not possible to create alternating rows longer than 8 by using the machine up to once.
Task
Given the illumination information, write a program to find the maximum possible length of the alternating rows in the array of light bulbs that can be obtained by using the machine up to once.
Limits
* 2 ≤ N ≤ 100 000 Number of light bulbs that make up the illumination
input
Read the following data from standard input.
* The integer N is written on the first line.
* On the second line, N 0s or 1s are written with a space as a delimiter. Each integer represents the information of the light bulb before operating the machine. The i (1 ≤ i ≤ N) th integer from the left represents the information of the i-th light bulb from the west, and if the integer is 1, the light bulb is on, and if it is 0, the light bulb is off.
output
Output an integer representing the maximum length of the alternating columns contained in the columns of light bulbs that can be created to the standard output on one line.
Input / output example
Input example 1
Ten
1 1 0 0 1 0 1 1 1 0
Output example 1
7
This is an example explained in the problem statement.
Input example 2
Ten
1 0 0 0 0 1 0 1 0 1
Output example 2
8
Manipulating only the fourth bulb from the west yields an alternating sequence that satisfies the maximum value of 8.
Input example 3
Five
1 1 0 1 1
Output example 3
Five
By manipulating the second to fourth light bulbs counting from the west, you can create an alternating row of all light bulbs.
Input example 4
3
0 1 0
Output example 4
3
Note that you may not need to use a machine.
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
10
1 1 0 0 1 0 1 1 1 0
Output
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.
| 0.5
|
{"tests": "{\"inputs\": [\"a\\naa\\n\", \"a\\na\\n\", \"vnssnssnssnssnssnssnssnssnssnssnssnssnssnssnssnssn\\nnssnssns\\n\", \"ababababab\\nabab\\n\", \"a\\nb\\n\", \"vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nvvvvvvvv\\n\", \"kpjmawawawawawawawawawawawawawawawawawawawawawawaw\\nwawawawa\\n\", \"a\\na`\\n\", \"vnssnssnssnssnssnssnssnssnssnssnssnssnssnssnrsnssn\\nnssnssns\\n\", \"ab`bababab\\nabab\\n\", \"vvvvwvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nvvvvvvvv\\n\", \"kpjmawaxawawawawawawawawawawawawawawawawawawawawaw\\nwawawawa\\n\", \"aaaba\\naba\\n\", \"welcometoroundtwohundredandeighsytwo\\nd\\n\", \"`\\n`\\n\", \"vnssnssnssnssnssnssnssnssnssnssnssnssnssnssnrsnssn\\nsnssnssn\\n\", \"vvvvwvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nvvwvvvvv\\n\", \"kpjmawaxawawawawawawawawawawawawawawawawawawawawaw\\nawawawaw\\n\", \"kpjmawaxavawawawawawawawawawawawawawawawawawawawaw\\nawawawaw\\n\", \"owtyshgiednaderdnuhowtdnuorntemoclew\\nc\\n\", \"a\\n`\\n\", \"a\\nc\\n\", \"ddd\\ne\\n\", \"`\\na`\\n\", \"ab`bab`bab\\nabab\\n\", \"a\\nd\\n\", \"aaaba\\n`ba\\n\", \"ddd\\nf\\n\", \"owtyshgiednaderdnuhowtdnuorotemoclew\\nd\\n\", \"`\\nb`\\n\", \"`\\n_\\n\", \"vnssnssnssnssnssnssnssnssnssnssnssnssnssnssnrsnssn\\nsnssnstn\\n\", \"ab`bab`bab\\nbaba\\n\", \"`\\nb\\n\", \"vvvvwvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nvvwvwvvv\\n\", \"aabba\\n`ba\\n\", \"dde\\nf\\n\", \"owtyshgiednaderdnuhowtdnuorntemoclew\\nd\\n\", \"_\\nb`\\n\", \"`\\n^\\n\", \"vnssnssnssnssnssnssnssnssnssnssnssnssnssnsssrnnssn\\nsnssnstn\\n\", \"bab`bab`ba\\nbaba\\n\", \"_\\nb\\n\", \"vvvvwvvvvvvvvvvvvvvvvuvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nvvwvwvvv\\n\", \"kpjmawaxavawawawawawawawawawawawawawawawawawawawaw\\nawawavaw\\n\", \"aabba\\nb`a\\n\", \"edd\\nf\\n\", \"_\\nb_\\n\", \"a\\n^\\n\", \"nssnnrsssnssnssnssnssnssnssnssnssnssnssnssnssnssnv\\nsnssnstn\\n\", \"bab`bab`ba\\nabab\\n\", \"`\\na\\n\", \"vvvvwvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nwvvvwvvv\\n\", \"kpjmawaxavawawawawawawawawawawawawawawawawbwawawaw\\nawawavaw\\n\", \"aabba\\nb_a\\n\", \"edd\\ne\\n\", \"owtyshgiednaderdnuhowtdnuorntemoclew\\nb\\n\", \"`\\nb_\\n\", \"a\\n]\\n\", \"nssnnrsssnssnssnssnssnssnssnssnssnssnssnssmssnssnv\\nsnssnstn\\n\", \"bac`bab`ba\\nabab\\n\", \"_\\na\\n\", \"vvvvwvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv\\nwuvvwvvv\\n\", \"ababa\\naba\\n\", \"ddd\\nd\\n\", \"welcometoroundtwohundredandeightytwo\\nd\\n\"], \"outputs\": [\"0\\n\", \"1\\n\", \"943392\\n\", \"35\\n\", \"0\\n\", \"2728075\\n\", \"834052\\n\", \"0\\n\", \"336243\\n\", \"17\\n\", \"1295664\\n\", \"354248\\n\", \"3\\n\", \"274201\\n\", \"1\\n\", \"411043\\n\", \"123\\n\", \"466127\\n\", \"294821\\n\", \"132\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"274201\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"274201\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"5\\n\", \"12\\n\", \"274201\\n\"]}", "source": "taco"}
|
Hamed has recently found a string t and suddenly became quite fond of it. He spent several days trying to find all occurrences of t in other strings he had. Finally he became tired and started thinking about the following problem. Given a string s how many ways are there to extract k ≥ 1 non-overlapping substrings from it such that each of them contains string t as a substring? More formally, you need to calculate the number of ways to choose two sequences a1, a2, ..., ak and b1, b2, ..., bk satisfying the following requirements:
* k ≥ 1
* <image>
* <image>
* <image>
* <image> t is a substring of string saisai + 1... sbi (string s is considered as 1-indexed).
As the number of ways can be rather large print it modulo 109 + 7.
Input
Input consists of two lines containing strings s and t (1 ≤ |s|, |t| ≤ 105). Each string consists of lowercase Latin letters.
Output
Print the answer in a single line.
Examples
Input
ababa
aba
Output
5
Input
welcometoroundtwohundredandeightytwo
d
Output
274201
Input
ddd
d
Output
12
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], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [20], [35], [36], [37], [100], [101], [102], [103], [104], [105], [190], [2890], [38890], [488890], [5888890], [3678608], [3678609], [3678610], [3678611], [3678612], [3678613], [3678614], [3897249], [3897189], [3897309], [3897369], [3898749], [3898809], [3898869], [3898929], [3898989], [3899049], [3899109], [999999999], [1000599563], [1000599564], [1000599565], [1000599566], [1000599567], [1000599568], [101800813569], [77199254740991], [501337501337101]], \"outputs\": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [1], [0], [4], [2], [2], [2], [4], [5], [5], [5], [6], [5], [9], [9], [9], [9], [9], [6], [1], [9], [6], [3], [1], [6], [5], [4], [6], [7], [0], [1], [2], [3], [4], [5], [6], [8], [1], [2], [3], [5], [2], [3], [6], [7], [3]]}", "source": "taco"}
|
Ho ho! So you think you know integers, do you? Well then, young wizard, tell us what the Nth digit of the [Champernowne constant](https://en.wikipedia.org/wiki/Champernowne_constant) is!
The constant proceeds like this: `0.12345678910111213141516...`
I hope you see the pattern!
Conjure a function that will accept an integer, `n`, and return the (one-indexed) `n`th digit of Champernowne's constant. Can you get it to run in _constant_ time?
For example:
`n = 1` should return `0` (the very first digit)
`n = 2` should return `1` (we ignore the period character since it's not a digit!)
`n = 20` should return `4` (that's the `4` in the number `14`, 20th in sequence)
For any invalid values, such as `0` and below, or non-integers, return... `NaN`!
I hope (for your sake) that you've been practicing your mathemagical spells, because a naïve solution will _not_ be fast enough to compete in this championship!
Invoke with _precision_, and be wary of rounding errors in the realms of enormity!
May the best integer win!
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\\n13 199 1\\n93 1000 1\\n37 350 10\\n27 300 2\\n99 200 1000\", \"3\\n9 100 1\\n13 200 20\\n12 300 3\", \"2\\n2 100 1\\n2 200 2\", \"5\\n13 199 1\\n93 1000 1\\n37 350 10\\n27 300 2\\n82 200 1000\", \"3\\n9 100 1\\n13 200 20\\n19 300 3\", \"5\\n13 199 1\\n93 1000 1\\n37 350 10\\n27 300 2\\n123 200 1100\", \"3\\n9 100 0\\n13 200 20\\n24 300 3\", \"3\\n9 100 0\\n26 200 20\\n24 300 3\", \"5\\n11 199 0\\n93 1000 1\\n37 350 10\\n27 300 2\\n123 200 1100\", \"3\\n9 100 0\\n26 30 20\\n24 300 3\", \"5\\n11 91 0\\n93 1000 1\\n37 350 10\\n27 300 2\\n123 200 1101\", \"3\\n9 100 0\\n26 30 11\\n20 300 3\", \"5\\n11 91 0\\n93 1000 1\\n37 350 10\\n12 300 2\\n123 200 1111\", \"5\\n11 91 0\\n93 1000 1\\n37 350 3\\n12 300 2\\n123 200 1111\", \"5\\n11 91 0\\n124 1000 1\\n37 350 3\\n12 300 2\\n123 200 1111\", \"3\\n10 100 0\\n26 30 6\\n20 300 0\", \"3\\n10 100 0\\n26 30 6\\n4 300 0\", \"3\\n0 100 0\\n26 30 6\\n4 300 0\", \"3\\n0 100 0\\n0 30 12\\n4 464 0\", \"3\\n1 100 0\\n0 30 12\\n4 464 0\", \"3\\n1 100 0\\n0 30 16\\n1 464 0\", \"3\\n1 100 0\\n-1 34 16\\n1 262 0\", \"3\\n2 100 0\\n-1 34 16\\n1 262 0\", \"3\\n2 000 0\\n0 53 30\\n1 411 0\", \"3\\n0 010 -1\\n-1 53 20\\n1 411 0\", \"3\\n0 010 -1\\n-1 53 20\\n2 608 1\", \"3\\n0 000 -1\\n-1 53 20\\n0 608 1\", \"3\\n0 000 -2\\n-1 106 20\\n1 891 1\", \"3\\n0 000 -3\\n-2 12 22\\n0 238 8\", \"3\\n0 000 -3\\n-2 16 9\\n-1 444 8\", \"3\\n0 000 -3\\n-2 16 9\\n0 444 10\", \"3\\n-1 000 -3\\n-2 16 9\\n0 444 10\", \"3\\n-2 010 -3\\n-2 20 9\\n0 655 10\", \"3\\n-2 110 -3\\n-2 20 6\\n-1 1151 10\", \"3\\n-2 110 -3\\n-2 20 6\\n-1 1324 1\", \"3\\n-1 011 -15\\n-2 26 12\\n-1 329 1\", \"3\\n-1 011 -15\\n0 13 12\\n-1 178 1\", \"3\\n-1 011 -15\\n0 13 12\\n0 178 2\", \"3\\n0 011 -15\\n0 13 12\\n0 178 2\", \"3\\n1 010 -52\\n0 6 9\\n0 178 4\", \"3\\n1 111 -120\\n-2 9 0\\n0 685 5\", \"3\\n-1 110 -143\\n-2 5 0\\n0 384 8\", \"3\\n-1 110 -143\\n-3 4 0\\n0 397 8\", \"3\\n-1 110 -143\\n-3 4 0\\n0 66 8\", \"3\\n0 110 -143\\n-3 7 0\\n0 66 8\", 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2\"]}", "source": "taco"}
|
The phantom thief "Lupin IV" is told by the beautiful "Fujiko Mine", a descendant of the Aizu clan, that the military funds left by the Aizu clan are sleeping in Aizuwakamatsu city. According to a report by Lupine's longtime companion, "Ishikawa Koshiemon," military funds are stored in several warehouses in a Senryobako box. There is no lookout in the warehouse, but it is tightly locked. However, Koshiemon says that if he uses the secret "steel slashing" technique taught by his father, he can instantly break the warehouse.
<image>
The remaining problem is the transportation of Senryobako. Lupine and Yuemon, who have no physical strength, cannot carry a Senryobako. So, I asked the reliable man "Infinity" to carry it. In order to carry out all the Senryobako, Lupine made the following plan.
First, drive Lupine to the first warehouse and drop off Koshiemon and Daisuke.
* Koshiemon breaks the warehouse
* Daisuke carries out all Senryobako
* While holding the Senryobako, head to the next warehouse decided by Lupine
Repeat this and carry out the Senryobako to the last warehouse. Meanwhile, Lupine prepares a helicopter and carries a thousand boxes with them in the last warehouse and escapes. Daisuke can carry anything heavy, but the speed of movement slows down depending on the weight of the luggage. Lupine must take this into consideration when deciding the order in which to break the warehouse.
Instead of Lupine, create a program that outputs the order of breaking the warehouse so that the travel time from breaking the first warehouse to reaching the last warehouse is minimized. However,
* All the warehouses face the street that runs straight north from Tsuruga Castle. The number of warehouses is at most 15, and the distance from the castle is at most 10,000 meters or less.
* Each Senryobako weighs 20 kilograms. The number of Senryobako in each warehouse is less than 10,000.
* To move from warehouse to warehouse, use the underground passage that is installed underground along the street.
* Daisuke travels at 2,000 / (70 + w) meters per minute to carry w kilograms of luggage.
The input data is given the number of the warehouse (integer of 100 or less), the distance from the castle (meters), and the number of Senryobako stored in the warehouse for each warehouse.
Input
The input is given in the following format:
n
s1 d1 v1
s2 d2 v2
::
sn dn vn
The number of warehouses n (n ≤ 15) is given in the first line, and the information of the i-th warehouse is given in the following n lines. As information on the warehouse, the number si (1 ≤ si ≤ 100), the distance from the castle di (1 ≤ di ≤ 10000), and the number of Senryobako vi (1 ≤ vi ≤ 10000) are given in one line.
Output
Please output the order of breaking the warehouse on one line. Please separate the warehouse numbers with a blank.
Examples
Input
2
1 100 1
2 200 2
Output
1 2
Input
3
11 100 1
13 200 20
12 300 3
Output
11 12 13
Input
5
13 199 1
51 1000 1
37 350 10
27 300 2
99 200 1000
Output
51 37 27 13 99
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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5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n...//\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n*..\\n.**\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n..*.\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*/*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n-*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n*...\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n-*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n3 4\\n*.**\\n....\\n*.+*\\n***.\\n\", \"9\\n5 5\\n..*..\\n.-*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n*...\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n-*.\\n*..\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n3 4\\n*.**\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..)**\\n1 4\\n****\\n5 5\\n./...\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n./*..\\n3 4\\n****\\n..*.\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n**.*\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n*...\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*-*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n-*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n3 4\\n*.**\\n....\\n*.+*\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*+***\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n**.*\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n.**.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*./\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n..*\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n*.**\\n*.*)\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n..*\\n*..\\n*..\\n5 5\\n*****\\n*/*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n**.*\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n*...\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n3 4\\n*.**\\n....\\n*.**\\n***-\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*./\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n**+.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*-.\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*/*.*\\n*****\\n..**.\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n*.**.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n..*\\n*.*\\n.*.\\n4 4\\n**.*\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n....-\\n..*..\\n.***.\\n..*..\\n...//\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n*..\\n.**\\n.*.\\n4 4\\n*.**\\n....\\n*.**\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*/.\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n**.*\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*./\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*/*.*\\n*****\\n..**.\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n*.**.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n..*\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n**.*\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*./\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*+***\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n**.*\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*./\\n*..\\n5 5\\n***+*\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 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3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n*.*+\\n*.**\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*/*.*\\n*****\\n..**.\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n*.**.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*-\\n3 3\\n..*\\n*.*\\n.*.\\n4 4\\n**.*\\n....\\n*.**\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n..*\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*/*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n4 4\\n*.**\\n....\\n*.)*\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n*...\\n.*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n.-*.*\\n..***\\n1 4\\n****\\n5 5\\n...-.\\n..*..\\n.***.\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n.*.\\n3 4\\n*.**\\n....\\n*.**\\n***-\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*-.\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n*.*+\\n*.*+\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*..\\n..*..\\n3 4\\n****\\n.*..\\n.*..\\n4 3\\n***\\n*..\\n..*\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*/*\\n..***\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n..***\\n..*..\\n.....\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n-*.\\n4 4\\n*.**\\n....\\n*.)*\\n***.\\n\", \"9\\n5 5\\n..*..\\n..*..\\n*****\\n..*-.\\n..*..\\n3 4\\n****\\n.*..\\n-*..\\n4 3\\n***\\n*..\\n*..\\n*..\\n5 5\\n*****\\n*.*.*\\n*****\\n..*.*\\n..*)*\\n1 4\\n****\\n5 5\\n.....\\n..*..\\n.***.\\n..*..\\n.../.\\n5 3\\n...\\n.*.\\n.*.\\n***\\n.*.\\n3 3\\n.*.\\n*.*\\n*..\\n4 4\\n*.**\\n....\\n*.*+\\n*.*+\\n\", \"9\\n5 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\"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n1\\n2\\n\", \"0\\n1\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n1\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n1\\n1\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n0\\n1\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n2\\n2\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n2\\n2\\n\", \"0\\n1\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\", \"0\\n0\\n0\\n0\\n0\\n4\\n1\\n1\\n2\\n\"]}", "source": "taco"}
|
You are given a picture consisting of $n$ rows and $m$ columns. Rows are numbered from $1$ to $n$ from the top to the bottom, columns are numbered from $1$ to $m$ from the left to the right. Each cell is painted either black or white.
You think that this picture is not interesting enough. You consider a picture to be interesting if there is at least one cross in it. A cross is represented by a pair of numbers $x$ and $y$, where $1 \le x \le n$ and $1 \le y \le m$, such that all cells in row $x$ and all cells in column $y$ are painted black.
For examples, each of these pictures contain crosses:
[Image]
The fourth picture contains 4 crosses: at $(1, 3)$, $(1, 5)$, $(3, 3)$ and $(3, 5)$.
Following images don't contain crosses:
[Image]
You have a brush and a can of black paint, so you can make this picture interesting. Each minute you may choose a white cell and paint it black.
What is the minimum number of minutes you have to spend so the resulting picture contains at least one cross?
You are also asked to answer multiple independent queries.
-----Input-----
The first line contains an integer $q$ ($1 \le q \le 5 \cdot 10^4$) — the number of queries.
The first line of each query contains two integers $n$ and $m$ ($1 \le n, m \le 5 \cdot 10^4$, $n \cdot m \le 4 \cdot 10^5$) — the number of rows and the number of columns in the picture.
Each of the next $n$ lines contains $m$ characters — '.' if the cell is painted white and '*' if the cell is painted black.
It is guaranteed that $\sum n \le 5 \cdot 10^4$ and $\sum n \cdot m \le 4 \cdot 10^5$.
-----Output-----
Print $q$ lines, the $i$-th line should contain a single integer — the answer to the $i$-th query, which is the minimum number of minutes you have to spend so the resulting picture contains at least one cross.
-----Example-----
Input
9
5 5
..*..
..*..
*****
..*..
..*..
3 4
****
.*..
.*..
4 3
***
*..
*..
*..
5 5
*****
*.*.*
*****
..*.*
..***
1 4
****
5 5
.....
..*..
.***.
..*..
.....
5 3
...
.*.
.*.
***
.*.
3 3
.*.
*.*
.*.
4 4
*.**
....
*.**
*.**
Output
0
0
0
0
0
4
1
1
2
-----Note-----
The example contains all the pictures from above in the same order.
The first 5 pictures already contain a cross, thus you don't have to paint anything.
You can paint $(1, 3)$, $(3, 1)$, $(5, 3)$ and $(3, 5)$ on the $6$-th picture to get a cross in $(3, 3)$. That'll take you $4$ minutes.
You can paint $(1, 2)$ on the $7$-th picture to get a cross in $(4, 2)$.
You can paint $(2, 2)$ on the $8$-th picture to get a cross in $(2, 2)$. You can, for example, paint $(1, 3)$, $(3, 1)$ and $(3, 3)$ to get a cross in $(3, 3)$ but that will take you $3$ minutes instead of $1$.
There are 9 possible crosses you can get in minimum time on the $9$-th picture. One of them is in $(1, 1)$: paint $(1, 2)$ and $(2, 1)$.
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.
| 0.25
|
{"tests": "{\"inputs\": [\"5 4\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 1\\n1 2 3\\n3 2 1\", \"5 8\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 11\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 2\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 6\\n1 2 3\\n3 2 1\", \"5 20\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 14\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 17\\n2 1 3\\n3 2 1\", \"3 10\\n2 1 3\\n3 2 1\", \"10 1000001000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"3 9\\n2 1 3\\n3 2 1\", \"10 1001000001\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"10 1000000001\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"10 1010001000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 6\\n4 5 1 2 3\\n2 3 1 5 4\", \"10 0010000000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 12\\n4 5 1 2 3\\n2 3 1 5 4\", \"5 15\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 1\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 7\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 10\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 11\\n1 2 3\\n3 2 1\", \"3 12\\n1 2 3\\n3 2 1\", \"3 13\\n1 2 3\\n3 2 1\", \"5 13\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 17\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 30\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 4\\n1 2 3\\n3 2 1\", \"3 2\\n1 2 3\\n3 2 1\", \"3 17\\n1 2 3\\n3 2 1\", \"3 9\\n1 2 3\\n3 2 1\", \"5 56\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 21\\n1 2 3\\n3 2 1\", \"5 3\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 20\\n1 2 3\\n3 2 1\", \"3 34\\n1 2 3\\n3 2 1\", \"3 62\\n1 2 3\\n3 2 1\", \"3 19\\n1 2 3\\n3 2 1\", \"3 8\\n1 2 3\\n3 2 1\", \"3 29\\n1 2 3\\n3 2 1\", \"3 23\\n1 2 3\\n3 2 1\", \"3 22\\n1 2 3\\n3 2 1\", \"3 53\\n1 2 3\\n3 2 1\", \"5 23\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 7\\n1 2 3\\n3 2 1\", \"5 26\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 6\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 18\\n1 2 3\\n3 2 1\", \"3 33\\n1 2 3\\n3 2 1\", \"3 59\\n1 2 3\\n3 2 1\", \"5 22\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 54\\n1 2 3\\n3 2 1\", \"3 27\\n1 2 3\\n3 2 1\", \"3 20\\n2 1 3\\n3 2 1\", \"3 60\\n1 2 3\\n3 2 1\", \"3 96\\n1 2 3\\n3 2 1\", \"5 33\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 51\\n1 2 3\\n3 2 1\", \"3 14\\n2 1 3\\n3 2 1\", \"3 58\\n1 2 3\\n3 2 1\", \"3 107\\n1 2 3\\n3 2 1\", \"3 8\\n2 1 3\\n3 2 1\", \"3 52\\n1 2 3\\n3 2 1\", \"3 40\\n1 2 3\\n3 2 1\", \"3 32\\n2 1 3\\n3 2 1\", \"3 15\\n2 1 3\\n3 2 1\", \"3 30\\n2 1 3\\n3 2 1\", \"5 9\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 18\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 22\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 6\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 27\\n4 5 1 2 3\\n3 2 1 5 4\", \"10 1001000000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 24\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 29\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 3\\n4 5 1 2 3\\n3 2 1 5 4\", \"10 1010000000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 45\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 2\\n4 5 1 2 3\\n3 2 1 5 4\", \"10 1000001000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 32\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 43\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 7\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 5\\n1 2 3\\n3 2 1\", \"5 12\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 8\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 11\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 14\\n4 5 1 2 3\\n3 2 1 5 4\", \"10 1001010000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"10 0010010000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"5 10\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 4\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 51\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 15\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 63\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 20\\n4 5 1 2 3\\n3 2 1 5 4\", \"3 8\\n1 2 3\\n3 2 1\", \"5 40\\n4 5 1 2 3\\n3 2 1 5 4\", \"5 2\\n4 5 2 1 3\\n3 2 1 5 4\", \"5 5\\n4 5 1 2 3\\n3 2 1 5 4\", \"10 1000000000\\n7 10 6 5 4 2 9 1 3 8\\n4 1 9 2 3 7 8 10 6 5\", \"3 3\\n1 2 3\\n3 2 1\"], \"outputs\": [\"4 5 1 2 3\", \"1 2 3\", \"5 4 3 2 1\", \"1 5 4 3 2\", \"3 2 1 5 4\", \"3 2 1\", \"4 3 2 1 5\", \"2 1 5 4 3\", \"1 3 2\", \"2 1 3\", \"8 4 6 5 2 7 9 10 1 3\", \"2 3 1\", \"4 8 10 6 9 2 1 3 5 7\", \"10 3 7 6 4 8 2 1 5 9\", \"7 6 5 2 4 9 3 10 1 8\", \"3 1 5 4 2\", \"7 9 4 8 2 5 1 6 10 3\", \"1 3 4 5 2\", \"5 4 3 2 1\", \"4 5 1 2 3\", \"4 5 1 2 3\", \"4 5 1 2 3\", \"3 2 1\", \"3 2 1\", \"1 2 3\", \"4 5 1 2 3\", \"3 2 1 5 4\", \"5 4 3 2 1\", \"1 2 3\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"1 5 4 3 2\", \"3 2 1\", \"1 5 4 3 2\", \"3 2 1\", \"1 2 3\", \"3 2 1\", \"1 2 3\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"1 2 3\", \"3 2 1\", \"5 4 3 2 1\", \"1 2 3\", \"1 5 4 3 2\", \"2 1 5 4 3\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"4 5 1 2 3\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"3 2 1\", \"1 5 4 3 2\", \"3 2 1\", \"2 1 3\", \"1 2 3\", \"3 2 1\", \"1 3 2\", \"1 2 3\", \"1 2 3\", \"2 1 3\", \"2 3 1\", \"2 3 1\", \"3 2 1 5 4\", \"1 5 4 3 2\", \"4 5 1 2 3\", \"2 1 5 4 3\", \"4 3 2 1 5\", \"8 4 6 5 2 7 9 10 1 3\", \"3 2 1 5 4\", \"2 1 5 4 3\", \"1 5 4 3 2\", \"8 4 6 5 2 7 9 10 1 3\", \"5 4 3 2 1\", \"3 2 1 5 4\", \"8 4 6 5 2 7 9 10 1 3\", \"3 2 1 5 4\", \"4 5 1 2 3\", \"4 5 1 2 3\", \"3 2 1\", \"4 3 2 1 5\", \"5 4 3 2 1\", \"1 5 4 3 2\", \"2 1 5 4 3\", \"7 6 5 2 4 9 3 10 1 8\", \"8 4 6 5 2 7 9 10 1 3\", \"4 5 1 2 3\", \"4 5 1 2 3\", \"2 1 5 4 3\", \"5 4 3 2 1\", \"1 5 4 3 2\", \"4 3 2 1 5\", \"3 2 1\", \"4 5 1 2 3\", \"3 2 1 5 4\", \"4 3 2 1 5\", \"7 9 4 8 2 5 1 6 10 3\", \"3 2 1\"]}", "source": "taco"}
|
For two permutations p and q of the integers from 1 through N, let f(p,q) be the permutation that satisfies the following:
* The p_i-th element (1 \leq i \leq N) in f(p,q) is q_i. Here, p_i and q_i respectively denote the i-th element in p and q.
You are given two permutations p and q of the integers from 1 through N. We will now define a sequence {a_n} of permutations of the integers from 1 through N, as follows:
* a_1=p, a_2=q
* a_{n+2}=f(a_n,a_{n+1}) ( n \geq 1 )
Given a positive integer K, find a_K.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq 10^9
* p and q are permutations of the integers from 1 through N.
Input
Input is given from Standard Input in the following format:
N K
p_1 ... p_N
q_1 ... q_N
Output
Print N integers, with spaces in between. The i-th integer (1 \leq i \leq N) should be the i-th element in a_K.
Examples
Input
3 3
1 2 3
3 2 1
Output
3 2 1
Input
5 5
4 5 1 2 3
3 2 1 5 4
Output
4 3 2 1 5
Input
10 1000000000
7 10 6 5 4 2 9 1 3 8
4 1 9 2 3 7 8 10 6 5
Output
7 9 4 8 2 5 1 6 10 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\": [[5, 1], [8, 3], [75, 34], [82, 49], [73, 38], [86, 71], [61, 17], [42, 38], [29, 5], [64, 49], [61, 20], [88, 52]], \"outputs\": [[[5, 24]], [[7, 51]], [[35, 4238]], [[48, 5091]], [[61, 3996]], [[10, 6275]], [[26, 3000]], [[12, 1578]], [[28, 740]], [[43, 3327]], [[32, 2922]], [[59, 5856]]]}", "source": "taco"}
|
# Task
The game starts with `n` people standing in a circle. The presenter counts `m` people starting with the first one, and gives `1` coin to each of them. The rest of the players receive `2` coins each. After that, the last person who received `1` coin leaves the circle, giving everything he had to the next participant (who will also be considered "the first in the circle" in the next round). This process continues until only 1 person remains.
Determine the `number` of this person and how many `coins` he has at the end of the game.
The result should be a pair of values in the format: `[person, coins]`.
## Example:
```
n = 8, m = 3
People
1 2 3 1 2 ∙ 1 2 ∙ ∙ 2 ∙ ∙ 2 ∙ ∙ ∙ ∙ ∙ ∙ ∙
8 4 => 8 4 => 8 4 => 8 4 => 8 4 => 8 4 => ∙ 4 => 7
7 6 5 7 6 5 7 ∙ 5 7 ∙ 5 7 ∙ ∙ 7 ∙ ∙ 7 ∙ ∙
Coins
0 0 0 1 1 ∙ 3 3 ∙ ∙ 9 ∙ ∙ 10 ∙ ∙ ∙ ∙ ∙ ∙ ∙
0 0 => 2 3 => 4 4 => 5 6 => 7 7 => 8 20 => ∙ 30 => 51
0 0 0 2 2 2 7 ∙ 3 8 ∙ 5 16 ∙ ∙ 17 ∙ ∙ 18 ∙ ∙
```
## Notes:
* The presenter can do several full circles during one counting.
* In this case, the same person will receive `1` coin multiple times, i.e. no matter how many people are left in the circle, at least `m` coins will always be distributed among the participants during the round.
* If a person had already received `1` coin (possibly multiple times), he won't receive any additional `2` coins **at once(!)** during that round.
* People are counted starting with `1`.
* `m` can be **bigger** than `n` at start
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\": [\"6\\n10\\n10\\n10\\n01\\n10\\n10\\n\", \"4\\n01\\n01\\n10\\n10\\n\", \"1\\n10\\n\", \"2\\n01\\n10\\n\", \"2\\n10\\n10\\n\", \"3\\n10\\n01\\n10\\n\", \"1\\n01\\n\", \"2\\n01\\n01\\n\", \"2\\n10\\n01\\n\", \"3\\n01\\n01\\n01\\n\", \"3\\n10\\n10\\n01\\n\", \"3\\n01\\n10\\n10\\n\", \"115\\n10\\n10\\n10\\n10\\n01\\n01\\n10\\n10\\n10\\n01\\n01\\n10\\n01\\n01\\n10\\n10\\n10\\n01\\n10\\n01\\n10\\n10\\n01\\n01\\n10\\n10\\n10\\n10\\n01\\n10\\n01\\n01\\n10\\n10\\n10\\n10\\n01\\n10\\n10\\n10\\n01\\n10\\n01\\n10\\n10\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n01\\n10\\n01\\n01\\n01\\n01\\n10\\n10\\n01\\n10\\n01\\n01\\n01\\n01\\n01\\n10\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n01\\n01\\n10\\n10\\n01\\n01\\n01\\n01\\n01\\n10\\n01\\n10\\n01\\n10\\n01\\n01\\n01\\n10\\n01\\n10\\n10\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n\", \"1\\n10\\n\", \"3\\n10\\n01\\n10\\n\", \"3\\n10\\n10\\n01\\n\", \"115\\n10\\n10\\n10\\n10\\n01\\n01\\n10\\n10\\n10\\n01\\n01\\n10\\n01\\n01\\n10\\n10\\n10\\n01\\n10\\n01\\n10\\n10\\n01\\n01\\n10\\n10\\n10\\n10\\n01\\n10\\n01\\n01\\n10\\n10\\n10\\n10\\n01\\n10\\n10\\n10\\n01\\n10\\n01\\n10\\n10\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n01\\n10\\n01\\n01\\n01\\n01\\n10\\n10\\n01\\n10\\n01\\n01\\n01\\n01\\n01\\n10\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n01\\n01\\n10\\n10\\n01\\n01\\n01\\n01\\n01\\n10\\n01\\n10\\n01\\n10\\n01\\n01\\n01\\n10\\n01\\n10\\n10\\n01\\n10\\n10\\n01\\n01\\n01\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n\", \"3\\n01\\n10\\n10\\n\", \"2\\n01\\n10\\n\", \"2\\n10\\n10\\n\", \"1\\n01\\n\", \"2\\n10\\n01\\n\", \"2\\n01\\n01\\n\", \"3\\n01\\n01\\n01\\n\", \"1\\n14\\n\", \"1\\n15\\n\", \"1\\n13\\n\", \"1\\n19\\n\", \"1\\n38\\n\", \"1\\n32\\n\", \"1\\n17\\n\", \"1\\n62\\n\", \"1\\n12\\n\", \"1\\n16\\n\", \"1\\n40\\n\", \"1\\n52\\n\", \"1\\n30\\n\", \"1\\n42\\n\", \"1\\n58\\n\", \"1\\n46\\n\", \"1\\n68\\n\", \"1\\n92\\n\", \"1\\n130\\n\", \"1\\n41\\n\", \"1\\n18\\n\", \"1\\n35\\n\", \"1\\n45\\n\", \"1\\n57\\n\", \"1\\n104\\n\", \"1\\n31\\n\", \"1\\n39\\n\", \"1\\n43\\n\", \"1\\n53\\n\", \"1\\n79\\n\", \"1\\n87\\n\", \"1\\n106\\n\", \"1\\n47\\n\", \"1\\n34\\n\", \"1\\n36\\n\", \"1\\n51\\n\", \"1\\n71\\n\", \"1\\n82\\n\", \"1\\n69\\n\", \"1\\n56\\n\", \"1\\n86\\n\", \"1\\n37\\n\", \"1\\n59\\n\", \"1\\n60\\n\", \"1\\n101\\n\", \"1\\n67\\n\", \"1\\n127\\n\", \"1\\n98\\n\", \"1\\n107\\n\", \"1\\n93\\n\", \"1\\n123\\n\", \"1\\n174\\n\", \"1\\n105\\n\", \"1\\n70\\n\", \"1\\n124\\n\", \"1\\n49\\n\", \"1\\n95\\n\", \"1\\n64\\n\", \"1\\n61\\n\", \"1\\n196\\n\", \"4\\n01\\n01\\n10\\n10\\n\", \"6\\n10\\n10\\n10\\n01\\n10\\n10\\n\"], \"outputs\": [\"3\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"55\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"55\\n\", \"2\\n\", \"2\\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\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"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\", \"3\\n\"]}", "source": "taco"}
|
Mad scientist Mike entertains himself by arranging rows of dominoes. He doesn't need dominoes, though: he uses rectangular magnets instead. Each magnet has two poles, positive (a "plus") and negative (a "minus"). If two magnets are put together at a close distance, then the like poles will repel each other and the opposite poles will attract each other.
Mike starts by laying one magnet horizontally on the table. During each following step Mike adds one more magnet horizontally to the right end of the row. Depending on how Mike puts the magnet on the table, it is either attracted to the previous one (forming a group of multiple magnets linked together) or repelled by it (then Mike lays this magnet at some distance to the right from the previous one). We assume that a sole magnet not linked to others forms a group of its own. [Image]
Mike arranged multiple magnets in a row. Determine the number of groups that the magnets formed.
-----Input-----
The first line of the input contains an integer n (1 ≤ n ≤ 100000) — the number of magnets. Then n lines follow. The i-th line (1 ≤ i ≤ n) contains either characters "01", if Mike put the i-th magnet in the "plus-minus" position, or characters "10", if Mike put the magnet in the "minus-plus" position.
-----Output-----
On the single line of the output print the number of groups of magnets.
-----Examples-----
Input
6
10
10
10
01
10
10
Output
3
Input
4
01
01
10
10
Output
2
-----Note-----
The first testcase corresponds to the figure. The testcase has three groups consisting of three, one and two magnets.
The second testcase has two groups, each consisting of two magnets.
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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|
Alice has just learned addition. However, she hasn't learned the concept of "carrying" fully — instead of carrying to the next column, she carries to the column two columns to the left.
For example, the regular way to evaluate the sum $2039 + 2976$ would be as shown:
However, Alice evaluates it as shown:
In particular, this is what she does:
add $9$ and $6$ to make $15$, and carry the $1$ to the column two columns to the left, i. e. to the column "$0$ $9$";
add $3$ and $7$ to make $10$ and carry the $1$ to the column two columns to the left, i. e. to the column "$2$ $2$";
add $1$, $0$, and $9$ to make $10$ and carry the $1$ to the column two columns to the left, i. e. to the column above the plus sign;
add $1$, $2$ and $2$ to make $5$;
add $1$ to make $1$.
Thus, she ends up with the incorrect result of $15005$.
Alice comes up to Bob and says that she has added two numbers to get a result of $n$. However, Bob knows that Alice adds in her own way. Help Bob find the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of $n$. Note that pairs $(a, b)$ and $(b, a)$ are considered different if $a \ne b$.
-----Input-----
The input consists of multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The description of the test cases follows.
The only line of each test case contains an integer $n$ ($2 \leq n \leq 10^9$) — the number Alice shows Bob.
-----Output-----
For each test case, output one integer — the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of $n$.
-----Examples-----
Input
5
100
12
8
2021
10000
Output
9
4
7
44
99
-----Note-----
In the first test case, when Alice evaluates any of the sums $1 + 9$, $2 + 8$, $3 + 7$, $4 + 6$, $5 + 5$, $6 + 4$, $7 + 3$, $8 + 2$, or $9 + 1$, she will get a result of $100$. The picture below shows how Alice evaluates $6 + 4$:
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\": [\"8587340257\\n\", \"9\\n\", \"81\\n\", \"27\\n\", \"1408514752349\\n\", \"25\\n\", \"49380563\\n\", \"266418\\n\", \"319757451841\\n\", \"6599669076000\\n\", \"8\\n\", \"1000000000000\\n\", \"30971726\\n\", \"274875809788\\n\", \"64\\n\", \"34280152201\\n\", \"236\\n\", \"472670214391\\n\", \"7938986881993\\n\", \"44\\n\", \"4\\n\", \"388\\n\", \"2\\n\", \"802241960524\\n\", \"3047527844089\\n\", \"5\\n\", \"12\\n\", \"614125\\n\", \"1716443237161\\n\", \"48855707\\n\", \"99\\n\", \"9999925100701\\n\", \"5839252225\\n\", \"3\\n\", \"50\\n\", \"1307514188557\\n\", \"9999926826034\\n\", \"1468526771489\\n\", \"2975\\n\", \"8110708459517\\n\", \"401120980262\\n\", \"5138168457911\\n\", \"1245373417369\\n\", \"128\\n\", \"16\\n\", \"2000000014\\n\", \"445538663413\\n\", \"57461344602\\n\", \"324\\n\", \"7420738134810\\n\", \"10803140200\\n\", \"14\\n\", \"11\\n\", \"174813966899\\n\", \"13753962\\n\", \"601828654335\\n\", \"11414141397807\\n\", \"10302705885747\\n\", \"1902165873922\\n\", \"144993\\n\", \"365292057641\\n\", \"1477562914357\\n\", \"1120127104869\\n\", \"4629281874338\\n\", \"3964991841\\n\", \"749785679266\\n\", \"575\\n\", \"12790022157571\\n\", \"322715\\n\", \"18446666\\n\", \"16843519638070\\n\", \"112\\n\", \"22\\n\", \"299384\\n\", \"7\\n\", \"1000001000000\\n\", \"10311174\\n\", \"346774033500\\n\", \"10\\n\", \"56787561660\\n\", \"375\\n\", \"61\\n\", \"458\\n\", \"1312973278146\\n\", \"20\\n\", \"13\\n\", \"1666448460762\\n\", \"92910644\\n\", \"18\\n\", \"10227774774808\\n\", \"51907547\\n\", \"40\\n\", \"12267984483444\\n\", \"1707\\n\", \"501925883142\\n\", \"12940951530\\n\", \"256\\n\", \"23\\n\", \"945192754\\n\", \"19\\n\", \"15\\n\", \"18686466796\\n\", \"26\\n\", \"36\\n\", \"33\\n\", \"64735700961\\n\", \"34\\n\", \"27035843\\n\", \"222097394644\\n\", \"20761030042485\\n\", \"1000001000010\\n\", \"431245125282\\n\", \"105380065192\\n\", \"17\\n\", \"56\\n\", \"2403828391173\\n\", \"1\\n\", \"6\\n\", \"30\\n\"], \"outputs\": [\"1\\n9409\", \"2\", \"1\\n9\", \"1\\n9\", \"1\\n72361\", \"2\", \"1\\n289\", \"1\\n6\", \"1\\n289\", \"1\\n4\", \"1\\n4\", \"1\\n4\", \"2\", \"1\\n4\", \"1\\n4\", \"2\", \"1\\n4\", \"1\\n23020027\", \"1\\n378028993\", \"1\\n4\", \"2\", \"1\\n4\", \"1\\n0\", \"1\\n4\", \"2\", \"1\\n0\", \"1\\n4\", \"1\\n25\", \"1\\n5329\", \"1\\n2603\", \"1\\n9\", \"1\\n0\", \"1\\n25\", \"1\\n0\", \"1\\n10\", \"1\\n39283\", \"2\", \"1\\n613783\", \"1\\n25\", \"2\", \"2\", \"2\", \"1\\n908209\", \"1\\n4\", \"1\\n4\", \"2\", \"1\\n0\", \"1\\n6\", \"1\\n4\", \"1\\n6\", \"1\\n4\\n\", \"2\\n\", \"1\\n0\\n\", \"1\\n143\\n\", \"1\\n6\\n\", \"1\\n15\\n\", \"1\\n87\\n\", \"1\\n33\\n\", \"1\\n118\\n\", \"1\\n51\\n\", \"1\\n126091\\n\", \"1\\n41161181\\n\", \"1\\n57\\n\", \"1\\n22\\n\", \"1\\n9\\n\", \"1\\n26\\n\", \"1\\n25\\n\", \"1\\n1003\\n\", \"1\\n95\\n\", \"1\\n14\\n\", \"1\\n10\\n\", \"1\\n4\\n\", \"2\\n\", \"1\\n4\\n\", \"1\\n0\\n\", \"1\\n4\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"2\\n\", \"1\\n4\\n\", \"1\\n15\\n\", \"1\\n0\\n\", \"2\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"1\\n0\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"2\\n\", \"1\\n4\\n\", \"1\\n4\\n\", \"2\\n\", \"1\\n6\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"1\\n0\\n\", \"1\\n22\\n\", \"1\\n0\\n\", \"2\\n\", \"1\\n4\\n\", \"2\\n\", \"1\\n4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n0\\n\", \"1\\n4\\n\", \"1\\n15\\n\", \"1\\n6\\n\", \"1\\n6\\n\", \"1\\n4\\n\", \"1\\n0\\n\", \"1\\n4\\n\", \"1\\n33\\n\", \"1\\n0\", \"2\", \"1\\n6\"]}", "source": "taco"}
|
You can't possibly imagine how cold our friends are this winter in Nvodsk! Two of them play the following game to warm up: initially a piece of paper has an integer q. During a move a player should write any integer number that is a non-trivial divisor of the last written number. Then he should run this number of circles around the hotel. Let us remind you that a number's divisor is called non-trivial if it is different from one and from the divided number itself.
The first person who can't make a move wins as he continues to lie in his warm bed under three blankets while the other one keeps running. Determine which player wins considering that both players play optimally. If the first player wins, print any winning first move.
Input
The first line contains the only integer q (1 ≤ q ≤ 1013).
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.
Output
In the first line print the number of the winning player (1 or 2). If the first player wins then the second line should contain another integer — his first move (if the first player can't even make the first move, print 0). If there are multiple solutions, print any of them.
Examples
Input
6
Output
2
Input
30
Output
1
6
Input
1
Output
1
0
Note
Number 6 has only two non-trivial divisors: 2 and 3. It is impossible to make a move after the numbers 2 and 3 are written, so both of them are winning, thus, number 6 is the losing number. A player can make a move and write number 6 after number 30; 6, as we know, is a losing number. Thus, this move will bring us the victory.
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\": [[\"13:00\"], [\"13:09\"], [\"13:15\"], [\"13:29\"], [\"13:30\"], [\"13:31\"], [\"13:45\"], [\"13:59\"], [\"00:48\"], [\"00:08\"], [\"12:00\"], [\"00:00\"], [\"19:01\"], [\"07:01\"], [\"01:59\"], [\"12:01\"], [\"00:01\"], [\"11:31\"], [\"23:31\"], [\"11:45\"], [\"11:59\"], [\"23:45\"], [\"23:59\"], [\"01:45\"]], \"outputs\": [[\"one o'clock\"], [\"nine minutes past one\"], [\"quarter past one\"], [\"twenty nine minutes past one\"], [\"half past one\"], [\"twenty nine minutes to two\"], [\"quarter to two\"], [\"one minute to two\"], [\"twelve minutes to one\"], [\"eight minutes past midnight\"], [\"twelve o'clock\"], [\"midnight\"], [\"one minute past seven\"], [\"one minute past seven\"], [\"one minute to two\"], [\"one minute past twelve\"], [\"one minute past midnight\"], [\"twenty nine minutes to twelve\"], [\"twenty nine minutes to midnight\"], [\"quarter to twelve\"], [\"one minute to twelve\"], [\"quarter to midnight\"], [\"one minute to midnight\"], [\"quarter to two\"]]}", "source": "taco"}
|
Given time in 24-hour format, convert it to words.
```
For example:
13:00 = one o'clock
13:09 = nine minutes past one
13:15 = quarter past one
13:29 = twenty nine minutes past one
13:30 = half past one
13:31 = twenty nine minutes to two
13:45 = quarter to two
00:48 = twelve minutes to one
00:08 = eight minutes past midnight
12:00 = twelve o'clock
00:00 = midnight
Note: If minutes == 0, use 'o'clock'. If minutes <= 30, use 'past', and for minutes > 30, use 'to'.
```
More examples in 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
|
{"tests": "{\"inputs\": [[\"ArNran u rstm5twob e ePb\"], [\"ArNran u rstm8twob e ePc\"], [\"92287a76 585a2y0\"], [\" a29068686a275y5\"], [\"8a 55y0y0y5a7 78\"], [\"9y98a877a95976a758726a89a5659957ya y\"], [\"aa297625 88a02670997 86ya880 00a9067\"], [\"826a976a508a9a 687600a2800 895055y a\"], [\" a702a067629y022ay865y9yy92a60226 9869y0 y88y077\"], [\"y0y 62 27059y ya6568588a956aa0 960969a52 5 2680\"], [\"662 y768867 9 765y9696a5980 5 7228562965597766y29\"], [\"2y0y7250 69222a98780 0 2769a0y5 8y9a5y0796 6259 y\"], [\"86a6yy776a87y 027 a5229 9678 60695656aa82550687y\"], [\"aa68y6 5 y9595a 9y6272727y7yaa6a7y9a06 7529y9 a 5\"], [\"y2y59087y9a627yy7995a668890 8y990a6027006668y a2\"], [\"796820 2 \"], [\"7a05y8 52\"], [\"a 57529a9\"], [\"aya960700\"], [\"y0 60 2685822260yaa98 500 yy67082 6628y2y9y567095ay859y5 8y999297 y0229 60a 95y80\"], [\"6y 70a5y6y5 a 7820y8ay58y852y055y6207ay6028958508y 9a 5 a a026626787 805a50 y0 9a\"], [\"a8y7067y7yyya 982672a006850 86yy 7988 y8a90 66y6y82a9 a6692y5670a552765 2a 5 78\"], [\"5 20a0 076705 5yy756 a88y26a6262a05059 a y09 829y885a6yy568877966565 yy6962y0055\"], [\"09y286 90 y y68y055908 068 500ay27 89522a 6a 529yy295a5y6628y96\"], [\"92752y9555 982887y6yy70 8292 0y9767 925y8a785929a69y25y5yy0a0a7\"], [\" 7569520897207a0y056yy79a88 5880886 8 a7592a5 595 9 270795a29 9\"], [\"5aa 0y06 86 y725 ay5768269 0 2808a277 0ay2628592077y62y627y92a98\"], [\"57067 y27 a8y7 8022059 0565yy2y9aaya6626y0 6227a6 880y72762y9\"], [\"\"], [\"8 d9dx0962x8067d x 760x272690 d852757d59 d552820d52dx767d 0dxxxd995x0676x59d6x7760x0d7 02dd7558770x2d0760x85d8x709d0x590\"], [\"5 9xx2788d0x207 9x85 008xx5 852056985508662x8 75 x92d0 8088585d882d 52967 d 292987d97695x59d52x505 5678082x98552625888 \"]], \"outputs\": [[\"Answer to Number 5 Part b\"], [\"Answer to Number 8 Part c\"], [\"97 a2a52278y8650\"], [\" 087a66528ay9625\"], [\"8507ayy 0575ya8\"], [\"9777a5y762579aa66y897a5aa5589 89899y\"], [\"a209a0a5278a2 6 899878007806 66a9y07\"], [\"8696002aa00565 0 5a06a8y98829 7a785a\"], [\" 005a9y 62y688a72906876ay29y02yy2y02989607ay62 7\"], [\"y2y8a6 07a8095y06a a 55995269656262y860 8 5a9 0\"], [\"6876567686a 272655796 7y9266y 9825y79608526 9 599\"], [\"20a00a y 9 y5606825y2y977 0572868792209y9 52 a96y\"], [\"87 28656602 55aa29660687 0a6y7 96a8yya69877 5752y\"], [\"a5a2aa9a 7a0y6y9266989y7a y56y77a6927y5 57y925\"], [\"y7y6 662yy6806y978y285a9897y969990 025000a87a a62\"], [\"78 92260 \"], [\"75 ay5082\"], [\"a79 5a529\"], [\"a97y60a00\"], [\"y5ay27y96089680570 287y9 a62 0258y 0258yay09 6029y925200 y892y6y 6559988ay6692 0\"], [\"6yy27852ay58ya5 65 a0y0a707ay568 8 0 550ya7ya78y2 0 058y68928 y2829a60960505 65a\"], [\"ay7 86 7 8y28 ya02yya6y66aa7a0y8y65 0 0ya895 696 9222578870ay7 y259 956776086 658\"], [\"565a5 696 76698y6920 2 2y6605a6a9552a 82 y66y058ay8850 yy0088 00y25957y57760 a7y5\"], [\"00y0y29y9 062ay6yy587 y62 5 6228 958a986y009 5y 68055a998 a2256\"], [\"95787y9525y268ay7 697a6y59y2 79028y 8yay2709520980y295a58 952y7\"], [\" 8ya8557790889 957586295626 a a90y585 257y8 292a78a57 00907909\"], [\"5 68y02a8a9a277a6y 267y 5072y90y7 7862y762 52a028809y96520a268\"], [\"5700962y7 25ay770a26a0a26805y 677y5ya 6 79y6 82y 2668y28 y2209\"], [\"\"], [\"88x256960x8 027275x22xd6758dx7dd797272 07d00dd6d0066779x 95dd7056d0x095x6x5009 2xx08xx67d dx5d785268dxd97759x05579d 0d0\"], [\"5x05x 2 958 20688d25 59089 0 9x55x7x87852562x x558299762 55 598d8279 0x8675058x88957d28888562d 9x28d526d8d75x80 0208 609 \"]]}", "source": "taco"}
|
Student A and student B are giving each other test answers during a test.
They don't want to be caught so they are sending each other coded messages.
Student A is sending student B the message: `Answer to Number 5 Part b`.
He starts of with a square grid (in this example the grid = 5x5).
He writes the message down (with spaces):
```
Answe
r to
Numbe
r 5 P
art b
```
He then starts writing the message down one column at a time (from the top to the bottom).
The new message is now: `ArNran u rstm5twob e ePb`
You are the teacher of this class.
Your job is to decipher this message and bust the students.
# Task
Write a function `decipher_message`.
This function will take one parameter (`message`).
This function will return the original message.
*** Note: The length of the string is always going to be a prefect square ***
Hint: You should probably decipher the example message first before you start coding
Have fun !!!
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\\n1 3 2 4\\n3\\n1 2 3\\n5\\n2 1 4 5 3\\n\", \"1\\n8\\n6 2 3 1 8 4 5 7\\n\", \"1\\n8\\n6 2 3 1 8 4 5 7\\n\", \"1\\n8\\n6 0 3 1 8 4 5 7\\n\", \"3\\n4\\n1 3 2 7\\n3\\n1 2 3\\n5\\n2 1 4 5 3\\n\", \"1\\n8\\n5 2 2 1 0 0 2 8\\n\", \"1\\n6\\n6 0 3 1 8 4 5 7\\n\", \"1\\n8\\n6 2 6 1 8 4 5 7\\n\", \"1\\n8\\n6 0 3 1 8 6 5 7\\n\", \"1\\n6\\n6 0 3 1 8 5 5 7\\n\", \"1\\n8\\n6 2 6 1 8 6 5 7\\n\", \"3\\n4\\n1 3 2 7\\n3\\n1 2 3\\n5\\n2 1 4 5 0\\n\", \"1\\n8\\n6 0 3 1 8 6 1 7\\n\", \"1\\n8\\n6 0 3 1 8 7 1 7\\n\", \"1\\n8\\n4 0 3 1 8 7 1 7\\n\", \"1\\n8\\n4 0 3 1 8 6 1 7\\n\", \"1\\n8\\n4 0 3 1 8 6 1 1\\n\", \"1\\n8\\n4 -1 3 1 8 6 1 1\\n\", \"1\\n8\\n4 -1 3 1 8 6 1 2\\n\", \"1\\n8\\n6 2 2 1 8 4 5 7\\n\", \"1\\n8\\n6 2 6 1 8 6 2 7\\n\", \"3\\n4\\n1 3 2 7\\n3\\n1 2 3\\n5\\n3 1 4 5 0\\n\", \"1\\n8\\n4 -1 3 1 8 4 1 2\\n\", \"1\\n8\\n6 2 2 1 8 4 4 7\\n\", \"1\\n8\\n4 -2 3 1 8 4 1 2\\n\", \"1\\n8\\n4 2 2 1 8 4 4 7\\n\", \"1\\n8\\n4 -2 3 1 8 4 1 4\\n\", \"1\\n8\\n6 2 3 1 8 4 3 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|
You are given a permutation $a$ consisting of $n$ numbers $1$, $2$, ..., $n$ (a permutation is an array in which each element from $1$ to $n$ occurs exactly once).
You can perform the following operation: choose some subarray (contiguous subsegment) of $a$ and rearrange the elements in it in any way you want. But this operation cannot be applied to the whole array.
For example, if $a = [2, 1, 4, 5, 3]$ and we want to apply the operation to the subarray $a[2, 4]$ (the subarray containing all elements from the $2$-nd to the $4$-th), then after the operation, the array can become $a = [2, 5, 1, 4, 3]$ or, for example, $a = [2, 1, 5, 4, 3]$.
Your task is to calculate the minimum number of operations described above to sort the permutation $a$ in ascending order.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 2000$) — the number of test cases.
The first line of the test case contains a single integer $n$ ($3 \le n \le 50$) — the number of elements in the permutation.
The second line of the test case contains $n$ distinct integers from $1$ to $n$ — the given permutation $a$.
-----Output-----
For each test case, output a single integer — the minimum number of operations described above to sort the array $a$ in ascending order.
-----Examples-----
Input
3
4
1 3 2 4
3
1 2 3
5
2 1 4 5 3
Output
1
0
2
-----Note-----
In the explanations, $a[i, j]$ defines the subarray of $a$ that starts from the $i$-th element and ends with the $j$-th element.
In the first test case of the example, you can select the subarray $a[2, 3]$ and swap the elements in it.
In the second test case of the example, the permutation is already sorted, so you don't need to apply any operations.
In the third test case of the example, you can select the subarray $a[3, 5]$ and reorder the elements in it so $a$ becomes $[2, 1, 3, 4, 5]$, and then select the subarray $a[1, 2]$ and swap the elements in it, so $a$ becomes $[1, 2, 3, 4, 5]$.
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
|
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\"220427628\\n433108807\\n197742755\\n197742755\\n133361044\\n133361044\\n433108807\\n197742755\\n197742755\\n142216854\\n142216854\\n197742755\\n220427628\\n433108807\\n\", \"4\\n\"]}", "source": "taco"}
|
After a successful field test, Heidi is considering deploying a trap along some Corridor, possibly not the first one. She wants to avoid meeting the Daleks inside the Time Vortex, so for abundance of caution she considers placing the traps only along those Corridors that are not going to be used according to the current Daleks' plan – which is to use a minimum spanning tree of Corridors. Heidi knows that all energy requirements for different Corridors are now different, and that the Daleks have a single unique plan which they are intending to use.
Your task is to calculate the number E_{max}(c), which is defined in the same way as in the easy version – i.e., the largest e ≤ 10^9 such that if we changed the energy of corridor c to e, the Daleks might use it – but now for every corridor that Heidi considers.
Input
The first line: number n of destinations, number m of Time Corridors (2 ≤ n ≤ 10^5, n - 1 ≤ m ≤ 10^6). The next m lines: destinations a, b and energy e (1 ≤ a, b ≤ n, a ≠ b, 0 ≤ e ≤ 10^9).
No pair \\{a, b\} will repeat. The graph is guaranteed to be connected. All energy requirements e are distinct.
Output
Output m-(n-1) lines, each containing one integer: E_{max}(c_i) for the i-th Corridor c_i from the input that is not part of the current Daleks' plan (minimum spanning tree).
Example
Input
3 3
1 2 8
2 3 3
3 1 4
Output
4
Note
If m = n-1, then you need not output anything.
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 world!\", \"hello\"], [\"hello world!\", \"HELLO\"], [\"nowai\", \"nowaisir\"], [\"\", \"\"], [\"abc\", \"\"], [\"\", \"abc\"]], \"outputs\": [[true], [false], [false], [true], [true], [false]]}", "source": "taco"}
|
Challenge:
Given two null-terminated strings in the arguments "string" and "prefix", determine if "string" starts with the "prefix" string. Return 1 (or any other "truthy" value) if true, 0 if false.
Example:
```
startsWith("hello world!", "hello"); // should return 1.
startsWith("hello world!", "HELLO"); // should return 0.
startsWith("nowai", "nowaisir"); // should return 0.
```
Addendum:
For this problem, an empty "prefix" string should always return 1 (true) for any value of "string".
If the length of the "prefix" string is greater than the length of the "string", return 0.
The check should be case-sensitive, i.e. startsWith("hello", "HE") should return 0, whereas startsWith("hello", "he") should return 1.
The length of the "string" as well as the "prefix" can be defined by the formula: 0 <= length < +Infinity
No characters should be ignored and/or omitted during the test, e.g. whitespace characters should not be ignored.
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\": [\"8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\ninura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0\", \"8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0\", \"8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0\", \"8\\n2\\nomura\\noihsot\\nraku\\nt`naka\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0\", \"8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\nimura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nabdxcef\\n0\", 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\"miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n\", \"inura,miura\\ninura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abzdefa\\npqrst,psqt\\n2\\n\", \"ioura,miura\\nioura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\n0\\n0\\nabcdef,abdxcef\\nabcdef,abzdefb\\npqrst,psqt\\n3\\n\", \"miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\npqrst,psqt\\n1\\n\", \"miura,omura\\n1\\ntanaka,tasaka\\n1\\n0\\npqrst,psqt\\n1\\n\", \"0\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n\", \"imura,miura\\nimura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\"]}", "source": "taco"}
|
Meikyokan University is very famous for its research and education in the area of computer science. This university has a computer center that has advanced and secure computing facilities including supercomputers and many personal computers connected to the Internet.
One of the policies of the computer center is to let the students select their own login names. Unfortunately, students are apt to select similar login names, and troubles caused by mistakes in entering or specifying login names are relatively common. These troubles are a burden on the staff of the computer center.
To avoid such troubles, Dr. Choei Takano, the chief manager of the computer center, decided to stamp out similar and confusing login names. To this end, Takano has to develop a program that detects confusing login names.
Based on the following four operations on strings, the distance between two login names is determined as the minimum number of operations that transforms one login name to the other.
1. Deleting a character at an arbitrary position.
2. Inserting a character into an arbitrary position.
3. Replacing a character at an arbitrary position with another character.
4. Swapping two adjacent characters at an arbitrary position.
For example, the distance between “omura” and “murai” is two, because the following sequence of operations transforms “omura” to “murai”.
delete ‘o’ insert ‘i’
omura --> mura --> murai
Another example is that the distance between “akasan” and “kaason” is also two.
swap ‘a’ and ‘k’ replace ‘a’ with ‘o’
akasan --> kaasan --> kaason
Takano decided that two login names with a small distance are confusing and thus must be avoided.
Your job is to write a program that enumerates all the confusing pairs of login names.
Beware that the rules may combine in subtle ways. For instance, the distance between “ant” and “neat” is two.
swap ‘a’ and ‘n’ insert ‘e’
ant --> nat --> neat
Input
The input consists of multiple datasets. Each dataset is given in the following format.
n
d
name1
name2
...
namen
The first integer n is the number of login names. Then comes a positive integer d. Two login names whose distance is less than or equal to d are deemed to be confusing. You may assume that 0 < n ≤ 200 and 0 < d ≤ 2. The i-th student’s login name is given by namei, which is composed of only lowercase letters. Its length is less than 16. You can assume that there are no duplicates in namei (1 ≤ i ≤ n).
The end of the input is indicated by a line that solely contains a zero.
Output
For each dataset, your program should output all pairs of confusing login names, one pair per line, followed by the total number of confusing pairs in the dataset.
In each pair, the two login names are to be separated only by a comma character (,), and the login name that is alphabetically preceding the other should appear first. The entire output of confusing pairs for each dataset must be sorted as follows. For two pairs “w1,w2” and “w3,w4”, if w1 alphabetically precedes w3, or they are the same and w2 precedes w4, then “w1,w2” must appear before “w3,w4”.
Example
Input
8
2
omura
toshio
raku
tanaka
imura
yoshoi
hayashi
miura
3
1
tasaka
nakata
tanaka
1
1
foo
5
2
psqt
abcdef
abzdefa
pqrst
abdxcef
0
Output
imura,miura
imura,omura
miura,omura
toshio,yoshoi
4
tanaka,tasaka
1
0
abcdef,abdxcef
abcdef,abzdefa
pqrst,psqt
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\": [\"9 9 1\\n1 2\\n1 3\\n2 3\\n1 5\\n5 6\\n6 1\\n1 8\\n9 8\\n7 1\\n\", \"5 4 5\\n1 2\\n2 3\\n3 4\\n4 1\\n\", \"5000 0 2956\\n\", \"2 0 2\\n\", \"2 1 1\\n1 2\\n\", \"2 1 2\\n1 2\\n\", \"2 2 2\\n1 2\\n2 1\\n\", \"5000 2 238\\n3212 238\\n238 3212\\n\", \"5000 2 3810\\n3225 1137\\n1137 3225\\n\", \"100 1 30\\n69 81\\n\", \"500 1 209\\n183 107\\n\", \"1000 1 712\\n542 916\\n\", \"39 40 38\\n4 8\\n24 28\\n16 17\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n28 16\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"8 8 1\\n3 2\\n3 4\\n4 5\\n5 3\\n6 4\\n6 7\\n7 8\\n8 6\\n\", \"7 7 1\\n2 3\\n4 2\\n7 4\\n5 7\\n4 5\\n4 6\\n6 4\\n\", \"2333 1 1\\n1 2\\n\", \"7 4 2\\n1 2\\n3 4\\n5 6\\n7 1\\n\", \"1 0 1\\n\", \"9 9 1\\n2 3\\n3 4\\n4 5\\n6 2\\n7 6\\n8 7\\n6 8\\n5 9\\n9 2\\n\", \"30 30 29\\n29 9\\n1 3\\n15 5\\n14 24\\n7 18\\n17 12\\n5 9\\n22 7\\n26 20\\n7 29\\n8 2\\n10 12\\n17 18\\n17 24\\n8 12\\n23 28\\n10 15\\n18 2\\n29 13\\n25 29\\n9 2\\n7 13\\n11 5\\n19 26\\n10 5\\n25 5\\n20 10\\n5 26\\n24 23\\n22 8\\n\", \"30 30 28\\n16 28\\n5 30\\n7 17\\n6 1\\n12 28\\n15 28\\n14 30\\n25 11\\n25 10\\n25 8\\n12 30\\n27 5\\n30 10\\n22 14\\n30 13\\n20 27\\n15 25\\n24 20\\n20 15\\n1 30\\n3 10\\n3 4\\n3 18\\n15 14\\n18 22\\n20 26\\n10 3\\n15 27\\n23 29\\n10 24\\n\", \"2333 1 1\\n1 2\\n\", \"1 0 1\\n\", \"30 30 28\\n16 28\\n5 30\\n7 17\\n6 1\\n12 28\\n15 28\\n14 30\\n25 11\\n25 10\\n25 8\\n12 30\\n27 5\\n30 10\\n22 14\\n30 13\\n20 27\\n15 25\\n24 20\\n20 15\\n1 30\\n3 10\\n3 4\\n3 18\\n15 14\\n18 22\\n20 26\\n10 3\\n15 27\\n23 29\\n10 24\\n\", \"8 8 1\\n3 2\\n3 4\\n4 5\\n5 3\\n6 4\\n6 7\\n7 8\\n8 6\\n\", \"100 1 30\\n69 81\\n\", \"30 30 29\\n29 9\\n1 3\\n15 5\\n14 24\\n7 18\\n17 12\\n5 9\\n22 7\\n26 20\\n7 29\\n8 2\\n10 12\\n17 18\\n17 24\\n8 12\\n23 28\\n10 15\\n18 2\\n29 13\\n25 29\\n9 2\\n7 13\\n11 5\\n19 26\\n10 5\\n25 5\\n20 10\\n5 26\\n24 23\\n22 8\\n\", \"2 0 2\\n\", \"7 4 2\\n1 2\\n3 4\\n5 6\\n7 1\\n\", \"39 40 38\\n4 8\\n24 28\\n16 17\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n28 16\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"500 1 209\\n183 107\\n\", \"2 1 2\\n1 2\\n\", \"5000 2 238\\n3212 238\\n238 3212\\n\", \"7 7 1\\n2 3\\n4 2\\n7 4\\n5 7\\n4 5\\n4 6\\n6 4\\n\", \"9 9 1\\n2 3\\n3 4\\n4 5\\n6 2\\n7 6\\n8 7\\n6 8\\n5 9\\n9 2\\n\", \"5000 2 3810\\n3225 1137\\n1137 3225\\n\", \"1000 1 712\\n542 916\\n\", \"2 1 1\\n1 2\\n\", \"5000 0 2956\\n\", \"2 2 2\\n1 2\\n2 1\\n\", \"2333 1 1\\n1 4\\n\", \"30 30 28\\n16 28\\n5 30\\n7 17\\n6 1\\n12 28\\n15 28\\n14 30\\n25 11\\n25 10\\n25 8\\n12 30\\n27 5\\n30 10\\n22 14\\n14 13\\n20 27\\n15 25\\n24 20\\n20 15\\n1 30\\n3 10\\n3 4\\n3 18\\n15 14\\n18 22\\n20 26\\n10 3\\n15 27\\n23 29\\n10 24\\n\", \"8 8 1\\n3 2\\n3 4\\n4 5\\n5 3\\n6 4\\n6 8\\n7 8\\n8 6\\n\", \"100 1 30\\n6 81\\n\", \"7 4 2\\n1 2\\n2 4\\n5 6\\n7 1\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n28 16\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"500 1 209\\n45 107\\n\", \"5000 2 287\\n3212 238\\n238 3212\\n\", \"7 7 1\\n2 3\\n4 1\\n7 4\\n5 7\\n4 5\\n4 6\\n6 4\\n\", \"5000 2 3810\\n3225 1137\\n413 3225\\n\", \"1000 1 712\\n282 916\\n\", \"5000 0 3178\\n\", \"185 1 1\\n1 4\\n\", \"500 0 7\\n45 107\\n\", \"9 9 1\\n1 1\\n1 3\\n2 3\\n1 5\\n5 6\\n9 1\\n1 8\\n8 8\\n7 1\\n\", \"526 0 7\\n45 107\\n\", \"526 1 7\\n45 107\\n\", \"101 1 6\\n6 11\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 31\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n18 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"2333 1 1\\n2 2\\n\", \"30 30 29\\n29 9\\n1 3\\n15 5\\n14 5\\n7 18\\n17 12\\n5 9\\n22 7\\n26 20\\n7 29\\n8 2\\n10 12\\n17 18\\n17 24\\n8 12\\n23 28\\n10 15\\n18 2\\n29 13\\n25 29\\n9 2\\n7 13\\n11 5\\n19 26\\n10 5\\n25 5\\n20 10\\n5 26\\n24 23\\n22 8\\n\", \"39 40 38\\n4 8\\n24 28\\n20 17\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n28 16\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"678 1 209\\n183 107\\n\", \"2 0 2\\n1 2\\n\", \"9 9 1\\n2 3\\n3 2\\n4 5\\n6 2\\n7 6\\n8 7\\n6 8\\n5 9\\n9 2\\n\", \"2 2 2\\n1 2\\n2 2\\n\", \"9 9 1\\n1 2\\n1 3\\n2 3\\n1 5\\n5 6\\n9 1\\n1 8\\n9 8\\n7 1\\n\", \"30 30 28\\n16 28\\n5 30\\n7 17\\n6 1\\n12 28\\n15 28\\n14 30\\n25 11\\n25 10\\n25 8\\n12 30\\n27 5\\n30 10\\n22 14\\n14 13\\n20 27\\n15 25\\n24 20\\n20 15\\n1 30\\n3 10\\n3 4\\n3 18\\n15 14\\n18 22\\n20 26\\n9 3\\n15 27\\n23 29\\n10 24\\n\", \"8 8 1\\n3 2\\n3 4\\n4 5\\n5 3\\n6 4\\n6 3\\n7 8\\n8 6\\n\", \"100 1 31\\n6 81\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n28 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"500 1 7\\n45 107\\n\", \"2 0 2\\n1 1\\n\", \"7 7 1\\n2 3\\n5 1\\n7 4\\n5 7\\n4 5\\n4 6\\n6 4\\n\", \"5000 2 3810\\n3225 1137\\n773 3225\\n\", \"9 9 1\\n1 2\\n1 3\\n2 3\\n1 5\\n5 6\\n9 1\\n1 8\\n8 8\\n7 1\\n\", \"8 8 1\\n3 2\\n3 4\\n8 5\\n5 3\\n6 4\\n6 3\\n7 8\\n8 6\\n\", \"100 1 31\\n6 13\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n15 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"7 7 1\\n2 3\\n5 1\\n7 4\\n5 5\\n4 5\\n4 6\\n6 4\\n\", \"5000 2 3810\\n3225 1556\\n773 3225\\n\", \"100 1 5\\n6 13\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 35\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"5000 1 3810\\n3225 1556\\n773 3225\\n\", \"9 9 1\\n1 1\\n1 3\\n2 3\\n1 5\\n5 6\\n8 1\\n1 8\\n8 8\\n7 1\\n\", \"100 1 6\\n6 13\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n19 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"5000 1 3810\\n2242 1556\\n773 3225\\n\", \"100 1 6\\n6 11\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 27\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n18 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n11 7\\n33 7\\n3 33\\n\", \"526 1 7\\n46 107\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 24\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 31\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n18 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n16 7\\n33 7\\n3 33\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 6\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n22 38\\n22 37\\n37 31\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n18 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n16 7\\n33 7\\n3 33\\n\", \"39 40 38\\n4 8\\n24 28\\n16 34\\n7 25\\n4 29\\n34 32\\n16 6\\n21 10\\n23 36\\n36 14\\n30 19\\n34 19\\n15 21\\n14 38\\n22 37\\n37 31\\n28 33\\n3 29\\n32 22\\n12 30\\n9 15\\n5 19\\n23 27\\n18 17\\n25 17\\n24 11\\n39 10\\n6 20\\n16 6\\n3 18\\n34 21\\n21 38\\n11 19\\n11 3\\n32 4\\n15 13\\n16 11\\n16 7\\n33 7\\n3 33\\n\", \"30 30 28\\n16 28\\n5 30\\n6 17\\n6 1\\n12 28\\n15 28\\n14 30\\n25 11\\n25 10\\n25 8\\n12 30\\n27 5\\n30 10\\n22 14\\n30 13\\n20 27\\n15 25\\n24 20\\n20 15\\n1 30\\n3 10\\n3 4\\n3 18\\n15 14\\n18 22\\n20 26\\n10 3\\n15 27\\n23 29\\n10 24\\n\", \"8 6 1\\n3 2\\n3 4\\n4 5\\n5 3\\n6 4\\n6 7\\n7 8\\n8 6\\n\", \"100 1 4\\n69 81\\n\", \"3 0 2\\n\", \"7 7 1\\n2 3\\n4 2\\n7 4\\n5 7\\n4 5\\n6 6\\n6 4\\n\", \"1000 1 712\\n364 916\\n\", \"2 1 1\\n2 2\\n\", \"5000 0 2233\\n\", \"5 4 5\\n1 2\\n2 3\\n3 2\\n4 1\\n\", \"100 1 30\\n6 3\\n\", \"5 4 5\\n1 2\\n2 3\\n3 4\\n4 1\\n\", \"9 9 1\\n1 2\\n1 3\\n2 3\\n1 5\\n5 6\\n6 1\\n1 8\\n9 8\\n7 1\\n\"], \"outputs\": [\"3\\n\", \"1\\n\", \"4999\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"4998\\n\", \"4998\\n\", \"98\\n\", \"498\\n\", \"998\\n\", \"12\\n\", \"1\\n\", \"1\\n\", \"2331\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"13\\n\", \"9\\n\", \"2331\\n\", \"0\\n\", \"9\\n\", \"1\\n\", \"98\\n\", \"13\\n\", \"1\\n\", \"3\\n\", \"12\\n\", \"498\\n\", \"1\\n\", \"4998\\n\", \"1\\n\", \"1\\n\", \"4998\\n\", \"998\\n\", \"0\\n\", \"4999\\n\", \"0\\n\", \"2331\\n\", \"9\\n\", \"1\\n\", \"98\\n\", \"3\\n\", \"11\\n\", \"498\\n\", \"4998\\n\", \"2\\n\", \"4997\\n\", \"998\\n\", \"4999\\n\", \"183\\n\", \"499\\n\", \"4\\n\", \"525\\n\", \"524\\n\", \"99\\n\", \"10\\n\", \"2332\\n\", \"13\\n\", \"12\\n\", \"676\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"9\\n\", \"1\\n\", \"98\\n\", \"11\\n\", \"498\\n\", \"1\\n\", \"2\\n\", \"4997\\n\", \"3\\n\", \"1\\n\", \"98\\n\", \"11\\n\", \"2\\n\", \"4997\\n\", \"98\\n\", \"11\\n\", \"4998\\n\", \"4\\n\", \"98\\n\", \"11\\n\", \"4998\\n\", \"98\\n\", \"11\\n\", \"524\\n\", \"10\\n\", \"11\\n\", \"11\\n\", \"9\\n\", \"2\\n\", \"98\\n\", \"2\\n\", \"1\\n\", \"998\\n\", \"1\\n\", \"4999\\n\", \"1\\n\", \"98\\n\", \"1\\n\", \"3\\n\"]}", "source": "taco"}
|
There are $n$ cities and $m$ roads in Berland. Each road connects a pair of cities. The roads in Berland are one-way.
What is the minimum number of new roads that need to be built to make all the cities reachable from the capital?
New roads will also be one-way.
-----Input-----
The first line of input consists of three integers $n$, $m$ and $s$ ($1 \le n \le 5000, 0 \le m \le 5000, 1 \le s \le n$) — the number of cities, the number of roads and the index of the capital. Cities are indexed from $1$ to $n$.
The following $m$ lines contain roads: road $i$ is given as a pair of cities $u_i$, $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$). For each pair of cities $(u, v)$, there can be at most one road from $u$ to $v$. Roads in opposite directions between a pair of cities are allowed (i.e. from $u$ to $v$ and from $v$ to $u$).
-----Output-----
Print one integer — the minimum number of extra roads needed to make all the cities reachable from city $s$. If all the cities are already reachable from $s$, print 0.
-----Examples-----
Input
9 9 1
1 2
1 3
2 3
1 5
5 6
6 1
1 8
9 8
7 1
Output
3
Input
5 4 5
1 2
2 3
3 4
4 1
Output
1
-----Note-----
The first example is illustrated by the following: [Image]
For example, you can add roads ($6, 4$), ($7, 9$), ($1, 7$) to make all the cities reachable from $s = 1$.
The second example is illustrated by the following: [Image]
In this example, you can add any one of the roads ($5, 1$), ($5, 2$), ($5, 3$), ($5, 4$) to make all the cities reachable from $s = 5$.
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\": [\"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n5 8\\n3 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n1 8\\n3 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 6\\n5 6\\n6 3\\n5 8\\n1 16\\n3 8\\n6 14\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n5 5\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n1 8\\n3 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n1 8\\n3 8\\n6 9\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 9\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 14\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 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2\\n0 0\\n1 3\\n3 4\\n2 8\\n5 2\\n1 -2\", \"1 6\\n3 4\\n3 3\\n3 6\\n5 6\\n4 7\\n4 7\\n5 6\\n2 3\\n1 8\\n1 11\\n3 8\\n6 14\\n7 0\\n8 5\\n9 2\\n0 0\\n1 3\\n3 4\\n2 8\\n1 2\\n1 -2\", \"1 6\\n3 4\\n3 3\\n3 6\\n5 6\\n4 7\\n4 7\\n5 6\\n2 3\\n2 8\\n1 11\\n3 8\\n6 14\\n7 0\\n8 5\\n9 2\\n0 0\\n1 3\\n3 4\\n2 8\\n1 2\\n1 -2\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n3 8\\n5 8\\n6 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n5 8\\n3 8\\n6 9\\n7 9\\n8 4\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n1 5\\n3 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 11\\n5 8\\n1 8\\n3 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n1 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n1 8\\n3 8\\n6 9\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 14\\n3 8\\n6 14\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 14\\n7 0\\n8 9\\n9 2\\n0 0\\n1 2\\n3 4\\n3 5\\n4 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 14\\n7 -1\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 5\\n3 2\\n1 0\", \"1 6\\n3 4\\n3 5\\n3 0\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 14\\n7 0\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 5\\n3 2\\n1 0\", \"1 6\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 3\\n5 8\\n1 8\\n3 8\\n6 14\\n7 0\\n8 5\\n9 3\\n0 0\\n1 3\\n3 4\\n3 5\\n3 2\\n1 0\", \"1 3\\n3 4\\n3 5\\n3 6\\n4 6\\n4 7\\n4 7\\n5 6\\n6 7\\n5 8\\n5 8\\n6 8\\n6 9\\n7 9\\n8 9\\n9 2\\n0 0\\n1 3\\n3 4\\n3 4\\n4 2\\n0 0\"], \"outputs\": [\"NG\\nNG\\n\", \"NG\\n\", \"NG\\nOK\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nOK\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\nOK\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\nOK\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\nNG\\n\", \"NG\\nNG\\n\", \"NG\\nNG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"NG\\n\", \"OK\\nNG\"]}", "source": "taco"}
|
In 1862, the lord of Aizu was ordered to serve as a guardian of Kyoto. The Kyoto Shugoshoku is an important role to protect Kyoto at the end of the Edo period when security has deteriorated. You have to patrol the city by sharing it with the shogunate and other clan. However, when it came time to decide the sharing route, the following order was received from a stubborn old man who is famous among his vassals.
<image>
It was a big deal. Even the lord cannot ignore the statement of this vassal. Depending on the selection of the sharing route, it will be "the samurai's face is not noticeable".
So, please make a program to judge whether the above three conditions are met by inputting the information of the start point, the goal point, and the intersection, and give it to the lord.
The start point is represented by 1, the goal point is represented by 2, and other intersections are represented by integers of 3 or more. A road is represented by a set of intersection numbers that the roads connect to. The number of intersections shall be 100 or less, and there shall be one or more routes from all intersections to the start point and goal point.
input
Given multiple datasets. Each dataset is given in the following format:
a1 b1
a2 b2
:
:
0 0
The two integers in each row indicate that there is a road connecting intersection ai and intersection bi. When both ai and bi are 0, it indicates the end of inputting intersection information.
The number of datasets does not exceed 50.
output
For each data set, if the samurai's face stands out (if the three conditions are met), OK, otherwise (if the three conditions are not met), output NG on one line.
Example
Input
1 3
3 4
3 5
3 6
4 6
4 7
4 7
5 6
6 7
5 8
5 8
6 8
6 9
7 9
8 9
9 2
0 0
1 3
3 4
3 4
4 2
0 0
Output
OK
NG
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, 2, 3], [5.5, 4.5, 10], [7, 3, 2], [5, 10, 5], [3, 3, 0], [3, 3, 1], [5, 5, 5], [122.14, 222.11, 250], [8, 5, 7], [100000, 100005, 111111], [3, 4, 5], [21, 220, 221], [8.625, 33.625, 32.5], [65, 56, 33], [68000, 285000, 293000], [2, 4, 5], [105, 100, 6], [102, 200, 250], [65, 55, 33], [7, 8, 12], [7.99999, 4, 4]], \"outputs\": [[0], [0], [0], [0], [0], [1], [1], [1], [1], [1], [2], [2], [2], [2], [2], [3], [3], [3], [3], [3], [3]]}", "source": "taco"}
|
In this kata, you should calculate type of triangle with three given sides ``a``, ``b`` and ``c`` (given in any order).
If all angles are less than ``90°``, this triangle is ``acute`` and function should return ``1``.
If one angle is strictly ``90°``, this triangle is ``right`` and function should return ``2``.
If one angle more than ``90°``, this triangle is ``obtuse`` and function should return ``3``.
If three sides cannot form triangle, or one angle is ``180°`` (which turns triangle into segment) - function should return ``0``.
Input parameters are ``sides`` of given triangle. All input values are non-negative floating point or integer numbers (or both).
Acute
Right
Obtuse
### Examples:
```python
triangle_type(2, 4, 6) # return 0 (Not triangle)
triangle_type(8, 5, 7) # return 1 (Acute, angles are approx. 82°, 38° and 60°)
triangle_type(3, 4, 5) # return 2 (Right, angles are approx. 37°, 53° and exactly 90°)
triangle_type(7, 12, 8) # return 3 (Obtuse, angles are approx. 34°, 106° and 40°)
```
If you stuck, this can help you: http://en.wikipedia.org/wiki/Law_of_cosines. But you can solve this kata even without angle calculation.
There is very small chance of random test to fail due to round-off error, in such case resubmit your solution.
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\": [[\"74/3\"], [\"9999/24\"], [\"74/30\"], [\"13/5\"], [\"5/3\"], [\"1/1\"], [\"10/10\"], [\"900/10\"], [\"9920/124\"], [\"6/2\"], [\"9/77\"], [\"96/100\"], [\"12/18\"], [\"6/36\"], [\"1/18\"], [\"-64/8\"], [\"-6/8\"], [\"-9/78\"], [\"-504/26\"], [\"-47/2\"], [\"-21511/21\"]], \"outputs\": [[\"24 2/3\"], [\"416 15/24\"], [\"2 14/30\"], [\"2 3/5\"], [\"1 2/3\"], [\"1\"], [\"1\"], [\"90\"], [\"80\"], [\"3\"], [\"9/77\"], [\"96/100\"], [\"12/18\"], [\"6/36\"], [\"1/18\"], [\"-8\"], [\"-6/8\"], [\"-9/78\"], [\"-19 10/26\"], [\"-23 1/2\"], [\"-1024 7/21\"]]}", "source": "taco"}
|
In Math, an improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number) For example: ```5/3``` (five third).
A mixed numeral is a whole number and a fraction combined into one "mixed" number. For example: ```1 1/2``` (one and a half) is a mixed numeral.
## Task
Write a function `convertToMixedNumeral` to convert the improper fraction into a mixed numeral.
The input will be given as a ```string``` (e.g. ```'4/3'```).
The output should be a ```string```, with a space in between the whole number and the fraction (e.g. ```'1 1/3'```). You do not need to reduce the result to its simplest form.
For the purpose of this exercise, there will be no ```0```, ```empty string``` or ```null``` input value. However, the input can be:
- a negative fraction
- a fraction that does not require conversion
- a fraction that can be converted into a whole number
## Example
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\": [\"6 3 1\\n\", \"100 1 2\\n\", \"6 3 2\\n\", \"60 34 30\\n\", \"8 4 1\\n\", \"100 100 100\\n\", \"100 51 100\\n\", \"60 31 29\\n\", \"100 18 82\\n\", \"100 52 50\\n\", \"100 51 51\\n\", \"8 4 4\\n\", \"4 2 2\\n\", \"100 19 99\\n\", \"2 1 1\\n\", \"6 3 3\\n\", \"6 4 4\\n\", \"100 1 8\\n\", \"4 3 3\\n\", \"100 100 50\\n\", \"2 2 1\\n\", \"100 61 30\\n\", \"4 2 3\\n\", \"100 50 50\\n\", \"20 10 1\\n\", \"2 1 2\\n\", \"6 1 6\\n\", \"6 3 5\\n\", \"60 30 30\\n\", \"8 2 5\\n\", \"4 2 4\\n\", \"6 0 1\\n\", \"100 1 3\\n\", \"10 3 2\\n\", \"12 34 30\\n\", \"10 4 1\\n\", \"100 110 100\\n\", \"100 73 100\\n\", \"60 30 29\\n\", \"110 18 82\\n\", \"110 52 50\\n\", \"100 5 51\\n\", \"6 2 2\\n\", \"110 19 99\\n\", \"10 3 3\\n\", \"6 1 4\\n\", \"100 2 8\\n\", \"100 000 50\\n\", \"100 61 56\\n\", \"4 2 1\\n\", \"100 50 25\\n\", \"20 12 1\\n\", \"6 0 6\\n\", \"6 2 1\\n\", \"60 6 30\\n\", \"9 2 5\\n\", \"6 0 0\\n\", \"100 2 3\\n\", \"10 3 1\\n\", \"12 37 30\\n\", \"10 4 0\\n\", \"110 110 100\\n\", \"60 30 36\\n\", \"110 18 42\\n\", \"110 67 50\\n\", \"100 10 51\\n\", \"6 2 0\\n\", \"110 19 119\\n\", \"10 4 3\\n\", \"6 0 4\\n\", \"110 2 8\\n\", \"110 000 50\\n\", \"101 50 25\\n\", \"8 12 1\\n\", \"11 0 6\\n\", \"6 4 1\\n\", \"60 5 30\\n\", \"9 2 3\\n\", \"4 0 0\\n\", \"100 4 3\\n\", \"20 3 1\\n\", \"12 1 30\\n\", \"110 110 110\\n\", \"102 30 36\\n\", \"110 18 45\\n\", \"110 118 50\\n\", \"101 10 51\\n\", \"6 1 0\\n\", \"110 19 194\\n\", \"10 4 2\\n\", \"4 0 1\\n\", \"110 4 8\\n\", \"100 000 20\\n\", \"101 50 28\\n\", \"8 12 2\\n\", \"11 -1 6\\n\", \"6 8 1\\n\", \"118 5 30\\n\", \"110 4 3\\n\", \"37 3 1\\n\", \"110 110 101\\n\", \"204 30 36\\n\", \"100 18 45\\n\", \"110 195 50\\n\", \"101 7 51\\n\", \"110 19 362\\n\", \"10 8 2\\n\", \"4 0 -1\\n\", \"110 5 8\\n\", \"8 12 4\\n\", \"8 -1 6\\n\", \"6 8 0\\n\", \"118 9 30\\n\", \"010 4 3\\n\", \"37 1 1\\n\", \"110 111 101\\n\", \"136 30 36\\n\", \"100 16 45\\n\", \"110 84 50\\n\", \"100 19 362\\n\", \"10 8 0\\n\", \"5 0 0\\n\", \"111 5 8\\n\", \"11 -1 2\\n\", \"12 8 0\\n\", \"118 9 46\\n\", \"011 4 3\\n\", \"37 0 1\\n\", \"010 111 101\\n\", \"136 56 36\\n\", \"4 1 1\\n\", \"2 2 2\\n\"], \"outputs\": [\"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\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\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\"]}", "source": "taco"}
|
Little Petya loves playing with squares. Mum bought him a square 2n × 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 ≤ 2n ≤ 100, 1 ≤ x, y ≤ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<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\": [\"2\\nP 1\\nP 2\\n2\\nP 2\\nM -2\\n0\", \"2\\nP 1\\nP 2\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nP 1\\nP 4\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 1\\nP 4\\n\\n2\\nP -1\\nM -2\\n\\n0\", \"2\\nQ 1\\nP 4\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 8\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nP 1\\nP 5\\n\\n2\\nQ 0\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 9\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nQ 0\\nP 8\\n\\n2\\nO -1\\nM -6\\n\\n0\", \"2\\nQ 0\\nP 8\\n\\n2\\nO -1\\nM -11\\n\\n0\", \"2\\nP 2\\nP 3\\n\\n2\\nP -1\\nM -2\\n\\n0\", \"2\\nQ 1\\nP 5\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nQ 0\\nP 16\\n\\n2\\nO -1\\nM -6\\n\\n0\", \"2\\nQ 0\\nP 8\\n\\n2\\nO -1\\nM -16\\n\\n0\", \"2\\nQ 2\\nP 6\\n\\n0\\nP 0\\nL -4\\n\\n2\", \"2\\nQ 2\\nP 5\\n\\n0\\nP 1\\nL -4\\n\\n2\", \"2\\nQ 2\\nP 8\\n\\n0\\nP 1\\nM -2\\n\\n1\", \"2\\nP 0\\nP 8\\n\\n2\\nO -1\\nM -5\\n\\n0\", \"2\\nQ -1\\nP 14\\n\\n2\\nN -1\\nM -3\\n\\n0\", \"2\\nQ 0\\nP 20\\n\\n2\\nO -1\\nM -6\\n\\n0\", \"2\\nP 0\\nP 15\\n\\n2\\nO -1\\nM -5\\n\\n0\", \"2\\nQ -1\\nP 8\\n\\n2\\nM -1\\nM -14\\n\\n0\", \"2\\nQ 0\\nP 20\\n\\n2\\nO -1\\nM -4\\n\\n0\", \"2\\nQ 2\\nP 7\\n\\n0\\nP 1\\nL -1\\n\\n2\", \"2\\nP 1\\nP 8\\n\\n2\\nP -1\\nM 0\\n\\n0\", \"2\\nQ 1\\nP 14\\n\\n0\\nO -1\\nM -16\\n\\n0\", \"2\\nP 0\\nP 11\\n\\n2\\nN -1\\nM -5\\n\\n0\", \"2\\nQ 1\\nP 27\\n\\n0\\nO -1\\nM -16\\n\\n0\", \"2\\nP 0\\nP 1\\n\\n2\\nN -1\\nM -5\\n\\n0\", \"2\\nQ 0\\nP 2\\n\\n0\\nQ 1\\nM -6\\n\\n1\", \"2\\nQ 2\\nP 24\\n\\n0\\nO -1\\nN -16\\n\\n0\", \"2\\nP 2\\nP 30\\n\\n0\\nO -1\\nN -16\\n\\n0\", \"2\\nP 1\\nP 26\\n\\n0\\nO -2\\nO -16\\n\\n0\", \"2\\nQ 0\\nP 7\\n\\n2\\nO -1\\nM -3\\n\\n0\", \"2\\nQ 2\\nP 9\\n\\n0\\nP -1\\nM -3\\n\\n0\", \"2\\nP 0\\nP 8\\n\\n2\\nO -1\\nM -12\\n\\n0\", \"2\\nP 4\\nP 3\\n\\n2\\nP -1\\nM -2\\n\\n0\", \"2\\nP 1\\nP 2\\n\\n2\\nP 1\\nM -4\\n\\n0\", \"2\\nQ 0\\nP 16\\n\\n2\\nO -1\\nM -9\\n\\n0\", \"2\\nQ 0\\nP 14\\n\\n2\\nO -1\\nM -16\\n\\n0\", \"2\\nR 2\\nP 6\\n\\n2\\nP 0\\nM -1\\n\\n0\", \"2\\nQ -1\\nP 8\\n\\n2\\nM -1\\nM -13\\n\\n0\", \"2\\nP 5\\nP 0\\n\\n2\\nQ 0\\nM -2\\n\\n0\", \"2\\nP 1\\nP 1\\n\\n2\\nP 1\\nM -4\\n\\n0\", \"2\\nP 2\\nP 11\\n\\n0\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 0\\nP 16\\n\\n2\\nO -1\\nM -5\\n\\n0\", \"2\\nR -1\\nP 8\\n\\n2\\nO -1\\nM -7\\n\\n0\", \"2\\nO 0\\nP 3\\n\\n0\\nP 1\\nN -8\\n\\n2\", \"2\\nP 1\\nP 2\\n\\n2\\nP -1\\nM -1\\n\\n0\", \"2\\nP 2\\nP 32\\n\\n0\\nO -1\\nN -10\\n\\n0\", \"2\\nP 1\\nP 48\\n\\n0\\nO -1\\nO -13\\n\\n0\", \"2\\nQ 1\\nP 8\\n\\n2\\nO 0\\nM -20\\n\\n0\", \"2\\nO 0\\nP 11\\n\\n2\\nO -1\\nM -4\\n\\n0\", \"2\\nO 2\\nP 15\\n\\n0\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 1\\nP 8\\n\\n2\\nO 0\\nM -34\\n\\n0\", \"2\\nP 1\\nP 16\\n\\n0\\nP 1\\nM -16\\n\\n1\", \"2\\nQ 0\\nP 18\\n\\n2\\nQ 1\\nM -3\\n\\n0\", \"2\\nQ 1\\nP 7\\n\\n2\\nO 0\\nM -34\\n\\n0\", \"2\\nO 0\\nP 11\\n\\n2\\nO 0\\nM -6\\n\\n0\", \"2\\nP 2\\nP 12\\n\\n0\\nQ 0\\nM 0\\n\\n0\", \"2\\nQ 1\\nP 7\\n\\n2\\nO 0\\nM -65\\n\\n0\", \"2\\nP 1\\nP 23\\n\\n0\\nP 1\\nM -16\\n\\n2\", \"2\\nQ 1\\nP 7\\n\\n2\\nO 0\\nM -124\\n\\n0\", \"2\\nP 2\\nP 1\\n\\n2\\nP 3\\nM -3\\n\\n0\", \"2\\nP 0\\nP 1\\n\\n2\\nP 2\\nM -2\\n\\n0\", \"2\\nP 1\\nP 2\\n\\n2\\nP 2\\nM -5\\n\\n0\", \"2\\nO 0\\nP 0\\n\\n2\\nP 2\\nM -6\\n\\n0\", \"2\\nO 0\\nP -1\\n\\n2\\nP 2\\nM -6\\n\\n0\", \"2\\nP 2\\nP 20\\n\\n0\\nP 3\\nM -2\\n\\n-1\", \"2\\nP 1\\nP 1\\n\\n0\\nQ 9\\nM -2\\n\\n0\", \"2\\nP 0\\nP 39\\n\\n0\\nP 3\\nN -2\\n\\n-1\", \"2\\nP 0\\nP 10\\n\\n0\\nP 3\\nL -2\\n\\n0\", \"2\\nQ 0\\nP 47\\n\\n0\\nP 3\\nN -4\\n\\n-1\", \"2\\nP 1\\nP 2\\n\\n2\\nP 6\\nM -3\\n\\n0\", \"2\\nP 2\\nP 4\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nP 1\\nP 2\\n\\n2\\nQ 0\\nM -2\\n\\n0\", \"2\\nQ 1\\nP 4\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nP 2\\nP 0\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nQ 0\\nP 4\\n\\n2\\nP -1\\nM -3\\n\\n0\", \"2\\nP 1\\nP 4\\n\\n2\\nQ 0\\nM -2\\n\\n0\", \"2\\nP 2\\nP 0\\n\\n2\\nQ 0\\nM -2\\n\\n0\", \"2\\nQ 0\\nP 4\\n\\n2\\nO -1\\nM -3\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 0\\nM -2\\n\\n1\", \"2\\nQ 0\\nP 8\\n\\n2\\nO -1\\nM -3\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 0\\nL -2\\n\\n1\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 0\\nL -2\\n\\n2\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 0\\nL -4\\n\\n2\", \"2\\nQ -1\\nP 8\\n\\n2\\nO -1\\nM -11\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 1\\nL -4\\n\\n2\", \"2\\nQ 0\\nP 4\\n\\n0\\nP 1\\nL -4\\n\\n2\", \"2\\nP 0\\nP 4\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nP 2\\nP 4\\n\\n2\\nP -1\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n2\\nP 0\\nM -1\\n\\n0\", \"2\\nQ 1\\nP 4\\n\\n2\\nP 1\\nM -2\\n\\n0\", \"2\\nP 4\\nP 0\\n\\n2\\nP 0\\nM -2\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n2\\nP 0\\nM -3\\n\\n0\", \"2\\nQ 1\\nP 4\\n\\n2\\nQ -1\\nM -3\\n\\n0\", \"2\\nQ 2\\nP 4\\n\\n0\\nP 1\\nM -2\\n\\n1\", \"2\\nP 1\\nP 2\\n\\n2\\nP 2\\nM -2\\n\\n0\"], \"outputs\": [\"1\\n1\", \"1\\n1\\n\", \"3\\n1\\n\", \"3\\n3\\n\", \"3\\n2\\n\", \"3\\n\", \"7\\n2\\n\", \"4\\n1\\n\", \"8\\n2\\n\", \"7\\n5\\n\", \"7\\n10\\n\", \"2\\n3\\n\", \"4\\n2\\n\", \"15\\n5\\n\", \"7\\n15\\n\", \"5\\n\", \"4\\n\", \"7\\n\", \"7\\n4\\n\", \"13\\n2\\n\", \"19\\n5\\n\", \"14\\n4\\n\", \"7\\n13\\n\", \"19\\n3\\n\", \"6\\n\", \"7\\n3\\n\", \"13\\n\", \"10\\n4\\n\", \"26\\n\", \"2\\n4\\n\", \"1\\n\", \"23\\n\", \"29\\n\", \"25\\n\", \"6\\n2\\n\", \"8\\n\", \"7\\n11\\n\", \"4\\n3\\n\", \"1\\n3\\n\", \"15\\n8\\n\", \"13\\n15\\n\", \"5\\n2\\n\", \"7\\n12\\n\", \"5\\n1\\n\", \"0\\n3\\n\", \"10\\n\", \"15\\n4\\n\", \"7\\n6\\n\", \"2\\n\", \"1\\n2\\n\", \"31\\n\", \"47\\n\", \"7\\n19\\n\", \"10\\n3\\n\", \"14\\n\", \"7\\n33\\n\", \"15\\n\", \"17\\n2\\n\", \"6\\n33\\n\", \"10\\n5\\n\", \"11\\n\", \"6\\n64\\n\", \"22\\n\", \"6\\n123\\n\", \"2\\n2\\n\", \"2\\n1\\n\", \"1\\n4\\n\", \"1\\n5\\n\", \"2\\n5\\n\", \"19\\n\", \"0\\n\", \"38\\n\", \"9\\n\", \"46\\n\", \"1\\n6\\n\", \"3\\n1\\n\", \"3\\n1\\n\", \"1\\n1\\n\", \"3\\n1\\n\", \"1\\n1\\n\", \"3\\n2\\n\", \"3\\n2\\n\", \"3\\n1\\n\", \"1\\n1\\n\", \"3\\n2\\n\", \"3\\n\", \"7\\n2\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"7\\n10\\n\", \"3\\n\", \"3\\n\", \"3\\n1\\n\", \"3\\n3\\n\", \"3\\n2\\n\", \"3\\n1\\n\", \"3\\n1\\n\", \"3\\n2\\n\", \"3\\n2\\n\", \"3\\n\", \"1\\n1\\n\"]}", "source": "taco"}
|
Did you ever hear about 'crossing the bridge noodle' ? Let me tell you that it's not some kind of bridge made of noodles. It's a dish, a kind of rice noodle soup. Mr.Ping makes the best noodle soup and his son Po is eagerly waiting for the user reviews in his father's blog. Users can vote with a (+) or a (-) and accordingly +1 or -1 is added to the total score respectively. Note that if a user votes multiple times, only his/her latest vote is counted towards the total score.
Po opens the blog to see initial score of 0. To see the updated score without refreshing the page, he has to keep voting himself. After each of Po's clicks on (+) or (-), he can see the current total score, of course that considers Po's vote too. He is wondering how many users other than him could have possibly voted. Given the sequence of clicks made by Po and the total score displayed just after each of his clicks, can you tell him the minimum number of users that could have possibly voted at least once, other than Po.
------ Input ------
There are multiple test cases ( at most 21 ). Each case starts with an integer N ( 1 ≤ N ≤ 1000 ), the number of Po's clicks. Sequence of N clicks follows, one on each line of the form "vote score" (without quotes, separated by a space), where vote is either a 'P' or a 'M', representing Plus(+) and Minus(-) respectively, the one clicked by Po and score is the score displayed after Po's click ( -1,000,000,000 ≤ score ≤ 1,000,000,000 ). The last case has N = 0 and should not be processed. Each case is followed by an empty line.
------ Output ------
For each test case, output the minimum number of users that could have possibly voted at least once.
----- Sample Input 1 ------
2
P 1
P 2
2
P 2
M -2
0
----- Sample Output 1 ------
1
1
----- explanation 1 ------
Case 1 :
P 1 , Po voted (+) and score = 1 is possibly Po's vote itself.
P 2 , Po again voted (+), but as only latest vote of a user is counted, Po contributed only +1 to the score, so possibly one more user voted with a (+). Remember that we have to find the number of users other than Po, so answer is 1
Case 2 :
P 2 , Po voted (+) and score = 2, possibly another user A also voted (+)
M -2 , Po voted (-) and score = -2. Possibly the same user A also voted (-)
So there can possibly be just one other user A
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\": [[153, 8], [255, 8], [256, 8], [1534, 32], [364334, 32], [2, 64], [164345, 64], [23, 128], [256245645346, 128], [6423, 256], [988847589347589798345, 256], [98, 512], [9827498275894278943758934789347, 512], [111, 1024], [859983475894789589772983457982345896389458937589738945435, 1024], [98345873489734895, 16], [893458278957389257892374587, 32], [3457892758927985892347589273895789, 64], [5315, 9], [9999, 124], [1355, 2], [5425, 4], [1111, 1], [24626, 666]], \"outputs\": [[153], [255], [null], [4261740544], [781124864], [144115188075855872], [17978653386462986240], [30572243903053065076787562386447925248], [45528303328508850820834438375932952576], [10447366694034586540826038121892877184087912282225534899373057468243260735488], [91242511062515682511683596760355486395666889244852199999154981214322488770560], [5132676473181150452180681444625675470675694728195525589909800865174737792762529702056967504767017718412590320712014191342452658263948296307619131260141568], [11930836310133384514326160681165088053924843877461649523769728440666263776393580347680430230979602503027248413303643954184674561174505233796513849034145792], [77946850769420728811700342256867869309216970571326574052151324251985652400041433233322816339012642571657549377600486963672365876321875957409008065628834483616922797539687769006521665530227798622106610186255607970082166897421927265014079512773561809863796510492144840252477126168637689491549705283548003434496], [109358791181702534675750459978375317655425491983637702648061053285141449541556750052943705607891736023254034131895692863702552970350431938079186312678981100327891943154445619222027830694165819898582344009910545707293292608754474937152496600707613861415524072325452544924390687309129714181920077788312386928640], [null], [null], [null], [null], [null], [null], [null], [null], [null]]}", "source": "taco"}
|
In computing, there are two primary byte order formats: big-endian and little-endian. Big-endian is used primarily for networking (e.g., IP addresses are transmitted in big-endian) whereas little-endian is used mainly by computers with microprocessors.
Here is an example (using 32-bit integers in hex format):
Little-Endian: 00 6D F4 C9 = 7,206,089
Big-Endian: C9 F4 6D 00 = 3,388,239,104
Your job is to write a function that switches the byte order of a given integer. The function should take an integer n for the first argument, and the bit-size of the integer for the second argument. The bit size must be a power of 2 greater than or equal to 8. Your function should return a None value if the integer is negative, if the specified bit size is not a power of 2 that is 8 or larger, or if the integer is larger than the specified bit size can handle. In this kata, assume that all integers are unsigned (non-negative) and that all input arguments are integers (no floats, strings, None/nil values, etc.). Remember that you will need to account for padding of null (00) bytes.
Hint: bitwise operators are very helpful! :)
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
|
{"tests": "{\"inputs\": [[\"\"], [{}], [\"abc\"], [\"2d6+3 abc\"], [\"abc 2d6+3\"], [\"2d6++4\"]], \"outputs\": [[false], [false], [false], [false], [false], [false]]}", "source": "taco"}
|
# The die is cast!
Your task in this kata is to write a "dice roller" that interprets a subset of [dice notation](http://en.wikipedia.org/wiki/Dice_notation).
# Description
In most role-playing games, die rolls required by the system are given in the form `AdX`. `A` and `X` are variables, separated by the letter **d**, which stands for *die* or *dice*.
- `A` is the number of dice to be rolled (usually omitted if 1).
- `X` is the number of faces of each die.
Here are some examples of input:
# Modifiers
As an addition to the above rules the input may also contain modifiers in the form `+N` or `-N` where `N` is an integer.
Here are some examples of input containing modifiers:
*Modifiers must be applied **after** all dice has been summed up.*
# Output
Your function must support two types of output depending on the second argument; *verbose* and *summed*.
## Summed output
If the verbose flag isn't set your function should sum up all the dice and modifiers and return the result as an integer.
## Verbose output
With the verbose flag your function should return an object/hash containing an array (`dice`) with all the dice rolls, and a integer (`modifier`) containing the sum of the modifiers which defaults to zero.
Example of verbose output:
# Invalid input
Here are some examples of invalid inputs:
# Additional information
- Your solution should ignore all whitespace.
- `roll` should return `false` for invalid input.
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\\n\", \"4\\n\", \"100\\n\", \"5\\n\", \"6\\n\", \"11\\n\", \"18\\n\", \"26\\n\", \"50\\n\", \"90\\n\", \"97\\n\", \"98\\n\", \"99\\n\", \"5\", \"6\", \"8\", \"15\", \"12\", \"9\", \"14\", \"7\", \"13\", \"20\", \"10\", \"11\", \"24\", \"26\", \"23\", \"16\", \"25\", \"28\", \"41\", \"36\", \"19\", \"27\", \"18\", \"32\", \"34\", \"22\", \"43\", \"44\", \"50\", \"69\", \"31\", \"39\", \"21\", \"49\", \"76\", \"59\", \"77\", \"60\", \"92\", \"17\", \"78\", \"29\", \"47\", \"37\", \"51\", \"61\", \"48\", \"38\", \"95\", \"68\", \"55\", \"66\", \"33\", \"58\", \"40\", \"42\", \"46\", \"56\", \"35\", \"67\", \"45\", \"85\", \"30\", \"82\", \"70\", \"74\", \"57\", \"87\", \"54\", \"98\", \"89\", \"73\", \"84\", \"65\", \"93\", \"52\", \"80\", \"90\", \"88\", \"53\", \"62\", \"72\", \"64\", \"91\", \"63\", \"75\", \"96\", \"94\", \"97\", \"71\", \"99\", \"83\", \"79\", \"81\", \"86\", \"6\", \"12\", \"5\", \"10\", \"13\", \"4\", \"3\", \"100\"], \"outputs\": [\"61\\n\", \"230\\n\", \"388130742\\n\", \"865\\n\", \"3247\\n\", \"2414454\\n\", \"261943303\\n\", \"858533109\\n\", \"113468411\\n\", \"252858375\\n\", \"329869205\\n\", \"616680192\\n\", \"597534442\\n\", \"865\\n\", \"3247\\n\", \"45719\\n\", \"478366600\\n\", \"9058467\\n\", \"171531\\n\", \"127504505\\n\", \"12185\\n\", \"33985227\\n\", \"580025381\\n\", \"643550\\n\", \"2414454\\n\", \"604119499\\n\", \"858533109\\n\", \"737209731\\n\", \"794717734\\n\", \"159693437\\n\", \"549054109\\n\", \"763737161\\n\", \"409213624\\n\", \"776803305\\n\", \"639056669\\n\", \"261943303\\n\", \"783022045\\n\", \"649970414\\n\", \"44657419\\n\", \"123883652\\n\", \"639213333\\n\", \"113468411\\n\", \"406959393\\n\", \"23314687\\n\", \"978442997\\n\", \"51688048\\n\", \"39816123\\n\", \"427196161\\n\", \"725438992\\n\", \"781042769\\n\", \"696683714\\n\", \"866398347\\n\", \"733354121\\n\", \"569725155\\n\", \"996291083\\n\", \"124885216\\n\", \"604356692\\n\", \"799008836\\n\", \"792638194\\n\", \"501575626\\n\", \"88638656\\n\", \"333099663\\n\", \"515140586\\n\", \"971550783\\n\", \"981760191\\n\", \"855462856\\n\", \"702530485\\n\", \"534833116\\n\", \"785892908\\n\", \"998121103\\n\", \"751629411\\n\", \"68697295\\n\", \"305799096\\n\", \"181836645\\n\", \"371653459\\n\", \"531294469\\n\", \"206282374\\n\", \"975058685\\n\", \"191483611\\n\", \"51018086\\n\", \"123820509\\n\", \"664630886\\n\", \"616680192\\n\", \"847205021\\n\", \"673385295\\n\", \"323137024\\n\", \"986519078\\n\", \"738390145\\n\", \"775465589\\n\", \"25328739\\n\", \"252858375\\n\", \"915711339\\n\", \"256852905\\n\", \"221791721\\n\", \"324759692\\n\", \"414054379\\n\", \"718889563\\n\", \"149602322\\n\", \"570246669\\n\", \"170591295\\n\", \"133009077\\n\", \"329869205\\n\", \"245601370\\n\", \"597534442\\n\", \"353770801\\n\", \"842176273\\n\", \"847501730\\n\", \"940737264\\n\", \"3247\\n\", \"9058467\\n\", \"865\\n\", \"643550\\n\", \"33985227\\n\", \"230\", \"61\", \"388130742\"]}", "source": "taco"}
|
You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:
- The string does not contain characters other than A, C, G and T.
- The string does not contain AGC as a substring.
- The condition above cannot be violated by swapping two adjacent characters once.
-----Notes-----
A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.
For example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.
-----Constraints-----
- 3 \leq N \leq 100
-----Input-----
Input is given from Standard Input in the following format:
N
-----Output-----
Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.
-----Sample Input-----
3
-----Sample Output-----
61
There are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.
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\": [\"6\\n9 english\\n6 mathematics\\n8 geography\\n-1\\n3 graphics\\n-1\", \"6\\n9 english\\n6 mathematics\\n14 geography\\n-1\\n3 graphics\\n-1\", \"6\\n9 english\\n9 lathematics\\n14 reoggaphy\\n-1\\n3 graphics\\n-1\", \"6\\n9 english\\n9 lathematics\\n14 reoggaphy\\n-1\\n3 scihparg\\n-1\", \"6\\n9 hsilgne\\n9 lathematics\\n14 reoggaphy\\n-1\\n3 sbihparg\\n-1\", \"6\\n1 hsilgne\\n9 lathematics\\n14 georgaphy\\n-1\\n2 sbihparg\\n-1\", \"6\\n9 english\\n6 mathematics\\n14 geography\\n-1\\n3 grcphias\\n-1\", \"6\\n9 english\\n9 lataemhtics\\n14 reoggaphy\\n-1\\n3 scihparg\\n-1\", \"6\\n1 hsilgne\\n0 lathematics\\n14 georgaphy\\n-1\\n2 sbihparg\\n-1\", \"6\\n4 hsilgne\\n9 lathematict\\n14 georgaphy\\n-1\\n2 graphibs\\n-1\", \"6\\n1 english\\n6 mathematics\\n10 geography\\n-1\\n3 graphics\\n-1\", \"6\\n9 english\\n6 mathematics\\n6 geography\\n-1\\n3 grcphias\\n-1\", \"6\\n9 hsilgne\\n9 lathemauics\\n24 reoggaphy\\n-1\\n3 sbihparg\\n-1\", \"6\\n1 hsilgne\\n-1 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sbihpaqg\\n-1\", \"6\\n1 engljsh\\n6 nathematics\\n10 yhpargoeg\\n-1\\n2 graphics\\n-1\", \"6\\n14 hrilgne\\n6 mathematics\\n-1 geography\\n-1\\n3 grcphias\\n-1\", \"6\\n23 hsilgne\\n9 scih`mettal\\n20 reoggaphy\\n-1\\n2 scihparg\\n-1\", \"6\\n3 heilgns\\n13 kathematics\\n0 zhpagroeg\\n-1\\n2 sbihparg\\n-1\", \"6\\n1 hsimgne\\n-1 lathematics\\n14 yhpagrofg\\n-1\\n1 graphibs\\n-1\", \"6\\n9 english\\n7 nathematics\\n0 geography\\n-1\\n3 gchpsias\\n-1\", \"6\\n2 gsilgne\\n0 lathematics\\n14 georgaphy\\n-1\\n2 sbihoarg\\n-1\", \"6\\n1 hsilgne\\n-1 scitamehtal\\n3 georgapiy\\n-1\\n2 srihnabg\\n-1\", \"6\\n16 english\\n6 mathematics\\n2 gegosapyh\\n-1\\n3 graphics\\n-1\", \"6\\n9 hsikgne\\n2 mathematics\\n14 rfoggaphy\\n-1\\n3 ghaprics\\n-1\", \"6\\n14 enhlisg\\n9 lathematict\\n17 reoggaphy\\n-1\\n0 scihparg\\n-1\", \"6\\n2 hsilgne\\n9 lathematict\\n14 geprgaphy\\n-1\\n2 tpihcarg\\n-1\", \"6\\n2 englirh\\n0 mathematics\\n14 yhpargoeg\\n-1\\n3 gparhics\\n-1\", \"6\\n0 hsilgne\\n1 lathematics\\n14 georgaphz\\n-1\\n2 sraphibg\\n-1\", \"6\\n23 hsilgne\\n2 lathematics\\n12 reoggaphy\\n-1\\n1 sdihpasg\\n-1\", \"6\\n9 hsilgne\\n7 scitamehtal\\n25 zhpagroeg\\n-1\\n4 sbihpbrg\\n-1\", \"6\\n3 snglieh\\n13 kathematics\\n0 zhpagroeg\\n-1\\n2 sbihparg\\n-1\", \"6\\n1 hsimgne\\n-1 lathematics\\n14 yhoagrpfg\\n-1\\n1 graphibs\\n-1\", \"6\\n9 english\\n7 nathematics\\n-1 geography\\n-1\\n3 gchpsias\\n-1\", \"6\\n2 gsingle\\n0 lathematics\\n14 georgaphy\\n-1\\n2 sbihoarg\\n-1\", \"6\\n9 english\\n6 mathematics\\n8 geography\\n-1\\n3 graphics\\n-1\"], \"outputs\": [\"1 mathematics\\n0 graphics\", \"1 mathematics\\n0 graphics\\n\", \"1 lathematics\\n0 graphics\\n\", \"1 lathematics\\n0 scihparg\\n\", \"1 lathematics\\n0 sbihparg\\n\", \"2 hsilgne\\n0 sbihparg\\n\", \"1 mathematics\\n0 grcphias\\n\", \"1 lataemhtics\\n0 scihparg\\n\", \"1 hsilgne\\n0 sbihparg\\n\", \"2 hsilgne\\n0 graphibs\\n\", \"2 english\\n0 graphics\\n\", \"0 geography\\n0 grcphias\\n\", \"1 lathemauics\\n0 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sbihparg\\n\", \"0 hsimgne\\n0 yhoagrpfg\\n0 graphibs\\n\", \"0 nathematics\\n0 english\\n0 gchpsias\\n\", \"1 gsingle\\n0 sbihoarg\\n\", \"1 mathematics\\n0 graphics\\n\"]}", "source": "taco"}
|
Harry is a bright student. To prepare thoroughly for exams, he completes all the exercises in his book! Now that the exams are approaching fast, he is doing book exercises day and night. He writes down and keeps updating the remaining number of exercises on the back cover of each book.
Harry has a lot of books messed on the floor. Therefore, he wants to pile up the books that still have some remaining exercises into a single pile. He will grab the books one-by-one and add the books that still have remaining exercises to the top of the pile.
Whenever he wants to do a book exercise, he will pick the book with the minimum number of remaining exercises from the pile. In order to pick the book, he has to remove all the books above it. Therefore, if there are more than one books with the minimum number of remaining exercises, he will take the one which requires the least number of books to remove. The removed books are returned to the messy floor. After he picks the book, he will do all the remaining exercises and trash the book.
Since number of books is rather large, he needs your help to tell him the number of books he must remove, for picking the book with the minimum number of exercises.
Note that more than one book can have the same name.
------ Input ------
The first line contains a single integer N denoting the number of actions. Then N lines follow. Each line starts with an integer. If the integer is -1, that means Harry wants to do a book exercise. Otherwise, the integer is number of the remaining exercises in the book he grabs next. This is followed by a string denoting the name of the book.
------ Output ------
For each -1 in the input, output a single line containing the number of books Harry must remove, followed by the name of the book that Harry must pick.
------ Constraints ------
1 < N ≤ 1,000,000
0 ≤ (the number of remaining exercises of each book) < 100,000
The name of each book consists of between 1 and 15 characters 'a' - 'z'.
Whenever he wants to do a book exercise, there is at least one book in the pile.
----- Sample Input 1 ------
6
9 english
6 mathematics
8 geography
-1
3 graphics
-1
----- Sample Output 1 ------
1 mathematics
0 graphics
----- explanation 1 ------
- For the first $-1$: Currently, there are $3$ books in the pile. The book with minimum exercises left amongst these is mathematics. Harry has to remove $1$ book from the top to pick mathematics book and solve the remaining exercises.
- For the second $-1$: The book on the top has the least number of remaining exercises. Thus, Harry has to remove $0$ books from the top pick up graphics book.
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 three integers $a \le b \le c$.
In one move, you can add $+1$ or $-1$ to any of these integers (i.e. increase or decrease any number by one). You can perform such operation any (possibly, zero) number of times, you can even perform this operation several times with one number. Note that you cannot make non-positive numbers using such operations.
You have to perform the minimum number of such operations in order to obtain three integers $A \le B \le C$ such that $B$ is divisible by $A$ and $C$ is divisible by $B$.
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.
The next $t$ lines describe test cases. Each test case is given on a separate line as three space-separated integers $a, b$ and $c$ ($1 \le a \le b \le c \le 10^4$).
-----Output-----
For each test case, print the answer. In the first line print $res$ — the minimum number of operations you have to perform to obtain three integers $A \le B \le C$ such that $B$ is divisible by $A$ and $C$ is divisible by $B$. On the second line print any suitable triple $A, B$ and $C$.
-----Example-----
Input
8
1 2 3
123 321 456
5 10 15
15 18 21
100 100 101
1 22 29
3 19 38
6 30 46
Output
1
1 1 3
102
114 228 456
4
4 8 16
6
18 18 18
1
100 100 100
7
1 22 22
2
1 19 38
8
6 24 48
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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|
problem
At IOI Confectionery, rice crackers are baked using the traditional method since the company was founded. This traditional method is to bake the front side for a certain period of time with charcoal, turn it over when the front side is baked, and bake the back side for a certain period of time with charcoal. While keeping this tradition, rice crackers are baked by machine. This machine arranges and bake rice crackers in a rectangular shape with vertical R (1 ≤ R ≤ 10) rows and horizontal C (1 ≤ C ≤ 10000) columns. Normally, it is an automatic operation, and when the front side is baked, the rice crackers are turned over and the back side is baked all at once.
One day, when I was baking rice crackers, an earthquake occurred just before turning over the rice crackers, and some rice crackers turned over. Fortunately, the condition of the charcoal fire remained appropriate, but if the front side was baked any more, the baking time set by the tradition since the establishment would be exceeded, and the front side of the rice cracker would be overcooked and could not be shipped as a product. .. Therefore, I hurriedly changed the machine to manual operation and tried to turn over only the rice crackers that had not been turned inside out. This machine can turn over several horizontal rows at the same time and several vertical columns at the same time, but unfortunately it cannot turn over rice crackers one by one.
If it takes time to turn it over, the front side of the rice cracker that was not turned over due to the earthquake will be overcooked and cannot be shipped as a product. Therefore, we decided to increase the number of rice crackers that can be baked on both sides without overcooking the front side, that is, the number of "rice crackers that can be shipped". Consider the case where no horizontal rows are flipped, or no vertical columns are flipped. Write a program that outputs the maximum number of rice crackers that can be shipped.
Immediately after the earthquake, the rice crackers are in the state shown in the following figure. The black circles represent the state where the front side is burnt, and the white circles represent the state where the back side is burnt.
<image>
If you turn the first line over, you will see the state shown in the following figure.
<image>
Furthermore, when the 1st and 5th columns are turned over, the state is as shown in the following figure. In this state, 9 rice crackers can be shipped.
<image>
input
The input consists of multiple datasets. Each dataset is given in the following format.
Two integers R and C (1 ≤ R ≤ 10, 1 ≤ C ≤ 10 000) are written on the first line of the input, separated by blanks. The following R line represents the state of the rice cracker immediately after the earthquake. In the (i + 1) line (1 ≤ i ≤ R), C integers ai, 1, ai, 2, ……, ai, C are written separated by blanks, and ai, j are i. It represents the state of the rice cracker in row j. If ai and j are 1, it means that the front side is burnt, and if it is 0, it means that the back side is burnt.
When both C and R are 0, it indicates the end of input. The number of data sets does not exceed 5.
output
For each data set, the maximum number of rice crackers that can be shipped is output on one line.
Examples
Input
2 5
0 1 0 1 0
1 0 0 0 1
3 6
1 0 0 0 1 0
1 1 1 0 1 0
1 0 1 1 0 1
0 0
Output
9
15
Input
None
Output
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.
| 0.625
|
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|
Alice is visiting New York City. To make the trip fun, Alice will take photos of the city skyline and give the set of photos as a present to Bob. However, she wants to find the set of photos with maximum beauty and she needs your help.
There are $n$ buildings in the city, the $i$-th of them has positive height $h_i$. All $n$ building heights in the city are different. In addition, each building has a beauty value $b_i$. Note that beauty can be positive or negative, as there are ugly buildings in the city too.
A set of photos consists of one or more photos of the buildings in the skyline. Each photo includes one or more buildings in the skyline that form a contiguous segment of indices. Each building needs to be in exactly one photo. This means that if a building does not appear in any photo, or if a building appears in more than one photo, the set of pictures is not valid.
The beauty of a photo is equivalent to the beauty $b_i$ of the shortest building in it. The total beauty of a set of photos is the sum of the beauty of all photos in it. Help Alice to find the maximum beauty a valid set of photos can have.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 3 \cdot 10^5$), the number of buildings on the skyline.
The second line contains $n$ distinct integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le n$). The $i$-th number represents the height of building $i$.
The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($-10^9 \le b_i \le 10^9$). The $i$-th number represents the beauty of building $i$.
-----Output-----
Print one number representing the maximum beauty Alice can achieve for a valid set of photos of the skyline.
-----Examples-----
Input
5
1 2 3 5 4
1 5 3 2 4
Output
15
Input
5
1 4 3 2 5
-3 4 -10 2 7
Output
10
Input
2
2 1
-2 -3
Output
-3
Input
10
4 7 3 2 5 1 9 10 6 8
-4 40 -46 -8 -16 4 -10 41 12 3
Output
96
-----Note-----
In the first example, Alice can achieve maximum beauty by taking five photos, each one containing one building.
In the second example, Alice can achieve a maximum beauty of $10$ by taking four pictures: three just containing one building, on buildings $1$, $2$ and $5$, each photo with beauty $-3$, $4$ and $7$ respectively, and another photo containing building $3$ and $4$, with beauty $2$.
In the third example, Alice will just take one picture of the whole city.
In the fourth example, Alice can take the following pictures to achieve maximum beauty: photos with just one building on buildings $1$, $2$, $8$, $9$, and $10$, and a single photo of buildings $3$, $4$, $5$, $6$, and $7$.
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.
| 0.125
|
{"tests": "{\"inputs\": [[2], [3], [4], [5], [6], [7], [8], [9], [10], [20], [30], [40], [50], [11], [24], [37], [19], [48], [59], [65], [73], [83], [64], [99], [100], [10000], [1500], [1534], [1978], [2763], [9999], [2673], [4578], [9876], [2659], [7777], [9364], [7280], [4998], [9283], [8234], [7622], [800], [782], [674], [4467], [1233], [3678], [7892], [5672]], \"outputs\": [[1], [2], [2], [3], [3], [4], [3], [4], [4], [5], [7], [6], [7], [5], [5], [7], [6], [6], [9], [7], [8], [9], [6], [9], [8], [17], [16], [18], [17], [17], [20], [16], [17], [18], [16], [18], [17], [17], [17], [17], [16], [19], [11], [13], [12], [18], [14], [18], [19], [16]]}", "source": "taco"}
|
# Summary:
Given a number, `num`, return the shortest amount of `steps` it would take from 1, to land exactly on that number.
# Description:
A `step` is defined as either:
- Adding 1 to the number: `num += 1`
- Doubling the number: `num *= 2`
You will always start from the number `1` and you will have to return the shortest count of steps it would take to land exactly on that number.
`1 <= num <= 10000`
Examples:
`num == 3` would return `2` steps:
```
1 -- +1 --> 2: 1 step
2 -- +1 --> 3: 2 steps
2 steps
```
`num == 12` would return `4` steps:
```
1 -- +1 --> 2: 1 step
2 -- +1 --> 3: 2 steps
3 -- x2 --> 6: 3 steps
6 -- x2 --> 12: 4 steps
4 steps
```
`num == 16` would return `4` steps:
```
1 -- +1 --> 2: 1 step
2 -- x2 --> 4: 2 steps
4 -- x2 --> 8: 3 steps
8 -- x2 --> 16: 4 steps
4 steps
```
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\\n1 -1\\n-1 4\\n-1 6\\n\", \"2\\n1 4\\n2 3\\n\", \"2\\n4 1\\n2 4\\n\", \"2\\n3 -1\\n-1 2\\n\", \"6\\n6 10\\n5 9\\n1 2\\n11 12\\n4 8\\n3 7\\n\", \"1\\n1 2\\n\", \"98\\n17 49\\n139 171\\n-1 114\\n147 179\\n26 58\\n-1 50\\n11 43\\n1 2\\n74 106\\n134 166\\n157 189\\n67 99\\n33 -1\\n155 187\\n25 57\\n156 -1\\n21 53\\n-1 126\\n98 130\\n6 38\\n153 185\\n8 40\\n81 113\\n69 101\\n84 116\\n150 182\\n89 121\\n34 66\\n154 186\\n32 64\\n95 127\\n162 194\\n-1 119\\n16 48\\n19 51\\n76 108\\n-1 45\\n75 107\\n79 111\\n149 181\\n161 -1\\n-1 104\\n3 35\\n93 125\\n22 -1\\n77 109\\n151 -1\\n85 -1\\n195 196\\n20 52\\n68 100\\n152 184\\n31 63\\n158 190\\n132 164\\n-1 180\\n160 192\\n140 172\\n78 110\\n-1 62\\n86 118\\n133 165\\n131 163\\n71 103\\n7 39\\n135 167\\n146 -1\\n27 59\\n5 37\\n15 47\\n4 36\\n12 44\\n97 129\\n137 -1\\n29 -1\\n143 175\\n136 168\\n159 191\\n91 123\\n24 56\\n88 120\\n145 177\\n14 46\\n96 128\\n90 122\\n144 176\\n92 124\\n28 60\\n138 170\\n142 174\\n70 102\\n23 55\\n10 42\\n9 41\\n73 105\\n-1 112\\n141 173\\n83 115\\n\", \"93\\n95 -1\\n137 140\\n144 147\\n81 84\\n131 133\\n9 -1\\n53 55\\n160 167\\n-1 111\\n92 99\\n32 39\\n58 -1\\n125 130\\n93 100\\n13 14\\n7 10\\n71 74\\n-1 114\\n158 165\\n143 146\\n28 35\\n172 175\\n145 148\\n151 153\\n118 120\\n132 134\\n155 162\\n60 65\\n156 163\\n17 20\\n15 18\\n24 26\\n149 150\\n8 11\\n61 66\\n31 38\\n43 46\\n182 184\\n68 70\\n107 110\\n-1 -1\\n44 47\\n79 82\\n-1 37\\n23 25\\n141 142\\n41 42\\n51 52\\n169 170\\n123 128\\n33 40\\n157 164\\n87 89\\n109 112\\n72 75\\n73 76\\n173 176\\n77 78\\n-1 6\\n171 174\\n88 90\\n49 50\\n1 2\\n-1 126\\n122 127\\n45 48\\n105 106\\n16 -1\\n96 103\\n-1 168\\n-1 34\\n91 -1\\n97 104\\n135 138\\n185 186\\n177 178\\n-1 83\\n57 62\\n159 166\\n115 116\\n179 180\\n67 69\\n3 5\\n117 119\\n136 139\\n-1 56\\n85 86\\n94 101\\n124 129\\n152 154\\n-1 36\\n59 64\\n21 22\\n\", \"98\\n-1 164\\n138 170\\n-1 55\\n-1 188\\n5 37\\n81 -1\\n11 43\\n142 174\\n146 178\\n-1 181\\n-1 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52\\n169 174\\n81 82\\n147 -1\\n166 168\\n153 154\\n-1 40\\n92 95\\n108 113\\n172 177\\n171 -1\\n149 150\\n53 54\\n133 136\\n91 94\\n-1 58\\n34 36\\n102 104\\n1 3\\n143 144\\n-1 137\\n115 -1\\n43 -1\\n13 14\\n162 164\\n106 111\\n77 78\\n83 84\\n63 68\\n151 152\\n187 188\\n181 182\\n-1 35\\n11 12\\n125 -1\\n70 73\\n-1 100\\n93 96\\n109 114\\n126 131\\n37 39\\n89 90\\n55 56\\n\", \"94\\n50 52\\n159 160\\n187 188\\n-1 45\\n124 128\\n80 82\\n97 100\\n59 63\\n162 -1\\n-1 90\\n-1 140\\n131 -1\\n83 84\\n53 -1\\n182 184\\n21 22\\n147 148\\n98 101\\n167 169\\n61 65\\n57 58\\n172 174\\n67 69\\n15 17\\n132 134\\n33 36\\n-1 180\\n117 119\\n141 -1\\n47 48\\n108 110\\n29 30\\n87 88\\n44 46\\n99 102\\n35 -1\\n19 20\\n114 -1\\n-1 32\\n161 164\\n72 -1\\n149 150\\n75 76\\n16 18\\n13 14\\n4 6\\n-1 129\\n23 24\\n-1 -1\\n-1 37\\n111 -1\\n-1 127\\n143 -1\\n1 2\\n175 176\\n157 158\\n79 81\\n177 179\\n3 -1\\n11 12\\n151 152\\n126 130\\n25 -1\\n155 156\\n-1 86\\n49 51\\n93 94\\n181 183\\n171 -1\\n54 56\\n68 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114\\n55 143\\n16 104\\n54 142\\n84 172\\n35 123\\n53 141\\n88 176\\n15 103\\n78 166\\n21 109\\n22 110\\n39 127\\n58 146\\n43 131\\n24 112\\n3 91\\n45 133\\n70 158\\n86 174\\n20 108\\n59 147\\n12 100\\n87 175\\n42 130\\n62 150\\n1 89\\n13 101\\n46 134\\n51 139\\n4 92\\n14 102\\n38 126\\n83 171\\n37 125\\n\", \"82\\n19 101\\n33 115\\n68 150\\n3 85\\n45 127\\n46 128\\n25 107\\n49 131\\n37 119\\n13 95\\n2 84\\n65 147\\n70 152\\n11 93\\n32 114\\n35 117\\n48 130\\n82 164\\n20 102\\n53 135\\n41 123\\n22 104\\n47 129\\n15 97\\n64 146\\n40 122\\n78 160\\n12 94\\n43 125\\n56 138\\n58 140\\n-1 110\\n28 -1\\n24 106\\n77 159\\n6 88\\n14 96\\n54 136\\n10 -1\\n9 91\\n52 134\\n42 124\\n17 99\\n27 109\\n75 157\\n60 142\\n34 116\\n16 98\\n1 83\\n51 133\\n80 162\\n-1 92\\n66 148\\n72 154\\n57 139\\n55 137\\n61 143\\n59 141\\n44 126\\n29 111\\n62 144\\n74 156\\n26 108\\n73 155\\n39 121\\n23 105\\n4 86\\n30 112\\n69 151\\n63 145\\n81 163\\n79 161\\n76 158\\n18 100\\n67 149\\n50 132\\n38 120\\n71 153\\n7 89\\n21 103\\n36 118\\n31 113\\n\", \"68\\n-1 -1\\n-1 -1\\n-1 -1\\n-1 81\\n-1 -1\\n1 69\\n-1 111\\n60 128\\n2 -1\\n49 -1\\n-1 -1\\n14 -1\\n55 -1\\n-1 -1\\n31 99\\n63 -1\\n-1 117\\n-1 -1\\n-1 -1\\n13 -1\\n-1 -1\\n-1 -1\\n67 -1\\n-1 -1\\n64 -1\\n-1 -1\\n-1 -1\\n47 115\\n4 -1\\n-1 97\\n-1 -1\\n-1 -1\\n52 120\\n40 -1\\n-1 74\\n57 -1\\n-1 -1\\n-1 -1\\n-1 -1\\n-1 -1\\n-1 -1\\n-1 -1\\n23 91\\n-1 -1\\n-1 -1\\n27 -1\\n-1 80\\n-1 126\\n-1 102\\n28 96\\n-1 133\\n-1 -1\\n-1 -1\\n-1 76\\n-1 -1\\n-1 131\\n-1 -1\\n68 136\\n3 -1\\n-1 124\\n-1 123\\n-1 -1\\n-1 82\\n-1 72\\n-1 -1\\n-1 -1\\n-1 113\\n-1 -1\\n\", \"3\\n3 6\\n1 -1\\n1 -1\\n\", \"3\\n1 4\\n-1 6\\n-1 6\\n\", \"4\\n3 6\\n2 -1\\n4 -1\\n1 8\\n\"], \"outputs\": [\"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\"]}", "source": "taco"}
|
There is a building with 2N floors, numbered 1, 2, \ldots, 2N from bottom to top.
The elevator in this building moved from Floor 1 to Floor 2N just once.
On the way, N persons got on and off the elevator. Each person i (1 \leq i \leq N) got on at Floor A_i and off at Floor B_i. Here, 1 \leq A_i < B_i \leq 2N, and just one person got on or off at each floor.
Additionally, because of their difficult personalities, the following condition was satisfied:
- Let C_i (= B_i - A_i - 1) be the number of times, while Person i were on the elevator, other persons got on or off. Then, the following holds:
- If there was a moment when both Person i and Person j were on the elevator, C_i = C_j.
We recorded the sequences A and B, but unfortunately, we have lost some of the records. If the record of A_i or B_i is lost, it will be given to you as -1.
Additionally, the remaining records may be incorrect.
Determine whether there is a pair of A and B that is consistent with the remaining records.
-----Constraints-----
- 1 \leq N \leq 100
- A_i = -1 or 1 \leq A_i \leq 2N.
- B_i = -1 or 1 \leq B_i \leq 2N.
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
:
A_N B_N
-----Output-----
If there is a pair of A and B that is consistent with the remaining records, print Yes; otherwise, print No.
-----Sample Input-----
3
1 -1
-1 4
-1 6
-----Sample Output-----
Yes
For example, if B_1 = 3, A_2 = 2, and A_3 = 5, all the requirements are met.
In this case, there is a moment when both Person 1 and Person 2 were on the elevator, which is fine since C_1 = C_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
|
{"tests": "{\"inputs\": [\"7\\n6 4\\n4 2\\n3 5\\n7 1\\n2 7\\n5 3\\n1 6\", \"4\\n2 4\\n1 3\\n3 1\\n4 2\", \"4\\n2 4\\n1 3\\n3 2\\n4 1\", \"4\\n1 4\\n2 3\\n3 2\\n4 1\", \"4\\n1 4\\n2 2\\n3 1\\n4 3\", \"4\\n2 4\\n1 2\\n3 1\\n4 3\", \"7\\n6 4\\n4 3\\n3 5\\n7 1\\n2 6\\n5 2\\n1 7\", \"4\\n2 4\\n1 3\\n3 1\\n4 2\", \"4\\n2 4\\n1 3\\n3 2\\n4 1\", \"4\\n1 4\\n3 3\\n2 1\\n4 2\", \"4\\n2 4\\n1 3\\n4 1\\n3 2\", \"7\\n6 4\\n4 3\\n3 5\\n7 1\\n2 7\\n5 2\\n1 6\", \"4\\n1 4\\n2 3\\n3 1\\n4 2\"], \"outputs\": [\"3\\n3\\n1\\n1\\n2\\n3\\n2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n2\\n1\\n1\\n\", \"1\\n1\\n1\\n1\\n\", \"1\\n3\\n3\\n3\\n\", \"4\\n4\\n4\\n4\\n\", \"3\\n3\\n1\\n1\\n1\\n3\\n1\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n2\\n1\\n1\\n\", \"1\\n3\\n3\\n3\\n\", \"2\\n2\\n1\\n1\\n\", \"3\\n3\\n1\\n1\\n2\\n3\\n2\", \"1\\n1\\n2\\n2\"]}", "source": "taco"}
|
There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).
For each k = 1,2,\dots,N, find the answer to the following question:
Rng is in City k. Rng can perform the following move arbitrarily many times:
* move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.
How many cities (including City k) are reachable from City k?
Constraints
* 1 \leq N \leq 200,000
* (x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).
* (y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print N lines. In i-th line print the answer to the question when k = i.
Examples
Input
4
1 4
2 3
3 1
4 2
Output
1
1
2
2
Input
7
6 4
4 3
3 5
7 1
2 7
5 2
1 6
Output
3
3
1
1
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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30\\n10\\n1 2 2 1 1 5 2 8 8\\n10 1 1 20 2 1 30 1 1\\n3\\n1 1\\n1 0\\n0\", \"4\\n1 2 2\\n10 35 30\\n10\\n1 2 2 2 5 5 1 8 9\\n10 1 1 20 2 2 5 1 1\\n3\\n1 1\\n2 1\\n0\", \"4\\n1 2 3\\n19 5 48\\n10\\n1 2 1 1 5 5 1 8 8\\n10 1 2 20 1 1 -1 2 1\\n0\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 1 1 5 5 2 8 8\\n10 1 2 40 2 1 30 1 1\\n3\\n1 2\\n1 1\\n0\", \"4\\n1 1 3\\n10 24 28\\n10\\n1 2 1 1 5 5 2 8 8\\n10 0 2 20 2 1 30 1 1\\n3\\n1 2\\n1 0\\n0\", \"4\\n1 1 3\\n10 24 30\\n10\\n1 2 1 1 5 5 2 8 5\\n10 0 2 20 2 2 54 1 1\\n3\\n1 2\\n1 0\\n0\", \"4\\n1 2 3\\n10 20 56\\n10\\n1 2 2 1 5 5 2 8 8\\n10 2 1 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 1 3\\n10 20 30\\n10\\n1 2 2 1 5 5 1 8 4\\n11 1 1 20 2 1 0 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 1 1 1 5 1 10 8\\n1 1 1 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n19 20 30\\n10\\n1 2 2 1 5 5 1 8 8\\n10 1 1 27 1 1 0 1 1\\n3\\n1 1\\n0 1\\n0\", \"4\\n1 2 3\\n10 30 60\\n10\\n1 2 2 1 1 5 1 8 8\\n10 1 2 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 2 1 5 5 1 5 9\\n10 1 1 20 2 1 30 1 1\\n3\\n1 1\\n2 0\\n0\", \"4\\n1 2 3\\n8 29 30\\n10\\n1 2 2 1 1 5 1 10 8\\n10 1 1 20 2 1 55 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n19 20 30\\n10\\n1 2 2 1 5 5 1 8 8\\n10 1 2 23 1 1 0 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 2\\n10 20 30\\n10\\n1 2 2 1 5 5 1 8 9\\n10 1 1 34 2 1 36 1 1\\n3\\n1 1\\n2 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 2 1 3 5 1 8 8\\n10 1 2 20 2 1 20 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n10 37 52\\n10\\n1 2 2 1 1 5 1 10 8\\n10 2 1 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n10 30 30\\n10\\n1 2 2 1 1 5 1 8 8\\n10 1 1 9 4 1 30 1 1\\n3\\n1 1\\n0 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 1 1 5 5 2 8 8\\n10 1 1 27 1 2 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n8 40 30\\n10\\n1 2 2 1 5 5 2 8 8\\n10 1 2 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 2\\n10 35 30\\n10\\n1 2 2 2 5 5 1 8 9\\n12 1 1 20 2 2 5 1 1\\n3\\n1 1\\n2 1\\n0\", \"4\\n1 2 2\\n10 20 47\\n10\\n1 2 3 2 5 2 1 8 9\\n9 1 1 35 2 4 5 1 2\\n3\\n1 1\\n2 2\\n0\", \"4\\n1 1 3\\n10 24 30\\n10\\n1 2 1 1 5 5 2 8 5\\n10 0 2 20 2 2 54 1 1\\n3\\n1 2\\n0 0\\n0\", \"4\\n1 2 3\\n10 20 19\\n10\\n1 2 2 1 5 5 2 8 8\\n10 2 1 20 2 1 30 1 1\\n3\\n1 1\\n1 1\\n0\", \"4\\n1 2 3\\n8 29 30\\n10\\n1 2 2 1 1 5 1 10 8\\n10 1 1 20 2 1 55 1 1\\n3\\n1 1\\n1 0\\n0\", \"4\\n1 2 3\\n10 30 30\\n10\\n1 2 2 1 1 5 1 8 8\\n10 1 1 9 0 1 30 1 1\\n3\\n1 1\\n0 1\\n0\", \"4\\n1 2 3\\n10 20 30\\n10\\n1 2 2 1 5 5 1 8 8\\n10 1 1 20 1 1 30 1 1\\n3\\n1 1\\n1 1\\n0\"], \"outputs\": [\"80\\n137\\n2\\n\", \"80\\n66\\n2\\n\", \"80\\n138\\n2\\n\", \"70\\n137\\n2\\n\", \"80\\n67\\n2\\n\", \"80\\n68\\n2\\n\", \"80\\n137\\n3\\n\", \"89\\n66\\n2\\n\", \"80\\n136\\n2\\n\", \"100\\n137\\n2\\n\", \"80\\n138\\n3\\n\", \"98\\n138\\n2\\n\", \"89\\n67\\n2\\n\", \"100\\n137\\n1\\n\", \"60\\n138\\n3\\n\", \"79\\n138\\n2\\n\", \"89\\n68\\n2\\n\", \"100\\n138\\n1\\n\", \"60\\n128\\n3\\n\", \"89\\n65\\n2\\n\", \"60\\n128\\n1\\n\", \"89\\n63\\n2\\n\", \"89\\n62\\n2\\n\", \"80\\n90\\n2\\n\", \"80\\n128\\n2\\n\", \"70\\n127\\n2\\n\", \"80\\n139\\n2\\n\", \"80\\n118\\n2\\n\", \"100\\n136\\n2\\n\", \"100\\n139\\n1\\n\", \"79\\n140\\n2\\n\", \"60\\n129\\n3\\n\", \"80\\n126\\n2\\n\", \"70\\n127\\n3\\n\", \"80\\n140\\n2\\n\", \"60\\n79\\n3\\n\", \"107\\n65\\n2\\n\", \"80\\n127\\n2\\n\", \"89\\n140\\n2\\n\", \"100\\n174\\n1\\n\", \"60\\n79\\n4\\n\", \"77\\n65\\n2\\n\", \"60\\n77\\n4\\n\", \"60\\n78\\n4\\n\", \"60\\n80\\n4\\n\", \"88\\n128\\n2\\n\", \"60\\n82\\n4\\n\", \"88\\n127\\n2\\n\", \"60\\n112\\n4\\n\", \"88\\n127\\n1\\n\", \"88\\n128\\n1\\n\", \"80\\n107\\n2\\n\", \"106\\n138\\n2\\n\", \"89\\n66\\n1\\n\", \"100\\n138\\n2\\n\", \"98\\n188\\n2\\n\", \"89\\n81\\n2\\n\", \"134\\n137\\n1\\n\", \"60\\n150\\n3\\n\", \"85\\n138\\n2\\n\", \"102\\n68\\n2\\n\", \"73\\n137\\n1\\n\", \"70\\n128\\n3\\n\", \"60\\n152\\n1\\n\", \"89\\n\", \"89\\n61\\n2\\n\", \"80\\n132\\n2\\n\", \"40\\n127\\n2\\n\", \"114\\n139\\n2\\n\", \"70\\n136\\n2\\n\", \"100\\n129\\n1\\n\", \"71\\n140\\n2\\n\", \"60\\n130\\n3\\n\", \"78\\n128\\n2\\n\", \"70\\n127\\n1\\n\", \"75\\n79\\n3\\n\", \"77\\n65\\n\", \"80\\n168\\n2\\n\", \"86\\n127\\n1\\n\", \"88\\n176\\n1\\n\", \"106\\n128\\n2\\n\", \"80\\n70\\n2\\n\", \"80\\n111\\n2\\n\", \"89\\n80\\n1\\n\", \"130\\n138\\n2\\n\", \"80\\n98\\n2\\n\", \"96\\n188\\n2\\n\", \"89\\n73\\n2\\n\", \"60\\n178\\n3\\n\", \"80\\n120\\n2\\n\", \"136\\n139\\n2\\n\", \"100\\n116\\n1\\n\", \"80\\n141\\n2\\n\", \"118\\n128\\n2\\n\", \"75\\n83\\n3\\n\", \"77\\n112\\n4\\n\", \"88\\n176\\n0\\n\", \"69\\n128\\n2\\n\", \"96\\n188\\n1\\n\", \"100\\n112\\n1\\n\", \"80\\n136\\n2\"]}", "source": "taco"}
|
Bridge Removal
ICPC islands once had been a popular tourist destination. For nature preservation, however, the government decided to prohibit entrance to the islands, and to remove all the man-made structures there. The hardest part of the project is to remove all the bridges connecting the islands.
There are n islands and n-1 bridges. The bridges are built so that all the islands are reachable from all the other islands by crossing one or more bridges. The bridge removal team can choose any island as the starting point, and can repeat either of the following steps.
* Move to another island by crossing a bridge that is connected to the current island.
* Remove one bridge that is connected to the current island, and stay at the same island after the removal.
Of course, a bridge, once removed, cannot be crossed in either direction. Crossing or removing a bridge both takes time proportional to the length of the bridge. Your task is to compute the shortest time necessary for removing all the bridges. Note that the island where the team starts can differ from where the team finishes the work.
Input
The input consists of at most 100 datasets. Each dataset is formatted as follows.
> n
> p2 p3 ... pn
> d2 d3 ... dn
The first integer n (3 ≤ n ≤ 800) is the number of the islands. The islands are numbered from 1 to n. The second line contains n-1 island numbers pi (1 ≤ pi < i), and tells that for each i from 2 to n the island i and the island pi are connected by a bridge. The third line contains n-1 integers di (1 ≤ di ≤ 100,000) each denoting the length of the corresponding bridge. That is, the length of the bridge connecting the island i and pi is di. It takes di units of time to cross the bridge, and also the same units of time to remove it. Note that, with this input format, it is assured that all the islands are reachable each other by crossing one or more bridges.
The input ends with a line with a single zero.
Output
For each dataset, print the minimum time units required to remove all the bridges in a single line. Each line should not have any character other than this number.
Sample Input
4
1 2 3
10 20 30
10
1 2 2 1 5 5 1 8 8
10 1 1 20 1 1 30 1 1
3
1 1
1 1
0
Output for the Sample Input
80
136
2
Example
Input
4
1 2 3
10 20 30
10
1 2 2 1 5 5 1 8 8
10 1 1 20 1 1 30 1 1
3
1 1
1 1
0
Output
80
136
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\": [[null, 0], [\"\", 0], [\"This is a test!\", 0], [\"This is a test!\", 1], [\"This is a test!\", 3], [\"This is a test!\", 4], [\"This is a test!\", -1], [\"This is a test!\", -5], [\"Brrrr\", 99], [\"AEIOUaeiou\", 1]], \"outputs\": [[null], [\"\"], [\"This is a test!\"], [\"Thes is i tast!\"], [\"This as e tist!\"], [\"This is a test!\"], [\"This as e tist!\"], [\"This as e tist!\"], [\"Brrrr\"], [\"uAEIOUaeio\"]]}", "source": "taco"}
|
You get a "text" and have to shift the vowels by "n" positions to the right.
(Negative value for n should shift to the left.)
"Position" means the vowel's position if taken as one item in a list of all vowels within the string.
A shift by 1 would mean, that every vowel shifts to the place of the next vowel.
Shifting over the edges of the text should continue at the other edge.
Example:
text = "This is a test!"
n = 1
output = "Thes is i tast!"
text = "This is a test!"
n = 3
output = "This as e tist!"
If text is null or empty return exactly this value.
Vowels are "a,e,i,o,u".
Have fun coding it and please don't forget to vote and rank this kata! :-)
I have created other katas. Have a look if you like coding and challenges.
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 2\\n1 2\\n1 3\\n1 4\\n3 5\\n3 6\\n3 7\\n2 7\\n\", \"6 4\\n1 2\\n2 3\\n2 4\\n4 5\\n4 6\\n2 4 5 6\\n\", \"2 1\\n2 1\\n1\\n\", \"1 1\\n1\\n\", \"10 2\\n6 9\\n6 2\\n1 6\\n4 10\\n3 7\\n9 4\\n9 5\\n6 7\\n2 8\\n7 6\\n\", \"15 2\\n7 12\\n13 11\\n6 8\\n2 15\\n10 9\\n5 1\\n13 5\\n5 4\\n14 3\\n8 9\\n8 4\\n4 7\\n12 14\\n5 2\\n7 4\\n\", \"20 2\\n1 16\\n12 5\\n15 19\\n18 9\\n8 4\\n10 16\\n9 16\\n20 15\\n14 19\\n7 4\\n18 12\\n17 12\\n2 20\\n6 14\\n3 19\\n7 19\\n18 15\\n19 13\\n9 11\\n12 18\\n\", \"4 2\\n4 3\\n3 1\\n1 2\\n3 4\\n\", \"8 5\\n2 5\\n1 8\\n6 7\\n3 4\\n6 8\\n8 5\\n5 3\\n1 6 7 3 8\\n\", \"16 8\\n16 12\\n16 15\\n15 9\\n15 13\\n16 3\\n15 2\\n15 10\\n1 2\\n6 16\\n5 15\\n2 7\\n15 4\\n14 15\\n11 16\\n8 5\\n5 10 14 6 8 3 1 9\\n\", \"32 28\\n30 12\\n30 27\\n24 32\\n6 13\\n11 5\\n4 30\\n8 28\\n9 20\\n8 20\\n7 20\\n5 30\\n18 5\\n20 14\\n23 20\\n17 20\\n8 26\\n20 1\\n15 2\\n20 13\\n24 20\\n22 24\\n25 16\\n2 3\\n19 5\\n16 10\\n31 2\\n29 5\\n20 16\\n2 20\\n5 21\\n5 20\\n32 11 6 12 22 30 23 21 14 13 1 20 7 25 9 29 10 27 5 19 24 31 15 26 8 3 28 17\\n\", \"10 3\\n10 5\\n3 2\\n6 8\\n1 5\\n10 4\\n6 1\\n9 8\\n2 9\\n7 3\\n3 9 1\\n\", \"7 5\\n6 4\\n5 6\\n6 7\\n2 3\\n5 2\\n2 1\\n4 6 1 7 3\\n\", \"15 7\\n5 4\\n12 5\\n7 13\\n10 11\\n3 8\\n6 12\\n3 15\\n1 3\\n5 14\\n7 9\\n1 10\\n6 1\\n12 7\\n10 2\\n4 10 8 13 1 7 9\\n\", \"31 16\\n3 25\\n8 1\\n1 9\\n1 23\\n16 15\\n10 6\\n25 30\\n20 29\\n2 24\\n3 7\\n19 22\\n2 12\\n16 4\\n7 26\\n31 10\\n17 13\\n25 21\\n7 18\\n28 2\\n6 27\\n19 5\\n13 3\\n17 31\\n10 16\\n20 14\\n8 19\\n6 11\\n28 20\\n13 28\\n31 8\\n31 27 25 20 26 8 28 15 18 17 10 23 4 16 30 22\\n\", \"63 20\\n35 26\\n54 5\\n32 56\\n56 53\\n59 46\\n37 31\\n46 8\\n4 1\\n2 47\\n59 42\\n55 11\\n62 6\\n30 7\\n60 24\\n41 36\\n34 22\\n24 34\\n21 2\\n12 52\\n8 44\\n60 21\\n24 30\\n48 35\\n48 25\\n32 57\\n20 37\\n11 54\\n11 62\\n42 58\\n31 43\\n12 23\\n55 48\\n51 55\\n41 27\\n25 33\\n21 18\\n42 12\\n4 15\\n51 60\\n62 39\\n46 41\\n57 9\\n30 61\\n31 4\\n58 13\\n34 29\\n37 32\\n18 16\\n57 45\\n2 49\\n40 51\\n43 17\\n40 20\\n20 59\\n8 19\\n58 10\\n43 63\\n54 50\\n18 14\\n25 38\\n56 28\\n35 3\\n41 36 18 28 54 22 20 6 23 38 33 52 48 44 29 56 63 4 27 50\\n\", \"4 2\\n2 3\\n2 1\\n2 4\\n3 4\\n\", \"13 11\\n4 11\\n2 7\\n4 13\\n8 12\\n8 9\\n8 6\\n3 8\\n4 1\\n2 10\\n2 5\\n3 4\\n3 2\\n10 4 5 6 1 2 3 9 13 7 12\\n\", \"7 5\\n1 5\\n4 1\\n1 3\\n7 1\\n1 6\\n1 2\\n2 4 1 3 7\\n\", \"12 9\\n11 12\\n1 10\\n1 7\\n5 6\\n8 7\\n9 8\\n4 5\\n1 4\\n2 3\\n1 2\\n10 11\\n4 9 11 3 5 12 8 6 7\\n\", \"56 34\\n7 31\\n47 6\\n13 4\\n51 29\\n13 12\\n10 52\\n10 41\\n1 47\\n47 54\\n9 1\\n4 27\\n4 40\\n49 19\\n21 26\\n24 33\\n56 49\\n41 56\\n7 23\\n41 48\\n16 34\\n35 9\\n56 51\\n5 43\\n44 46\\n10 25\\n49 2\\n1 21\\n9 32\\n33 20\\n16 5\\n5 35\\n55 50\\n55 53\\n37 44\\n43 15\\n4 55\\n8 10\\n8 24\\n21 42\\n37 8\\n39 13\\n49 38\\n39 16\\n50 3\\n55 7\\n51 45\\n21 11\\n51 28\\n50 18\\n50 30\\n5 37\\n7 17\\n35 22\\n47 36\\n35 14\\n3 38 47 22 34 10 54 50 9 52 36 1 21 29 28 6 13 39 4 40 53 51 35 55 45 18 44 20 42 31 11 46 41 12\\n\", \"26 22\\n20 16\\n2 7\\n7 19\\n5 9\\n20 23\\n22 18\\n24 3\\n8 22\\n16 10\\n5 2\\n7 15\\n22 14\\n25 4\\n25 11\\n24 13\\n8 24\\n13 1\\n20 8\\n22 6\\n7 26\\n16 12\\n16 5\\n13 21\\n25 17\\n2 25\\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\\n\", \"43 13\\n7 28\\n17 27\\n39 8\\n21 3\\n17 20\\n17 2\\n9 6\\n35 23\\n43 22\\n7 41\\n5 24\\n26 11\\n21 43\\n41 17\\n16 5\\n25 15\\n39 10\\n18 7\\n37 33\\n39 13\\n39 16\\n10 12\\n1 21\\n2 25\\n14 36\\n12 7\\n16 34\\n24 4\\n25 40\\n5 29\\n37 31\\n3 32\\n22 14\\n16 35\\n5 37\\n10 38\\n25 19\\n9 1\\n26 42\\n43 26\\n10 30\\n33 9\\n28 6 42 38 27 32 8 11 36 7 41 29 19\\n\", \"21 20\\n16 9\\n7 11\\n4 12\\n2 17\\n17 7\\n5 2\\n2 8\\n4 10\\n8 19\\n6 15\\n2 6\\n12 18\\n16 5\\n20 16\\n6 14\\n5 3\\n5 21\\n20 1\\n17 13\\n6 4\\n6 4 18 11 14 1 19 15 10 8 9 17 16 3 20 13 2 5 12 21\\n\", \"29 6\\n16 9\\n20 13\\n24 3\\n24 28\\n22 12\\n10 11\\n10 26\\n22 4\\n10 27\\n5 1\\n2 23\\n23 5\\n16 7\\n8 24\\n7 19\\n19 17\\n8 10\\n20 16\\n20 25\\n24 20\\n23 15\\n22 29\\n2 8\\n7 22\\n2 21\\n23 14\\n19 18\\n19 6\\n19 17 18 27 29 4\\n\", \"31 29\\n10 14\\n16 6\\n23 22\\n25 23\\n2 27\\n24 17\\n20 8\\n5 2\\n8 24\\n16 5\\n10 26\\n8 7\\n5 29\\n20 16\\n13 9\\n13 21\\n24 30\\n13 1\\n10 15\\n23 3\\n25 10\\n2 25\\n20 13\\n25 11\\n8 12\\n30 28\\n20 18\\n5 4\\n23 19\\n16 31\\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10\\n\", \"54 8\\n33 9\\n39 36\\n22 14\\n24 13\\n8 50\\n34 52\\n47 2\\n35 44\\n16 54\\n34 25\\n1 3\\n39 11\\n9 17\\n43 19\\n10 40\\n47 38\\n5 37\\n21 47\\n37 12\\n16 6\\n37 7\\n32 26\\n39 42\\n44 10\\n1 18\\n37 8\\n9 1\\n8 24\\n10 33\\n33 53\\n5 4\\n21 30\\n9 31\\n24 28\\n24 49\\n16 5\\n34 35\\n21 48\\n47 43\\n13 34\\n39 16\\n10 27\\n22 32\\n43 22\\n13 46\\n33 23\\n44 15\\n1 21\\n8 41\\n43 45\\n5 29\\n35 20\\n13 51\\n40 50 33 14 48 25 44 9\\n\", \"17 12\\n5 2\\n4 3\\n8 17\\n2 4\\n2 8\\n17 12\\n8 10\\n6 11\\n16 7\\n4 14\\n15 13\\n6 9\\n4 6\\n15 16\\n16 5\\n9 1\\n4 8 1 9 3 12 15 10 13 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31\\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10\\n\", \"21 20\\n16 9\\n7 11\\n4 12\\n2 17\\n17 7\\n5 2\\n2 8\\n4 10\\n8 19\\n6 15\\n2 12\\n12 18\\n16 5\\n20 16\\n6 14\\n5 3\\n5 21\\n20 1\\n17 13\\n6 4\\n6 4 18 11 14 1 19 15 10 8 9 17 16 3 20 13 2 5 12 21\\n\", \"15 7\\n5 4\\n12 5\\n7 13\\n10 11\\n3 8\\n6 12\\n3 15\\n1 3\\n5 14\\n13 9\\n1 10\\n6 1\\n12 7\\n10 2\\n4 10 8 13 1 7 9\\n\", \"17 12\\n5 2\\n7 3\\n8 17\\n2 4\\n2 8\\n17 12\\n8 10\\n6 11\\n16 7\\n4 14\\n15 13\\n6 9\\n4 6\\n15 16\\n16 5\\n9 1\\n4 8 1 9 3 12 15 10 13 6 14 16\\n\", \"5 4\\n2 3\\n2 1\\n4 5\\n4 3\\n4 2 5 1\\n\", \"10 5\\n4 5\\n9 1\\n1 2\\n7 1\\n5 1\\n10 1\\n7 3\\n6 3\\n5 8\\n5 2 7 4 1\\n\", \"5 1\\n1 2\\n2 3\\n3 4\\n3 5\\n4\\n\", \"29 6\\n16 9\\n20 13\\n24 3\\n24 28\\n22 12\\n10 11\\n10 26\\n22 4\\n10 27\\n5 1\\n2 23\\n23 5\\n16 7\\n8 24\\n7 19\\n7 17\\n8 10\\n20 16\\n20 25\\n24 20\\n23 15\\n22 29\\n2 8\\n7 22\\n2 21\\n23 14\\n19 18\\n19 6\\n19 17 18 27 29 4\\n\", \"4 2\\n1 3\\n2 1\\n2 4\\n3 4\\n\", \"19 11\\n8 9\\n10 13\\n16 15\\n6 4\\n3 2\\n17 16\\n4 7\\n1 14\\n10 11\\n15 14\\n4 3\\n10 12\\n4 5\\n2 1\\n16 19\\n8 1\\n10 9\\n18 16\\n10 14 18 12 17 11 19 8 2 3 9\\n\", \"10 9\\n2 9\\n4 8\\n10 1\\n2 3\\n5 6\\n4 3\\n1 2\\n5 4\\n6 7\\n9 1 5 8 7 3 4 6 10\\n\", \"10 3\\n10 5\\n3 2\\n5 8\\n1 5\\n10 4\\n6 1\\n9 8\\n2 9\\n7 3\\n3 10 1\\n\", \"15 2\\n7 12\\n13 11\\n6 8\\n2 15\\n10 9\\n5 1\\n13 5\\n5 4\\n14 3\\n7 9\\n8 4\\n4 7\\n12 14\\n5 2\\n7 4\\n\", \"26 22\\n20 4\\n2 7\\n7 19\\n5 9\\n20 23\\n13 18\\n24 3\\n8 22\\n16 10\\n5 2\\n7 15\\n22 14\\n25 4\\n25 11\\n24 13\\n8 24\\n13 1\\n20 8\\n22 6\\n7 26\\n16 12\\n16 5\\n13 21\\n25 17\\n2 25\\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\\n\", \"43 13\\n7 28\\n17 27\\n39 8\\n21 3\\n17 20\\n17 2\\n9 6\\n35 23\\n43 22\\n7 41\\n5 24\\n26 11\\n21 43\\n41 17\\n16 5\\n25 15\\n39 10\\n18 7\\n37 33\\n39 13\\n39 14\\n10 12\\n1 21\\n2 25\\n14 36\\n12 7\\n16 34\\n24 4\\n25 40\\n5 29\\n7 31\\n3 32\\n22 14\\n16 35\\n5 37\\n10 38\\n25 19\\n9 1\\n26 42\\n43 26\\n10 30\\n33 9\\n28 6 42 38 27 32 8 11 36 7 41 29 19\\n\", \"53 30\\n41 42\\n27 24\\n13 11\\n10 11\\n32 33\\n34 33\\n37 40\\n21 22\\n21 20\\n46 47\\n2 1\\n31 30\\n29 30\\n11 14\\n42 43\\n50 51\\n34 35\\n36 35\\n24 23\\n48 47\\n41 1\\n28 29\\n45 44\\n16 15\\n5 4\\n6 5\\n18 19\\n9 8\\n37 38\\n11 12\\n39 37\\n49 48\\n50 49\\n43 44\\n50 53\\n3 4\\n50 52\\n24 25\\n7 6\\n46 45\\n2 3\\n17 18\\n31 32\\n19 20\\n7 8\\n15 1\\n36 37\\n23 22\\n9 10\\n17 16\\n24 26\\n28 1\\n38 52 41 35 53 43 3 29 36 4 23 20 46 6 40 30 49 25 16 48 17 18 21 9 45 44 15 13 14 2\\n\", \"53 30\\n41 42\\n27 24\\n13 11\\n10 11\\n32 33\\n34 33\\n37 40\\n21 22\\n21 20\\n46 47\\n2 1\\n31 30\\n29 30\\n18 14\\n42 43\\n50 51\\n34 35\\n36 35\\n24 23\\n48 47\\n41 1\\n28 29\\n45 44\\n16 15\\n5 4\\n6 5\\n18 19\\n9 8\\n37 38\\n11 12\\n39 37\\n49 48\\n50 49\\n43 44\\n50 53\\n3 4\\n50 52\\n24 25\\n7 6\\n46 45\\n2 3\\n17 18\\n31 32\\n19 20\\n7 8\\n15 1\\n36 37\\n23 22\\n9 10\\n17 16\\n24 26\\n28 1\\n38 52 41 35 53 43 3 29 36 4 23 20 46 6 40 30 49 25 16 48 17 18 21 9 45 44 15 13 14 2\\n\", \"10 4\\n2 3\\n4 2\\n8 9\\n6 5\\n8 1\\n5 2\\n9 10\\n7 5\\n1 2\\n4 10 2 5\\n\", \"7 2\\n1 2\\n1 3\\n1 4\\n3 5\\n3 6\\n3 7\\n2 7\\n\", \"6 4\\n1 2\\n2 3\\n2 4\\n4 5\\n4 6\\n2 4 5 6\\n\"], \"outputs\": [\"2\\n3\\n\", \"2\\n4\\n\", \"1\\n0\\n\", \"1\\n0\\n\", \"6\\n1\\n\", \"4\\n1\\n\", \"12\\n1\\n\", \"3\\n1\\n\", \"3\\n6\\n\", \"1\\n16\\n\", \"3\\n53\\n\", \"1\\n5\\n\", \"1\\n8\\n\", \"4\\n14\\n\", \"4\\n34\\n\", \"6\\n66\\n\", \"3\\n2\\n\", \"1\\n18\\n\", \"2\\n6\\n\", \"6\\n16\\n\", \"3\\n70\\n\", \"1\\n37\\n\", \"19\\n41\\n\", \"1\\n32\\n\", \"4\\n16\\n\", \"3\\n46\\n\", \"14\\n21\\n\", \"1\\n20\\n\", \"27\\n13\\n\", \"7\\n11\\n\", \"5\\n6\\n\", \"11\\n18\\n\", \"12\\n21\\n\", \"3\\n1\\n\", \"13\\n74\\n\", \"4\\n6\\n\", \"2\\n6\\n\", \"4\\n6\\n\", \"1\\n5\\n\", \"4\\n0\\n\", \"1\\n5\", \"1\\n16\", \"3\\n6\", \"4\\n1\", \"3\\n46\", \"1\\n18\", \"1\\n32\", \"5\\n6\", \"1\\n37\", \"1\\n0\", \"12\\n21\", \"4\\n14\", \"1\\n20\", \"19\\n41\", \"12\\n1\", \"3\\n1\", \"6\\n66\", \"4\\n34\", \"3\\n70\", \"1\\n8\", \"13\\n74\", \"1\\n5\", \"2\\n6\", \"4\\n0\", \"6\\n16\", \"3\\n53\", \"14\\n21\", \"4\\n16\", \"6\\n1\", \"27\\n13\", \"2\\n6\", \"4\\n6\", \"3\\n2\", \"3\\n1\", \"1\\n0\", \"4\\n6\", \"11\\n18\", \"7\\n11\\n\", \"3\\n7\\n\", \"4\\n1\\n\", \"1\\n36\\n\", \"12\\n21\\n\", \"1\\n20\\n\", \"4\\n7\\n\", \"7\\n10\\n\", \"1\\n7\\n\", \"5\\n17\\n\", \"1\\n37\\n\", \"29\\n14\\n\", \"19\\n40\\n\", \"13\\n72\\n\", \"6\\n14\\n\", \"14\\n26\\n\", \"20\\n13\\n\", \"3\\n1\\n\", \"2\\n0\\n\", \"6\\n22\\n\", \"29\\n16\\n\", \"6\\n37\\n\", \"3\\n46\\n\", \"1\\n32\\n\", \"8\\n13\\n\", \"1\\n22\\n\", \"1\\n4\\n\", \"2\\n5\\n\", \"4\\n0\\n\", \"4\\n16\\n\", \"3\\n3\\n\", \"11\\n18\\n\", \"7\\n11\\n\", \"1\\n7\\n\", \"4\\n1\\n\", \"1\\n36\\n\", \"19\\n40\\n\", \"13\\n72\\n\", \"13\\n72\\n\", \"4\\n7\\n\", \"2\\n3\", \"2\\n4\"]}", "source": "taco"}
|
Ari the monster is not an ordinary monster. She is the hidden identity of Super M, the Byteforces’ superhero. Byteforces is a country that consists of n cities, connected by n - 1 bidirectional roads. Every road connects exactly two distinct cities, and the whole road system is designed in a way that one is able to go from any city to any other city using only the given roads. There are m cities being attacked by humans. So Ari... we meant Super M have to immediately go to each of the cities being attacked to scare those bad humans. Super M can pass from one city to another only using the given roads. Moreover, passing through one road takes her exactly one kron - the time unit used in Byteforces. [Image]
However, Super M is not on Byteforces now - she is attending a training camp located in a nearby country Codeforces. Fortunately, there is a special device in Codeforces that allows her to instantly teleport from Codeforces to any city of Byteforces. The way back is too long, so for the purpose of this problem teleportation is used exactly once.
You are to help Super M, by calculating the city in which she should teleport at the beginning in order to end her job in the minimum time (measured in krons). Also, provide her with this time so she can plan her way back to Codeforces.
-----Input-----
The first line of the input contains two integers n and m (1 ≤ m ≤ n ≤ 123456) - the number of cities in Byteforces, and the number of cities being attacked respectively.
Then follow n - 1 lines, describing the road system. Each line contains two city numbers u_{i} and v_{i} (1 ≤ u_{i}, v_{i} ≤ n) - the ends of the road i.
The last line contains m distinct integers - numbers of cities being attacked. These numbers are given in no particular order.
-----Output-----
First print the number of the city Super M should teleport to. If there are many possible optimal answers, print the one with the lowest city number.
Then print the minimum possible time needed to scare all humans in cities being attacked, measured in Krons.
Note that the correct answer is always unique.
-----Examples-----
Input
7 2
1 2
1 3
1 4
3 5
3 6
3 7
2 7
Output
2
3
Input
6 4
1 2
2 3
2 4
4 5
4 6
2 4 5 6
Output
2
4
-----Note-----
In the first sample, there are two possibilities to finish the Super M's job in 3 krons. They are:
$2 \rightarrow 1 \rightarrow 3 \rightarrow 7$ and $7 \rightarrow 3 \rightarrow 1 \rightarrow 2$.
However, you should choose the first one as it starts in the city with the lower number.
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\\n1 4 6\\n\", \"4\\n2 3 6 6\\n\", \"3\\n6 15 10\\n\", \"4\\n2 3 5 7\\n\", \"6\\n10 8 75 6 7 35\\n\", \"1\\n1\\n\", \"2\\n1 1\\n\", \"2\\n8 32\\n\", \"1\\n97969\\n\", \"2\\n313 313\\n\", \"2\\n97969 97969\\n\", \"8\\n6 15 35 77 143 221 34 26\\n\", \"1\\n998\\n\", \"3\\n2 2 2\\n\", \"2\\n313 313\\n\", \"1\\n97969\\n\", \"6\\n10 8 75 6 7 35\\n\", \"2\\n8 32\\n\", \"3\\n2 2 2\\n\", \"1\\n998\\n\", \"1\\n1\\n\", \"8\\n6 15 35 77 143 221 34 26\\n\", \"2\\n97969 97969\\n\", \"2\\n1 1\\n\", \"6\\n19 8 75 6 7 35\\n\", \"2\\n8 55\\n\", \"3\\n3 2 2\\n\", \"2\\n97969 150417\\n\", \"8\\n6 11 35 129 143 221 3 51\\n\", \"1\\n1636\\n\", \"8\\n6 15 35 129 143 221 34 26\\n\", \"2\\n2 1\\n\", \"3\\n12 15 10\\n\", \"4\\n2 3 6 7\\n\", \"4\\n2 3 5 12\\n\", \"3\\n1 4 5\\n\", \"6\\n19 8 75 6 7 5\\n\", \"2\\n8 62\\n\", \"3\\n4 2 2\\n\", \"8\\n6 15 35 129 143 221 3 26\\n\", \"2\\n2 2\\n\", \"3\\n7 15 10\\n\", \"4\\n2 3 6 12\\n\", \"3\\n1 4 10\\n\", \"6\\n19 8 85 6 7 5\\n\", \"2\\n8 111\\n\", \"8\\n6 15 35 129 143 221 3 51\\n\", \"2\\n1 2\\n\", \"3\\n7 18 10\\n\", \"4\\n2 2 6 12\\n\", \"3\\n1 8 10\\n\", \"6\\n19 8 122 6 7 5\\n\", \"2\\n8 011\\n\", \"3\\n7 34 10\\n\", \"4\\n2 2 2 12\\n\", \"3\\n1 8 17\\n\", \"6\\n19 15 122 6 7 5\\n\", \"2\\n4 111\\n\", \"8\\n6 11 35 129 143 11 3 51\\n\", \"3\\n7 22 10\\n\", \"4\\n2 2 4 12\\n\", \"3\\n1 3 17\\n\", \"3\\n6 15 10\\n\", \"4\\n2 3 6 6\\n\", \"4\\n2 3 5 7\\n\", \"3\\n1 4 6\\n\"], \"outputs\": [\"1\", \"2\", \"3\", \"-1\", \"3\", \"1\", \"1\", \"2\", \"1\", \"2\", \"1\", \"3\", \"-1\", \"2\", \"2\", \"1\", \"3\", \"2\", \"2\", \"-1\", \"1\", \"3\", \"1\", \"1\", \"3\\n\", \"-1\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"-1\\n\", \"3\\n\", \"1\\n\", \"-1\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"3\\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\", \"2\\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\", \"3\", \"2\", \"-1\", \"1\"]}", "source": "taco"}
|
You are given an array $a$ of length $n$ that has a special condition: every element in this array has at most 7 divisors. Find the length of the shortest non-empty subsequence of this array product of whose elements is a perfect square.
A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 10^5$) — the length of $a$.
The second line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_{n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$.
-----Output-----
Output the length of the shortest non-empty subsequence of $a$ product of whose elements is a perfect square. If there are several shortest subsequences, you can find any of them. If there's no such subsequence, print "-1".
-----Examples-----
Input
3
1 4 6
Output
1
Input
4
2 3 6 6
Output
2
Input
3
6 15 10
Output
3
Input
4
2 3 5 7
Output
-1
-----Note-----
In the first sample, you can choose a subsequence $[1]$.
In the second sample, you can choose a subsequence $[6, 6]$.
In the third sample, you can choose a subsequence $[6, 15, 10]$.
In the fourth sample, there is no such subsequence.
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
|
{"tests": "{\"inputs\": [\"5 3 6 9\\n9 1 5 3 1\", \"21 10 0 4\\n5 2 13 -1 0\", \"21 7 1 4\\n0 2 23 -1 2\", \"9 3 1 9\\n22 2 6 2 0\", \"21 14 1 4\\n2 2 0 -1 2\", \"5 3 6 9\\n9 1 6 3 1\", \"8 3 6 9\\n9 1 6 3 1\", \"8 3 6 9\\n15 1 6 3 1\", \"8 3 6 9\\n15 0 6 3 1\", \"8 3 6 9\\n22 0 6 3 1\", \"11 3 6 9\\n22 0 6 3 1\", \"11 3 6 9\\n22 0 6 2 1\", \"11 3 6 9\\n22 0 6 2 0\", \"9 3 6 9\\n22 0 6 2 0\", \"9 3 6 9\\n11 0 6 2 0\", \"9 3 5 9\\n22 0 6 2 0\", \"9 3 5 9\\n22 1 6 2 0\", \"9 3 5 9\\n22 2 6 2 0\", \"9 3 5 9\\n22 2 6 2 1\", \"9 3 5 9\\n22 2 6 0 1\", \"16 3 5 9\\n22 2 6 0 1\", \"29 3 5 9\\n22 2 6 0 1\", \"29 3 5 9\\n14 2 6 0 1\", \"29 3 5 9\\n14 2 6 0 0\", \"29 3 5 1\\n14 2 6 0 0\", \"29 3 10 1\\n14 2 6 0 0\", \"29 3 10 0\\n14 2 6 0 0\", \"9 3 10 0\\n14 2 6 0 0\", \"9 3 10 0\\n24 2 6 0 0\", \"9 6 10 0\\n24 2 6 0 0\", \"9 6 10 0\\n24 2 6 0 1\", \"11 6 10 0\\n24 2 6 0 1\", \"11 6 10 0\\n24 2 4 0 1\", \"11 6 10 0\\n24 1 4 0 1\", \"16 6 10 0\\n24 1 4 0 1\", \"16 6 10 -1\\n24 1 4 0 1\", \"16 6 10 -1\\n24 1 4 0 0\", \"16 6 10 -1\\n24 1 4 -1 0\", \"16 6 10 -1\\n24 1 5 -1 0\", \"16 6 10 0\\n24 1 5 -1 0\", \"16 6 10 0\\n40 1 5 -1 0\", \"16 6 10 0\\n30 1 5 -1 0\", \"16 6 10 0\\n30 1 8 -1 0\", \"16 4 10 0\\n30 1 8 -1 0\", \"16 4 10 0\\n30 1 8 -1 1\", \"16 4 10 1\\n30 1 8 -1 1\", \"16 4 10 1\\n30 1 8 -1 0\", \"16 4 3 1\\n30 1 8 -1 0\", \"16 4 3 1\\n30 1 7 -1 0\", \"16 4 3 2\\n30 1 7 -1 0\", \"16 4 3 4\\n30 1 7 -1 0\", \"16 4 3 4\\n30 2 7 -1 0\", \"16 4 3 4\\n30 2 7 -2 0\", \"16 4 3 4\\n5 2 7 -1 0\", \"16 6 3 4\\n5 2 7 -1 0\", \"16 8 3 4\\n5 2 7 -1 0\", \"16 8 3 4\\n5 2 13 -1 0\", \"21 8 3 4\\n5 2 13 -1 0\", \"21 10 3 4\\n5 2 13 -1 0\", \"21 11 0 4\\n5 2 13 -1 0\", \"21 11 0 4\\n5 2 13 -1 1\", \"21 11 0 4\\n5 2 13 -1 2\", \"21 11 0 4\\n9 2 13 -1 2\", \"21 11 1 4\\n9 2 13 -1 2\", \"21 7 1 4\\n9 2 13 -1 2\", \"21 7 1 4\\n9 2 23 -1 2\", \"21 7 1 4\\n17 2 23 -1 2\", \"21 10 1 4\\n0 2 23 -1 2\", \"21 10 1 4\\n0 1 23 -1 2\", \"21 10 1 4\\n1 1 23 -1 2\", \"21 10 1 4\\n1 2 23 -1 2\", \"21 10 1 4\\n1 2 34 -1 2\", \"21 10 1 4\\n1 2 60 -1 2\", \"21 10 1 4\\n1 2 60 -1 0\", \"21 10 1 4\\n1 2 66 -1 0\", \"21 4 1 4\\n1 2 66 -1 0\", \"21 4 1 4\\n0 2 66 -1 0\", \"21 4 2 4\\n0 2 66 -1 0\", \"21 6 2 4\\n0 2 66 -1 0\", \"21 6 2 4\\n-1 2 66 -1 0\", \"21 6 2 4\\n-1 2 3 -1 0\", \"21 6 2 4\\n-1 2 3 -1 1\", \"21 6 2 4\\n-1 2 3 -1 2\", \"21 4 2 4\\n-1 2 3 -1 2\", \"21 4 1 4\\n-1 2 3 -1 2\", \"21 4 1 1\\n-1 2 3 -1 2\", \"21 4 1 1\\n0 2 3 -1 2\", \"21 2 1 1\\n0 2 3 -1 2\", \"21 2 1 1\\n0 4 3 -1 2\", \"21 2 1 1\\n1 4 3 -1 2\", \"21 2 0 1\\n1 4 3 -1 2\", \"21 1 0 1\\n1 4 3 -1 2\", \"21 1 0 2\\n1 4 3 -1 2\", \"2 3 6 9\\n9 7 5 3 1\", \"5 3 6 8\\n9 1 5 3 1\", \"5 3 11 9\\n9 1 6 3 1\", \"8 3 6 9\\n15 1 6 6 1\", \"8 3 6 9\\n15 1 6 3 0\", \"8 3 6 8\\n15 0 6 3 1\", \"8 3 6 9\\n22 0 4 3 1\", \"5 3 6 9\\n9 7 5 3 1\"], \"outputs\": [\"1\\n\", \"3\\n\", \"0\\n\", \"4\\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\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\"]}", "source": "taco"}
|
Problem statement
AOR Ika got a cabbage with $ N $ leaves. The leaves of this cabbage are numbered $ 1, \ ldots, N $ in order from the outside, and the dirtiness of the $ i $ th leaf is $ D_i $. The larger this value is, the worse the degree of dirt is. AOR Ika-chan decided to use the cabbage leaves for cooking, so she decided to select the dirty leaves to be discarded according to the following procedure.
1. Initialize the discard candidates to empty.
2. Focus on the outermost leaves that have not yet been examined. If all the items have been checked, the process ends.
3. If the leaf is dirty for $ A $ or more, add it to the discard candidate and return to 2. Otherwise it ends.
However, as a result of this operation, I noticed that the number of leaves that can be used for cooking may be extremely reduced. Therefore, I decided to reconsider the leaves to be discarded after the above operation and perform the following operations.
1. If there are less than $ M $ leaves that are not candidates for disposal, proceed to 2. Otherwise it ends.
2. Focus on the innermost leaf that has not been examined yet among the leaves that are candidates for disposal. If there are no leaves that are candidates for disposal, the process ends.
3. If the leaf is less than $ B $, remove it from the discard candidates and return to 2. Otherwise, discard all the leaves remaining in the discard candidates and finish.
When you perform these operations, find the number of leaves to be finally discarded.
Input constraints
$ 1 \ leq N \ leq 1000 $
$ 0 \ leq M \ leq N $
$ 1 \ leq A \ leq B \ leq 1000 $
$ 1 \ leq D_ {i} \ leq 1000 $
sample
Sample input 1
5 3 6 9
9 7 5 3 1
Sample output 1
2
Discard the first and second sheets.
Sample input 2
5 3 6 9
5 4 3 2 1
Sample output 2
0
Do not throw away from the first piece.
Sample input 3
5 3 6 9
10 8 6 4 2
Sample output 3
1
I tried to throw away the third one, but I reconsidered and decided not to throw away the second and third ones.
Sample input 4
5 3 6 9
5 10 8 6 4
Sample output 4
0
AOR Ika doesn't know that the second piece is dirty.
Sample input 5
5 0 6 9
9 9 8 8 7
Sample output 5
Five
I don't mind throwing everything away.
input
$ N \ M \ A \ B $
$ D_ {1} \ D_ {2} \ \ cdots \ D_ {N} $
output
Output the number of leaves to be finally thrown away.
Example
Input
5 3 6 9
9 7 5 3 1
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\": [[\"hello world!\", \" |\"], [\"hello world!\", \"o|rl\"], [\"hello world!\", \"ello| \"], [\"hello world!\", \"hello wo|rld!\"], [\"hello world!\", \"h|ello world!\"], [\"hello world! hello world!\", \" |\"], [\"hello world! hello world!\", \"o|rl\"], [\"hello world! hello world!\", \"ello| \"], [\"hello world! hello world!\", \"hello wo|rld!\"], [\"hello hello hello\", \" | \"], [\" hello world\", \" |\"], [\"aaaa\", \"|aa\"], [\"aaa\", \"|aa\"], [\"aaaaa\", \"|aa\"], [\"ababa\", \"|ab\"], [\"abababa\", \"|ab\"], [\"abababa\", \"|a\"], [\" hello hello hello\", \" |\"], [\"aaaa\", \"aa|\"], [\" hello hello hello \", \" |\"], [\"aaaaaa\", \"aa|\"], [\"hello hello hello \", \"| \"], [\"aaaaaa\", \"|aa\"], [\" hello hello hello\", \"| \"], [\"aaaaaaaa\", \"|aa\"]], \"outputs\": [[[\"hello \", \"world!\"]], [[\"hello wo\", \"rld!\"]], [[\"hello\", \" world!\"]], [[\"hello wo\", \"rld!\"]], [[\"h\", \"ello world!\"]], [[\"hello \", \"world! \", \"hello \", \"world!\"]], [[\"hello wo\", \"rld! hello wo\", \"rld!\"]], [[\"hello\", \" world! hello\", \" world!\"]], [[\"hello wo\", \"rld! hello wo\", \"rld!\"]], [[\"hello \", \" hello \", \" hello\"]], [[\" \", \"hello \", \"world\"]], [[\"aa\", \"aa\"]], [[\"aaa\"]], [[\"aa\", \"aaa\"]], [[\"ab\", \"aba\"]], [[\"ab\", \"ab\", \"aba\"]], [[\"ab\", \"ab\", \"ab\", \"a\"]], [[\" \", \" \", \"hello \", \"hello \", \"hello\"]], [[\"aa\", \"aa\"]], [[\" \", \" \", \"hello \", \"hello \", \"hello \", \" \"]], [[\"aa\", \"aa\", \"aa\"]], [[\"hello\", \" hello\", \" hello\", \" \"]], [[\"aa\", \"aa\", \"aa\"]], [[\" \", \" hello\", \" hello\", \" hello\"]], [[\"aa\", \"aa\", \"aa\", \"aa\"]]]}", "source": "taco"}
|
Most languages have a `split` function that lets you turn a string like `“hello world”` into an array like`[“hello”, “world”]`. But what if we don't want to lose the separator? Something like `[“hello”, “ world”]`.
#### Task:
Your job is to implement a function, (`split_without_loss` in Ruby/Crystal, and `splitWithoutLoss` in JavaScript/CoffeeScript), that takes two arguments, `str` (`s` in Python), and `split_p`, and returns the string, split by `split_p`, but with the separator intact. There will be one '|' marker in `split_p`. `str` or `s` will never have a '|' in it. All the text before the marker is moved to the first string of the split, while all the text that is after it is moved to the second one. **Empty strings must be removed from the output, and the input should NOT be modified.**
When tests such as `(str = "aaaa", split_p = "|aa")` are entered, do not split the string on overlapping regions. For this example, return `["aa", "aa"]`, not `["aa", "aa", "aa"]`.
#### Examples (see example test cases for more):
```python
split_without_loss("hello world!", " |") #=> ["hello ", "world!"]
split_without_loss("hello world!", "o|rl") #=> ["hello wo", "rld!"]
split_without_loss("hello world!", "h|ello world!") #=> ["h", "ello world!"]
split_without_loss("hello world! hello world!", " |")
#=> ["hello ", "world! ", "hello ", "world!"]
split_without_loss("hello world! hello world!", "o|rl")
#=> ["hello wo", "rld! hello wo", "rld!"]
split_without_loss("hello hello hello", " | ")
#=> ["hello ", " hello ", " hello"]
split_without_loss(" hello world", " |")
#=> [" ", "hello ", "world"]
split_without_loss(" hello hello hello", " |")
#=> [" ", " ", "hello ", "hello ", "hello"]
split_without_loss(" hello hello hello ", " |")
#=> [" ", " ", "hello ", "hello ", "hello ", " "]
split_without_loss(" hello hello hello", "| ")
#=> [" ", " hello", " hello", " hello"]
```
Also check out my other creations — [Identify Case](https://www.codewars.com/kata/identify-case), [Adding Fractions](https://www.codewars.com/kata/adding-fractions),
[Random Integers](https://www.codewars.com/kata/random-integers), [Implement String#transpose](https://www.codewars.com/kata/implement-string-number-transpose), [Implement Array#transpose!](https://www.codewars.com/kata/implement-array-number-transpose), [Arrays and Procs #1](https://www.codewars.com/kata/arrays-and-procs-number-1), and [Arrays and Procs #2](https://www.codewars.com/kata/arrays-and-procs-number-2)
If you notice any issues/bugs/missing test cases whatsoever, do not hesitate to report an issue or suggestion. Enjoy!
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, 10, 9, 3]], [[3, 4, 5, 7]], [[0, 2, 19, 4, 4]], [[3, 2, 1, 0]], [[3, 2, 10, 4, 1, 6]], [[1, 1, 8, 3, 1, 1]], [[0, 1, 2, 3]], [[1, 2, 3, 4]], [[0, -1, 1]], [[0, 2, 3]], [[0]], [[]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], [[0, 1, 3, -2, 5, 4]], [[0, -1, -2, -3, -4]], [[1, -1, 3]], [[1, -1, 2, -2, 3, -3, 6]], [[2, 2, 3, 3, 3]], [[1, 1, 1, 2, 1, 1]]], \"outputs\": [[true], [false], [false], [true], [false], [false], [true], [true], [true], [false], [false], [false], [true], [false], [true], [false], [false], [true], [true]]}", "source": "taco"}
|
A `Nice array` is defined to be an array where for every value `n` in the array, there is also an element `n-1` or `n+1` in the array.
example:
```
[2,10,9,3] is Nice array because
2=3-1
10=9+1
3=2+1
9=10-1
```
Write a function named `isNice`/`IsNice` that returns `true` if its array argument is a Nice array, else `false`. You should also return `false` if `input` array has `no` elements.
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, [0, 0]], [2, [1, 0]], [2, [1, 1]], [3, [1, 0]], [5, [4, 0]], [6, [5, 0]], [7, [6, 0]]], \"outputs\": [[0], [2], [1], [3], [70], [252], [924]]}", "source": "taco"}
|
Happy traveller [Part 1]
There is a play grid NxN; Always square!
0 1 2 3
0 [o, o, o, X]
1 [o, o, o, o]
2 [o, o, o, o]
3 [o, o, o, o]
You start from a random point. I mean, you are given the coordinates of your start position in format (row, col).
And your TASK is to define the number of unique paths to reach position X (always in the top right corner).
From any point you can go only UP or RIGHT.
Implement a function count_paths(N, (row, col)) which returns int;
Assume input params are always valid.
Example:
count_paths(1, (0, 0))
grid 1x1:
[X]
You are already in the target point, so return 0
count_paths(2, (1, 0))
grid 2x2:
[o, X]
[@, o]
You are at point @; you can move UP-RIGHT or RIGHT-UP, and there are 2 possible unique paths here
count_paths(2, (1, 1))
grid 2x2:
[o, X]
[o, @]
You are at point @; you can move only UP, so there is 1 possible unique path here
count_paths(3, (1, 0))
grid 3x3:
[o, o, X]
[@, o, o]
[o, o, o]
You are at point @; you can move UP-RIGHT-RIGHT or RIGHT-UP-RIGHT, or RIGHT-RIGHT-UP, and there are 3 possible unique paths here
I think it's pretty clear =)
btw. you can use preloaded Grid class, which constructs 2d array for you. It's very very basic and simple. You can use numpy instead or any other way to produce the correct answer =)
grid = Grid(2, 2, 0)
samegrid = Grid.square(2) will give you a grid[2][2], which you can print easily to console.
print(grid)
[0, 0]
[0, 0]
Enjoy!
You can continue adventures:
Happy traveller [Part 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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7 8 4 4 8 8 8 8 8 10 10 11\\n\", \"100\\n1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 4 4 4 4 6 8 8 8 8 8 8 8 10 16 16 16 16 16 16 16 17 22 24 24 30 32 32 32 46 32 32 48 62 64 64 65 65 67 70 74 88 89 98 99 101 101 109 121 127 128 128 137 143 152 153 155 156 160 161 114 183 186 196 196 214 220 226 228 230 238 240 241 245 249 249 250 253 254 256 256 512 1024 1703\\n\", \"2\\n1 1001001000000\\n\", \"41\\n1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 448720 2097152 5532714 8388608 16777216 33554432 67108864 134217728 268435456 536870912 1073741824 2147483648 4294967296 8589934592 17179869184 34359738368 68719476736 137438953472 274877906944 549755813888 1000000000000\\n\", \"25\\n1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8 13 15 16 16 59 32 36 41 76\\n\", \"25\\n2 1 1 1 2 2 2 2 4 4 4 4 8 8 8 9 16 16 32 40 43 53 61 65 128\\n\", \"1\\n14\\n\", \"20\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3\\n\", \"1\\n1000011010000\\n\", \"96\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 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2 2 2 2 4 4 4 4 8 8 8 9 16 16 32 40 43 53 61 65 128\\n\", \"1\\n16\\n\", \"1\\n1000001010000\\n\", \"96\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 9 12 12 16 16 16 32 16 16 16 16 16 16 16 16 16 16 14 16 16 16 16 16 16 16 16 16 16 18 9\\n\", \"100\\n1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 4 4 4 6 6 8 8 8 8 8 8 8 10 16 16 16 16 16 16 16 17 22 24 24 30 32 32 32 46 32 32 48 62 64 108 65 65 67 70 74 88 89 98 99 101 101 109 121 127 128 128 137 143 152 153 155 156 160 161 114 183 186 196 196 214 220 226 228 230 238 240 241 245 249 249 250 253 254 256 256 512 1024 1703\\n\", \"2\\n2 1001001000001\\n\", \"41\\n1 2 4 8 16 32 64 128 256 512 1135 2048 4096 8192 16384 32768 65536 131072 262144 524288 448720 2097152 5532714 8388608 16777216 33554432 67108864 210318214 268435456 536870912 1073741824 2147483648 4294967296 8589934592 17179869184 34359738368 68719476736 137438953472 274877906944 549755813888 1000000000000\\n\", \"25\\n1 1 1 1 2 2 2 2 2 4 7 4 8 8 8 8 13 15 16 16 59 32 36 41 76\\n\", \"25\\n2 1 1 2 2 2 2 2 4 4 4 4 8 8 8 9 16 16 32 40 43 53 61 65 108\\n\", \"1\\n23\\n\", \"96\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 6 4 4 4 4 4 4 4 4 4 4 4 4 7 4 8 8 8 8 8 8 8 8 8 8 8 9 12 12 16 16 16 32 16 16 16 16 16 16 16 16 16 16 14 16 16 16 16 16 16 16 16 16 16 18 9\\n\", \"100\\n1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 4 4 4 6 6 8 8 8 8 8 8 8 10 16 16 16 16 16 16 16 17 22 24 24 30 32 32 32 46 32 32 48 62 64 108 65 65 67 70 74 88 89 98 99 101 101 109 121 127 128 128 137 143 152 153 155 156 160 161 114 183 186 196 196 214 220 226 228 230 238 240 241 245 249 285 250 253 254 256 256 512 1024 1703\\n\", \"2\\n2 1001001001001\\n\", \"41\\n1 2 4 8 16 32 64 128 256 512 1135 2048 4096 8192 16384 32768 65536 131072 262144 524288 448720 2097152 5532714 8388608 16777216 33554432 67108864 210318214 268435456 536870912 1073741824 2147483648 4294967296 13664105971 17179869184 34359738368 68719476736 137438953472 274877906944 549755813888 1000000000000\\n\", \"25\\n1 1 1 1 2 2 2 2 2 4 7 4 8 8 8 8 13 15 16 16 114 32 36 41 76\\n\", \"25\\n2 1 1 2 2 2 2 2 4 4 4 4 8 8 8 9 16 16 32 40 43 26 61 65 108\\n\", \"1\\n6\\n\", \"96\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 6 4 4 4 4 2 4 4 4 4 4 4 4 7 4 8 8 8 8 8 8 8 8 8 8 8 9 12 12 16 16 16 32 16 16 16 16 16 16 16 16 16 16 14 16 16 16 16 16 16 16 16 16 16 18 9\\n\", \"100\\n1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 4 4 4 6 6 8 8 8 8 8 8 8 10 16 16 16 16 16 16 16 17 22 24 24 30 32 32 32 41 32 32 48 62 64 108 65 65 67 70 74 88 89 98 99 101 101 109 121 127 128 128 137 143 152 153 155 156 160 161 114 183 186 196 196 214 220 226 228 230 238 240 241 245 249 285 250 253 254 256 256 512 1024 1703\\n\", \"2\\n4 1001001001001\\n\", \"41\\n1 2 4 8 16 32 64 128 256 512 1135 2048 4096 8192 16384 32768 65536 131072 262144 524288 448720 2097152 5532714 8388608 16777216 33554432 67108864 210318214 268435456 536870912 1073741824 2147483648 422949348 13664105971 17179869184 34359738368 68719476736 137438953472 274877906944 549755813888 1000000000000\\n\", \"25\\n2 1 1 2 2 2 2 2 4 4 4 4 8 8 8 9 19 16 32 40 43 26 61 65 108\\n\", \"1\\n11\\n\", \"96\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 6 4 4 4 4 2 4 4 4 4 4 4 4 7 4 8 8 8 8 8 8 8 8 7 8 8 9 12 12 16 16 16 32 16 16 16 16 16 16 16 16 16 16 14 16 16 16 16 16 16 16 16 16 16 18 9\\n\", \"100\\n1 1 1 1 2 1 1 2 2 2 2 2 2 2 4 4 4 4 4 4 6 6 8 8 8 8 8 8 8 10 16 16 16 16 16 16 16 17 22 24 24 30 32 32 32 41 32 32 48 62 64 108 65 65 67 70 74 88 89 98 99 101 101 109 121 127 128 128 137 143 152 153 155 156 160 161 114 183 186 196 196 214 220 226 228 230 238 240 241 245 249 285 250 253 254 256 256 512 1024 1703\\n\", \"41\\n1 2 4 8 16 32 64 128 256 512 1135 2048 4096 8192 16384 32768 65536 211460 262144 524288 448720 2097152 5532714 8388608 16777216 33554432 67108864 210318214 268435456 536870912 1073741824 2147483648 422949348 13664105971 17179869184 34359738368 68719476736 137438953472 274877906944 549755813888 1000000000000\\n\", \"5\\n1 2 4 4 4\\n\", \"6\\n1 1 1 2 2 2\\n\", \"8\\n1 1 2 2 3 4 5 8\\n\"], \"outputs\": [\"1\\n\", \"9 10 11 12 13 14 15 16 17\\n\", \"-1\\n\", \"-1\\n\", \"1 2\\n\", \"-1\\n\", \"11 12\\n\", \"4\\n\", \"1\\n\", \"5\\n\", \"-1\\n\", \"1 2\\n\", \"-1\\n\", \"1\\n\", \"27 28 29 30 31 32 33 34 35 36 37 38\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"9 10 11 12 13 14 15 16 17 18\\n\", \"11 12\\n\", \"9 10 11 12 13 14 15 16 17\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-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 3\\n\", \"2\\n\"]}", "source": "taco"}
|
It can be shown that any positive integer x can be uniquely represented as x = 1 + 2 + 4 + ... + 2k - 1 + r, where k and r are integers, k ≥ 0, 0 < r ≤ 2k. Let's call that representation prairie partition of x.
For example, the prairie partitions of 12, 17, 7 and 1 are:
12 = 1 + 2 + 4 + 5,
17 = 1 + 2 + 4 + 8 + 2,
7 = 1 + 2 + 4,
1 = 1.
Alice took a sequence of positive integers (possibly with repeating elements), replaced every element with the sequence of summands in its prairie partition, arranged the resulting numbers in non-decreasing order and gave them to Borys. Now Borys wonders how many elements Alice's original sequence could contain. Find all possible options!
Input
The first line contains a single integer n (1 ≤ n ≤ 105) — the number of numbers given from Alice to Borys.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1012; a1 ≤ a2 ≤ ... ≤ an) — the numbers given from Alice to Borys.
Output
Output, in increasing order, all possible values of m such that there exists a sequence of positive integers of length m such that if you replace every element with the summands in its prairie partition and arrange the resulting numbers in non-decreasing order, you will get the sequence given in the input.
If there are no such values of m, output a single integer -1.
Examples
Input
8
1 1 2 2 3 4 5 8
Output
2
Input
6
1 1 1 2 2 2
Output
2 3
Input
5
1 2 4 4 4
Output
-1
Note
In the first example, Alice could get the input sequence from [6, 20] as the original sequence.
In the second example, Alice's original sequence could be either [4, 5] or [3, 3, 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\": [\"6\\n12345\\n54321\\n10901\\n211011\\n7\\n90\", \"6\\n12345\\n43634\\n10901\\n211011\\n7\\n90\", \"6\\n12345\\n43634\\n21427\\n211011\\n7\\n90\", \"6\\n12345\\n43634\\n21427\\n211011\\n7\\n166\", \"6\\n23325\\n43634\\n21427\\n211011\\n7\\n166\", \"6\\n23325\\n43634\\n21427\\n211011\\n1\\n166\", \"6\\n1466\\n43634\\n21427\\n211011\\n1\\n166\", \"6\\n1466\\n20536\\n21427\\n211011\\n1\\n166\", \"6\\n1466\\n20536\\n14761\\n211011\\n1\\n166\", \"6\\n1466\\n20536\\n14761\\n211011\\n2\\n166\", \"6\\n1466\\n20536\\n14761\\n211011\\n2\\n68\", \"6\\n1466\\n20536\\n14761\\n211011\\n3\\n68\", \"6\\n1466\\n7692\\n14761\\n211011\\n3\\n68\", \"6\\n1689\\n7692\\n14761\\n211011\\n3\\n68\", \"6\\n1689\\n7692\\n14761\\n289316\\n3\\n68\", \"6\\n1689\\n7692\\n14761\\n5838\\n3\\n68\", \"6\\n1689\\n7692\\n14761\\n8668\\n3\\n68\", \"6\\n3024\\n7692\\n14761\\n8668\\n3\\n68\", \"6\\n3024\\n5909\\n14761\\n8668\\n3\\n68\", \"6\\n3024\\n5909\\n14761\\n8668\\n5\\n68\", 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\"6\\n3024\\n5909\\n31114\\n8668\\n2\\n59\", \"6\\n3024\\n5909\\n27077\\n8668\\n2\\n59\", \"6\\n3024\\n5909\\n14361\\n8746\\n2\\n47\", \"6\\n374\\n5909\\n14361\\n14934\\n2\\n59\", \"6\\n3024\\n3327\\n14361\\n14934\\n2\\n125\", \"6\\n3024\\n5909\\n14361\\n14934\\n4\\n123\", \"6\\n4630\\n5909\\n14361\\n25287\\n4\\n125\", \"6\\n5760\\n9609\\n14361\\n25287\\n4\\n125\", \"6\\n1738\\n9609\\n14361\\n25287\\n4\\n125\", \"6\\n3030\\n5607\\n14361\\n25287\\n4\\n125\", \"6\\n3030\\n8140\\n14361\\n14658\\n4\\n223\", \"6\\n3030\\n8140\\n19479\\n14658\\n4\\n114\", \"6\\n3030\\n8140\\n26374\\n6527\\n4\\n125\", \"6\\n3030\\n10899\\n26374\\n14658\\n6\\n125\", \"6\\n5172\\n8140\\n24291\\n14658\\n6\\n125\", \"6\\n5172\\n8140\\n26374\\n14696\\n6\\n125\", \"6\\n4844\\n8140\\n26374\\n9239\\n6\\n129\", \"6\\n134\\n8140\\n26374\\n9239\\n4\\n129\", \"6\\n12345\\n54321\\n10901\\n211011\\n7\\n90\"], \"outputs\": [\"51234\\n54321\\n11090\\n211011\\n7\\n9\", \"51234\\n63443\\n11090\\n211011\\n7\\n9\\n\", \"51234\\n63443\\n72142\\n211011\\n7\\n9\\n\", \"51234\\n63443\\n72142\\n211011\\n7\\n661\\n\", \"52332\\n63443\\n72142\\n211011\\n7\\n661\\n\", \"52332\\n63443\\n72142\\n211011\\n1\\n661\\n\", \"6614\\n63443\\n72142\\n211011\\n1\\n661\\n\", \"6614\\n62053\\n72142\\n211011\\n1\\n661\\n\", \"6614\\n62053\\n76114\\n211011\\n1\\n661\\n\", \"6614\\n62053\\n76114\\n211011\\n2\\n661\\n\", \"6614\\n62053\\n76114\\n211011\\n2\\n86\\n\", \"6614\\n62053\\n76114\\n211011\\n3\\n86\\n\", \"6614\\n9276\\n76114\\n211011\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n211011\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n931628\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n8583\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n8866\\n3\\n86\\n\", \"4302\\n9276\\n76114\\n8866\\n3\\n86\\n\", \"4302\\n9590\\n76114\\n8866\\n3\\n86\\n\", \"4302\\n9590\\n76114\\n8866\\n5\\n86\\n\", \"4302\\n9590\\n76114\\n8866\\n1\\n86\\n\", \"4302\\n9590\\n94752\\n8866\\n1\\n86\\n\", \"4302\\n9590\\n94752\\n8866\\n1\\n95\\n\", 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\"724\\n63443\\n72142\\n211011\\n1\\n661\\n\", \"6614\\n62053\\n72142\\n211011\\n1\\n715\\n\", \"6614\\n8802\\n76114\\n211011\\n1\\n661\\n\", \"6614\\n62053\\n76114\\n211011\\n2\\n921\\n\", \"6614\\n62053\\n76114\\n211011\\n4\\n86\\n\", \"725\\n62053\\n76114\\n211011\\n3\\n86\\n\", \"6614\\n9276\\n76114\\n93760\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n931628\\n2\\n86\\n\", \"9168\\n9276\\n76114\\n9911\\n3\\n86\\n\", \"9168\\n9276\\n76114\\n82211\\n3\\n86\\n\", \"4302\\n9276\\n76114\\n94413\\n3\\n86\\n\", \"4302\\n9590\\n76114\\n8866\\n2\\n86\\n\", \"9912\\n9590\\n76114\\n8866\\n5\\n86\\n\", \"4302\\n9590\\n76114\\n9812\\n1\\n86\\n\", \"4302\\n9590\\n94752\\n51310\\n1\\n86\\n\", \"5234\\n9590\\n94752\\n8866\\n1\\n95\\n\", \"4302\\n9590\\n43111\\n8866\\n2\\n95\\n\", \"4302\\n9590\\n77270\\n8866\\n2\\n95\\n\", \"4302\\n9590\\n61143\\n8746\\n2\\n74\\n\", \"743\\n9590\\n61143\\n93414\\n2\\n95\\n\", \"4302\\n7332\\n61143\\n93414\\n2\\n512\\n\", \"4302\\n9590\\n61143\\n93414\\n4\\n312\\n\", \"6304\\n9590\\n61143\\n87252\\n4\\n512\\n\", \"7605\\n9960\\n61143\\n87252\\n4\\n512\\n\", \"8173\\n9960\\n61143\\n87252\\n4\\n512\\n\", \"330\\n7560\\n61143\\n87252\\n4\\n512\\n\", \"330\\n8140\\n61143\\n81465\\n4\\n322\\n\", \"330\\n8140\\n94791\\n81465\\n4\\n411\\n\", \"330\\n8140\\n74263\\n7652\\n4\\n512\\n\", \"330\\n99108\\n74263\\n81465\\n6\\n512\\n\", \"7251\\n8140\\n91242\\n81465\\n6\\n512\\n\", \"7251\\n8140\\n74263\\n96146\\n6\\n512\\n\", \"8444\\n8140\\n74263\\n9923\\n6\\n912\\n\", \"413\\n8140\\n74263\\n9923\\n4\\n912\\n\", \"51234\\n54321\\n11090\\n211011\\n7\\n9\\n\"]}", "source": "taco"}
|
For any positive integer, we define a digit rotation as either moving the first digit
to the end of the number (left digit rotation), or the last digit to the front of the number (right digit rotation).
For example, the number 12345 could be left digit rotated to 23451, or right digit rotated to 51234.
If there are any leading zeros after digit rotation, they must be removed.
So 10203 could be left digit rotated to 2031, then left digit rotated again to 312.
Given an integer N, determine the largest integer that can result from performing a series of one or more
digit rotations on N.
------ Input ------
Input will begin with an integer T (at most 1000), the number of test cases.
Each test case consists of a positive integer N<100000000 (10^{8}) on a line by itself.
------ Output ------
For each test case, print the largest integer that can result from performing one or more
digit rotations on N.
----- Sample Input 1 ------
6
12345
54321
10901
211011
7
90
----- Sample Output 1 ------
51234
54321
11090
211011
7
9
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\": [[0, 1], [1, 2], [5, -1], [505, 4], [321, 123], [0, -1], [-50, 0], [-1, -5], [-5, -5], [-505, 4], [-321, 123], [0, 0], [-5, -1], [5, 1], [-17, -17], [17, 17]], \"outputs\": [[1], [3], [14], [127759], [44178], [-1], [-1275], [-15], [-5], [-127755], [-44055], [0], [-15], [15], [-17], [17]]}", "source": "taco"}
|
Given two integers `a` and `b`, which can be positive or negative, find the sum of all the numbers between including them too and return it. If the two numbers are equal return `a` or `b`.
**Note:** `a` and `b` are not ordered!
## Examples
```python
get_sum(1, 0) == 1 // 1 + 0 = 1
get_sum(1, 2) == 3 // 1 + 2 = 3
get_sum(0, 1) == 1 // 0 + 1 = 1
get_sum(1, 1) == 1 // 1 Since both are same
get_sum(-1, 0) == -1 // -1 + 0 = -1
get_sum(-1, 2) == 2 // -1 + 0 + 1 + 2 = 2
```
```C
get_sum(1, 0) == 1 // 1 + 0 = 1
get_sum(1, 2) == 3 // 1 + 2 = 3
get_sum(0, 1) == 1 // 0 + 1 = 1
get_sum(1, 1) == 1 // 1 Since both are same
get_sum(-1, 0) == -1 // -1 + 0 = -1
get_sum(-1, 2) == 2 // -1 + 0 + 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
|
{"tests": "{\"inputs\": [[[0, 0], [1, 1]], [[2, 6], [-2, -6]], [[10, -10], [-10, 10]], [[1, -35], [-12, 1]], [[1000, 15], [-7, -214]], [[0, 0], [0, 0]]], \"outputs\": [[[2, 2]], [[-6, -18]], [[-30, 30]], [[-25, 37]], [[-1014, -443]], [[0, 0]]]}", "source": "taco"}
|
"Point reflection" or "point symmetry" is a basic concept in geometry where a given point, P, at a given position relative to a mid-point, Q has a corresponding point, P1, which is the same distance from Q but in the opposite direction.
## Task
Given two points P and Q, output the symmetric point of point P about Q.
Each argument is a two-element array of integers representing the point's X and Y coordinates. Output should be in the same format, giving the X and Y coordinates of point P1. You do not have to validate the input.
This kata was inspired by the Hackerrank challenge [Find Point](https://www.hackerrank.com/challenges/find-point)
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\\n10 8\\n3 2\\n9 7\\n1 5\\n5 3\\n7 6\\n8 4\\n10 9\\n2 6\\nqbilfkqcll\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n4 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"5\\n3 1\\n3 5\\n5 4\\n5 2\\nticdm\\n\", \"10\\n10 8\\n3 2\\n9 7\\n1 5\\n5 3\\n7 6\\n8 4\\n10 9\\n2 6\\nqbhlfkqcll\\n\", \"7\\n6 2\\n4 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n12 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 2\\n1 2\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"7\\n6 2\\n4 3\\n3 7\\n5 3\\n7 2\\n1 4\\nafefdfs\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n11 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n12 7\\n12 13\\n5 9\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 2\\n1 2\\n3 7\\n5 3\\n7 2\\n1 4\\nefafdfs\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n11 16\\n2 1\\n18 19\\n20 7\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 2\\n1 5\\n3 7\\n5 2\\n7 2\\n2 4\\nafefdfs\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n4 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"5\\n3 1\\n3 2\\n5 4\\n5 2\\nticdm\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n12 7\\n12 13\\n5 9\\n7 3\\n13 14\\n18 17\\n12 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n11 16\\n2 1\\n18 19\\n20 7\\n1 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n1 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n4 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n8 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 5\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n8 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 3\\n1 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafegdfs\\n\", \"20\\n12 2\\n15 14\\n11 12\\n2 5\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n8 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 3\\n1 3\\n1 7\\n5 2\\n3 2\\n1 4\\nafegdfs\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n5 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 2\\n4 6\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"5\\n1 2\\n2 3\\n2 4\\n3 5\\nabcbb\\n\", \"7\\n6 1\\n1 2\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"20\\n10 3\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n4 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 3\\n13 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 2\\n2 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 18\\n8 9\\n7 6\\n12 7\\n12 13\\n5 9\\n7 3\\n13 14\\n18 17\\n12 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n1 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 7\\n12 13\\n5 6\\n4 3\\n13 14\\n18 17\\n11 10\\n16 17\\n9 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 2\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n15 19\\n20 19\\n8 9\\n7 6\\n8 7\\n8 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n12 2\\n15 14\\n11 12\\n2 5\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n7 6\\n8 3\\n8 13\\n5 6\\n7 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"20\\n10 9\\n15 14\\n11 12\\n2 3\\n15 16\\n2 1\\n18 19\\n20 19\\n8 9\\n12 6\\n8 7\\n12 13\\n5 6\\n5 3\\n13 14\\n18 17\\n11 10\\n16 17\\n5 4\\naabbccddeeffgghhiijj\\n\", \"7\\n6 3\\n4 6\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"5\\n1 2\\n4 3\\n2 4\\n3 5\\nabcbb\\n\", \"7\\n6 2\\n1 3\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"7\\n6 2\\n1 2\\n3 7\\n5 2\\n7 2\\n1 4\\nefafdfs\\n\", \"7\\n6 2\\n1 5\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"7\\n6 2\\n1 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"7\\n6 2\\n1 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafegdfs\\n\", \"5\\n3 1\\n3 5\\n1 4\\n5 2\\nticdm\\n\", \"7\\n6 2\\n1 2\\n3 7\\n5 1\\n7 2\\n1 4\\nefafdfs\\n\", \"7\\n6 2\\n1 5\\n3 7\\n5 2\\n7 2\\n2 4\\nsfdfefa\\n\", \"5\\n3 1\\n3 2\\n5 4\\n5 1\\nticdm\\n\", \"7\\n6 3\\n1 3\\n1 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"7\\n6 2\\n4 3\\n3 7\\n5 2\\n7 2\\n1 4\\nafefdfs\\n\", \"5\\n1 2\\n2 3\\n3 4\\n3 5\\nabcbb\\n\"], \"outputs\": [\"1 1 1 2 1 1 2 3 4 5\\n\", \"20 29 45 52 64 69 77 80 84 85 85 84 80 77 69 64 52 45 29 20\\n\", \"1 1 1 1 1\\n\", \"1 1 1 2 1 1 2 3 4 5 \", \"1 4 1 1 2 4 2 \", \"11 11 18 11 26 33 58 61 66 69 70 71 68 67 60 57 46 41 26 19 \", \"5 5 6 5 10 11 14 13 26 31 40 43 36 37 36 35 30 27 18 13 \", \"3 6 1 2 2 5 2 \", \"1 3 1 1 1 3 2 \", \"8 8 12 8 18 22 36 36 36 36 43 41 30 26 11 14 14 14 10 8 \", \"4 4 4 1 8 3 8 11 30 35 42 45 40 41 39 38 32 29 19 14 \", \"3 5 1 2 1 4 2 \", \"8 8 12 8 18 22 40 40 39 39 42 40 29 25 10 10 9 8 3 5 \", \"1 8 1 5 3 5 3 \", \"15 24 23 24 25 24 21 18 11 18 25 29 32 34 33 33 28 26 17 13 \", \"1 1 1 1 1 \", \"11 11 6 5 9 10 12 9 3 12 20 24 28 30 30 30 26 24 16 12 \", \"3 3 2 1 3 1 3 4 13 14 15 25 24 26 27 27 24 22 15 11 \", \"24 21 15 8 11 12 17 11 26 27 33 32 24 21 9 10 9 8 3 2 \", \"47 44 46 47 42 41 32 29 16 41 45 48 48 49 45 44 36 33 21 16 \", \"11 11 14 9 21 26 44 45 3 4 4 4 44 45 42 41 34 31 20 15 \", \"17 25 7 8 41 45 56 57 6 6 5 5 52 52 48 46 38 34 22 16 \", \"1 1 1 1 1 1 1 \", \"18 32 7 8 46 50 60 61 5 4 13 14 56 56 51 49 40 36 23 17 \", \"1 2 2 1 1 2 1 \", \"12 12 20 11 42 47 56 61 66 69 70 71 68 67 60 57 46 41 26 19 \", \"2 5 1 4 2 7 2 \", \"2 5 3 4 2 \", \"4 3 1 3 1 3 1 \", \"9 12 46 47 42 41 32 29 16 35 40 43 44 45 42 41 34 31 20 15 \", \"8 8 6 5 9 10 12 9 3 6 9 10 17 16 8 11 12 12 9 7 \", \"1 5 2 1 2 5 2 \", \"3 3 2 1 3 1 3 4 12 13 15 23 22 23 24 23 20 18 6 6 \", \"65 64 62 61 18 25 39 44 54 63 65 66 64 63 57 54 44 39 25 18 \", \"10 10 12 8 19 23 38 38 3 4 4 4 36 36 37 31 20 15 11 9 \", \"13 16 27 13 30 29 29 30 2 3 7 8 32 34 33 33 28 26 17 13 \", \"8 8 12 7 26 27 19 26 41 46 57 64 48 48 45 43 36 32 21 15 \", \"2 1 2 4 1 4 1 \", \"2 4 3 5 2 \", \"1 4 1 1 2 4 2 \", \"3 6 1 2 2 5 2 \", \"1 4 1 1 2 4 2 \", \"1 4 1 1 2 4 2 \", \"1 4 1 1 2 4 2 \", \"1 1 1 1 1 \", \"3 5 1 2 1 4 2 \", \"1 8 1 5 3 5 3 \", \"1 1 1 1 1 \", \"1 1 1 1 1 1 1 \", \"1 4 1 1 2 4 2\\n\", \"1 3 4 3 3\\n\"]}", "source": "taco"}
|
You are given a tree (a connected acyclic undirected graph) of n vertices. Vertices are numbered from 1 to n and each vertex is assigned a character from a to t.
A path in the tree is said to be palindromic if at least one permutation of the labels in the path is a palindrome.
For each vertex, output the number of palindromic paths passing through it.
Note: The path from vertex u to vertex v is considered to be the same as the path from vertex v to vertex u, and this path will be counted only once for each of the vertices it passes through.
Input
The first line contains an integer n (2 ≤ n ≤ 2·105) — the number of vertices in the tree.
The next n - 1 lines each contain two integers u and v (1 ≤ u, v ≤ n, u ≠ v) denoting an edge connecting vertex u and vertex v. It is guaranteed that the given graph is a tree.
The next line contains a string consisting of n lowercase characters from a to t where the i-th (1 ≤ i ≤ n) character is the label of vertex i in the tree.
Output
Print n integers in a single line, the i-th of which is the number of palindromic paths passing through vertex i in the tree.
Examples
Input
5
1 2
2 3
3 4
3 5
abcbb
Output
1 3 4 3 3
Input
7
6 2
4 3
3 7
5 2
7 2
1 4
afefdfs
Output
1 4 1 1 2 4 2
Note
In the first sample case, the following paths are palindromic:
2 - 3 - 4
2 - 3 - 5
4 - 3 - 5
Additionally, all paths containing only one vertex are palindromic. Listed below are a few paths in the first sample that are not palindromic:
1 - 2 - 3
1 - 2 - 3 - 4
1 - 2 - 3 - 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\": [\"5\\n3 4\\n3 2\\n3 1\\n13 7\\n1010000 9999999\\n\", \"1\\n1 1\\n\", \"1\\n632934461 955818012\\n\", \"1\\n632934461 955818012\\n\", \"1\\n1 1\\n\", \"1\\n632934461 286939621\\n\", \"1\\n1 2\\n\", \"5\\n3 4\\n3 2\\n3 1\\n13 7\\n1010000 14106652\\n\", \"1\\n632934461 107730378\\n\", \"1\\n2 2\\n\", \"1\\n3 2\\n\", \"5\\n3 4\\n3 2\\n5 1\\n13 9\\n1010000 14106652\\n\", \"1\\n615335118 7172205\\n\", \"1\\n3 0\\n\", \"5\\n3 4\\n3 4\\n5 1\\n13 9\\n1010000 14106652\\n\", \"1\\n615335118 12225770\\n\", \"5\\n3 4\\n2 4\\n5 1\\n13 9\\n1010000 14106652\\n\", \"1\\n615335118 5786737\\n\", \"5\\n3 4\\n2 4\\n5 1\\n13 9\\n1010100 14106652\\n\", \"5\\n5 4\\n2 4\\n5 1\\n13 9\\n1010000 14106652\\n\", \"1\\n698999820 2204665\\n\", \"1\\n698999820 1980472\\n\", \"5\\n2 4\\n2 4\\n5 1\\n13 9\\n1010000 8762115\\n\", \"1\\n706510299 2463249\\n\", \"5\\n2 4\\n2 4\\n5 1\\n13 7\\n1010000 8762115\\n\", \"5\\n0 4\\n2 4\\n5 1\\n13 7\\n1010000 8762115\\n\", \"1\\n698922220 978339\\n\", \"5\\n0 4\\n2 4\\n7 1\\n13 4\\n1010000 7665241\\n\", \"1\\n698922220 608354\\n\", \"5\\n0 4\\n2 4\\n7 0\\n13 4\\n1010000 7665241\\n\", \"1\\n698922220 1208296\\n\", \"1\\n698922220 1540583\\n\", \"1\\n1172057 1540583\\n\", \"1\\n1172057 33335\\n\", \"1\\n1172057 59689\\n\", \"1\\n2319969 6867\\n\", \"1\\n1986594 11059\\n\", \"1\\n3783639 9495\\n\", \"1\\n158122 2539\\n\", \"1\\n49170 1394\\n\", \"1\\n55211 1006\\n\", \"1\\n3055 30\\n\", \"1\\n10750 42\\n\", \"1\\n22807 46\\n\", \"1\\n22807 37\\n\", \"1\\n25573 58\\n\", \"1\\n864 101\\n\", \"1\\n365 111\\n\", \"1\\n691 110\\n\", \"1\\n820874153 955818012\\n\", \"5\\n3 4\\n3 2\\n3 1\\n13 13\\n1010000 9999999\\n\", \"5\\n6 4\\n3 2\\n3 1\\n13 7\\n1010000 14106652\\n\", \"1\\n615335118 4845337\\n\", \"5\\n3 4\\n3 2\\n5 1\\n13 3\\n1010000 14106652\\n\", \"5\\n3 4\\n3 2\\n5 1\\n13 7\\n1010000 14106652\\n\", \"1\\n615335118 107730378\\n\", \"1\\n5 0\\n\", \"1\\n0 0\\n\", \"1\\n698999820 5786737\\n\", \"5\\n5 4\\n2 4\\n5 1\\n13 9\\n1010000 12964098\\n\", \"5\\n5 4\\n2 4\\n5 1\\n13 9\\n1010000 8762115\\n\", \"1\\n706510299 1980472\\n\", \"1\\n621799751 2463249\\n\", \"1\\n380647494 2463249\\n\", \"5\\n0 4\\n2 4\\n5 1\\n13 7\\n1010000 7665241\\n\", \"1\\n698922220 2463249\\n\", \"5\\n0 4\\n2 4\\n7 1\\n13 7\\n1010000 7665241\\n\", \"5\\n0 4\\n2 4\\n7 0\\n13 4\\n1010000 7511699\\n\", \"5\\n1 4\\n2 4\\n7 0\\n13 4\\n1010000 7511699\\n\", \"1\\n61905845 1540583\\n\", \"1\\n69275660 1540583\\n\", \"1\\n20708319 1540583\\n\", \"1\\n2028686 1540583\\n\", \"1\\n2084098 1540583\\n\", \"1\\n1172057 1647029\\n\", \"1\\n2319969 59689\\n\", \"1\\n1483476 6867\\n\", \"1\\n1253279 6867\\n\", \"1\\n1986594 6867\\n\", \"1\\n3783639 11059\\n\", \"1\\n4252349 9495\\n\", \"1\\n432417 9495\\n\", \"1\\n195797 9495\\n\", \"1\\n158122 9495\\n\", \"1\\n49170 2539\\n\", \"1\\n55211 1394\\n\", \"1\\n3055 1006\\n\", \"1\\n5725 30\\n\", \"1\\n10750 30\\n\", \"1\\n12710 42\\n\", \"1\\n22807 42\\n\", \"1\\n25573 42\\n\", \"1\\n864 58\\n\", \"1\\n503 101\\n\", \"1\\n365 101\\n\", \"1\\n691 111\\n\", \"1\\n1094484201 286939621\\n\", \"1\\n2 1\\n\", \"1\\n279455931 107730378\\n\", \"5\\n3 4\\n3 2\\n5 1\\n13 7\\n1010000 9742721\\n\", \"1\\n6 2\\n\", \"5\\n3 4\\n3 2\\n3 1\\n13 7\\n1010000 9999999\\n\"], \"outputs\": [\"4\\n3\\n1\\n28\\n510049495001\\n\", \"1\\n\", \"200303015644213031\\n\", \"200303015644213031\\n\", \"1\\n\", \"41167173193281631\\n\", \"1\\n\", \"4\\n3\\n1\\n28\\n510049495001\\n\", \"5802917225876631\\n\", \"2\\n\", \"3\\n\", \"4\\n3\\n1\\n45\\n510049495001\\n\", \"25720265867115\\n\", \"0\\n\", \"4\\n4\\n1\\n45\\n510049495001\\n\", \"74734732159335\\n\", \"4\\n2\\n1\\n45\\n510049495001\\n\", \"16743165446953\\n\", \"4\\n2\\n1\\n45\\n510150499951\\n\", \"10\\n2\\n1\\n45\\n510049495001\\n\", \"2430274983445\\n\", \"1961135661628\\n\", \"2\\n2\\n1\\n45\\n510049495001\\n\", \"3033799049625\\n\", \"2\\n2\\n1\\n28\\n510049495001\\n\", \"1\\n2\\n1\\n28\\n510049495001\\n\", \"478574088630\\n\", \"1\\n2\\n1\\n10\\n510049495001\\n\", \"185047598835\\n\", \"1\\n2\\n0\\n10\\n510049495001\\n\", \"729990215956\\n\", \"1186698760236\\n\", \"686858219597\\n\", \"555627780\\n\", \"1781418205\\n\", \"23581278\\n\", \"61156270\\n\", \"45082260\\n\", \"3224530\\n\", \"972315\\n\", \"506521\\n\", \"465\\n\", \"903\\n\", \"1081\\n\", \"703\\n\", \"1711\\n\", \"5151\\n\", \"6216\\n\", \"6105\\n\", \"336917187121296629\\n\", \"4\\n3\\n1\\n79\\n510049495001\\n\", \"10\\n3\\n1\\n28\\n510049495001\\n\", \"11738647744453\\n\", \"4\\n3\\n1\\n6\\n510049495001\\n\", \"4\\n3\\n1\\n28\\n510049495001\\n\", \"5802917225876631\\n\", \"0\\n\", \"1\\n\", \"16743165446953\\n\", \"10\\n2\\n1\\n45\\n510049495001\\n\", \"10\\n2\\n1\\n45\\n510049495001\\n\", \"1961135661628\\n\", \"3033799049625\\n\", \"3033799049625\\n\", \"1\\n2\\n1\\n28\\n510049495001\\n\", \"3033799049625\\n\", \"1\\n2\\n1\\n28\\n510049495001\\n\", \"1\\n2\\n0\\n10\\n510049495001\\n\", \"1\\n2\\n0\\n10\\n510049495001\\n\", \"1186698760236\\n\", \"1186698760236\\n\", \"1186698760236\\n\", \"1186698760236\\n\", \"1186698760236\\n\", \"686858219597\\n\", \"1781418205\\n\", \"23581278\\n\", \"23581278\\n\", \"23581278\\n\", \"61156270\\n\", \"45082260\\n\", \"45082260\\n\", \"45082260\\n\", \"45082260\\n\", \"3224530\\n\", \"972315\\n\", \"506521\\n\", \"465\\n\", \"465\\n\", \"903\\n\", \"903\\n\", \"903\\n\", \"1711\\n\", \"5151\\n\", \"5151\\n\", \"6216\\n\", \"41167173193281631\\n\", \"1\\n\", \"5802917225876631\\n\", \"4\\n3\\n1\\n28\\n510049495001\\n\", \"3\\n\", \"4\\n3\\n1\\n28\\n510049495001\\n\"]}", "source": "taco"}
|
A competitive eater, Alice is scheduling some practices for an eating contest on a magical calendar. The calendar is unusual because a week contains not necessarily $7$ days!
In detail, she can choose any integer $k$ which satisfies $1 \leq k \leq r$, and set $k$ days as the number of days in a week.
Alice is going to paint some $n$ consecutive days on this calendar. On this calendar, dates are written from the left cell to the right cell in a week. If a date reaches the last day of a week, the next day's cell is the leftmost cell in the next (under) row.
She wants to make all of the painted cells to be connected by side. It means, that for any two painted cells there should exist at least one sequence of painted cells, started in one of these cells, and ended in another, such that any two consecutive cells in this sequence are connected by side.
Alice is considering the shape of the painted cells. Two shapes are the same if there exists a way to make them exactly overlapped using only parallel moves, parallel to the calendar's sides.
For example, in the picture, a week has $4$ days and Alice paints $5$ consecutive days. [1] and [2] are different shapes, but [1] and [3] are equal shapes. [Image]
Alice wants to know how many possible shapes exists if she set how many days a week has and choose consecutive $n$ days and paints them in calendar started in one of the days of the week. As was said before, she considers only shapes, there all cells are connected by side.
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. Next $t$ lines contain descriptions of test cases.
For each test case, the only line contains two integers $n$, $r$ ($1 \le n \le 10^9, 1 \le r \le 10^9$).
-----Output-----
For each test case, print a single integer — the answer to the problem.
Please note, that the answer for some test cases won't fit into $32$-bit integer type, so you should use at least $64$-bit integer type in your programming language.
-----Example-----
Input
5
3 4
3 2
3 1
13 7
1010000 9999999
Output
4
3
1
28
510049495001
-----Note-----
In the first test case, Alice can set $1,2,3$ or $4$ days as the number of days in a week.
There are $6$ possible paintings shown in the picture, but there are only $4$ different shapes. So, the answer is $4$. Notice that the last example in the picture is an invalid painting because all cells are not connected by sides. [Image]
In the last test case, be careful with the overflow issue, described in the output format.
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 1\\n1 2\\n2 1\\n2 2\\n\", \"2\\n-1 -1\\n0 1\\n\", \"1\\n0 0\\n\", \"9\\n1 1\\n2 2\\n3 3\\n1 2\\n2 1\\n3 1\\n1 3\\n3 2\\n2 3\\n\", \"10\\n504155727 -77293021\\n-155983273 -43296260\\n-548837441 -43296260\\n88335251 -77293021\\n970294418 -43296260\\n-155983273 850521645\\n-852404258 -77293021\\n518823261 -77293021\\n-89661323 -43296260\\n-155983273 -406914114\\n\", \"30\\n4 3\\n4 0\\n0 -1\\n-2 4\\n3 4\\n-1 1\\n-3 -2\\n-2 0\\n-1 2\\n3 -4\\n-3 2\\n1 -4\\n-4 -4\\n2 -1\\n1 -2\\n1 -1\\n1 2\\n3 0\\n-2 1\\n3 -3\\n-4 -2\\n2 -4\\n1 3\\n3 -1\\n-2 2\\n0 -4\\n-2 3\\n-4 2\\n-1 3\\n3 2\\n\", \"4\\n2 1\\n0 2\\n-2 1\\n0 0\\n\", \"6\\n-2 1\\n-1 -2\\n-2 -2\\n-2 2\\n1 2\\n2 -2\\n\", \"6\\n1 -2\\n-2 -1\\n-1 1\\n1 2\\n0 -1\\n-2 0\\n\", \"4\\n1 0\\n0 0\\n0 1\\n1 -1\\n\", \"4\\n1 -2\\n2 1\\n-1 2\\n0 1\\n\", \"7\\n0 0\\n2 2\\n-2 2\\n-1 2\\n-1 -2\\n-2 -2\\n-2 -1\\n\", \"4\\n-2 -1\\n0 0\\n1 -2\\n1 0\\n\", \"3\\n2 0\\n2 1\\n1 -2\\n\", \"6\\n-1 2\\n0 -1\\n-1 -2\\n0 1\\n-1 0\\n1 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|
You are given n distinct points on a plane with integral coordinates. For each point you can either draw a vertical line through it, draw a horizontal line through it, or do nothing.
You consider several coinciding straight lines as a single one. How many distinct pictures you can get? Print the answer modulo 10^9 + 7.
-----Input-----
The first line contains single integer n (1 ≤ n ≤ 10^5) — the number of points.
n lines follow. The (i + 1)-th of these lines contains two integers x_{i}, y_{i} ( - 10^9 ≤ x_{i}, y_{i} ≤ 10^9) — coordinates of the i-th point.
It is guaranteed that all points are distinct.
-----Output-----
Print the number of possible distinct pictures modulo 10^9 + 7.
-----Examples-----
Input
4
1 1
1 2
2 1
2 2
Output
16
Input
2
-1 -1
0 1
Output
9
-----Note-----
In the first example there are two vertical and two horizontal lines passing through the points. You can get pictures with any subset of these lines. For example, you can get the picture containing all four lines in two ways (each segment represents a line containing it). The first way: [Image] The second way: [Image]
In the second example you can work with two points independently. The number of pictures is 3^2 = 9.
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\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n2\\n2\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n3\\n2\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n\", \"1\\n-1\\n3\\n2\\n\"]}", "source": "taco"}
|
Polycarp has $n$ coins, the value of the $i$-th coin is $a_i$. It is guaranteed that all the values are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$).
Polycarp wants to know answers on $q$ queries. The $j$-th query is described as integer number $b_j$. The answer to the query is the minimum number of coins that is necessary to obtain the value $b_j$ using some subset of coins (Polycarp can use only coins he has). If Polycarp can't obtain the value $b_j$, the answer to the $j$-th query is -1.
The queries are independent (the answer on the query doesn't affect Polycarp's coins).
-----Input-----
The first line of the input contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of coins and the number of queries.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ — values of coins ($1 \le a_i \le 2 \cdot 10^9$). It is guaranteed that all $a_i$ are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$).
The next $q$ lines contain one integer each. The $j$-th line contains one integer $b_j$ — the value of the $j$-th query ($1 \le b_j \le 10^9$).
-----Output-----
Print $q$ integers $ans_j$. The $j$-th integer must be equal to the answer on the $j$-th query. If Polycarp can't obtain the value $b_j$ the answer to the $j$-th query is -1.
-----Example-----
Input
5 4
2 4 8 2 4
8
5
14
10
Output
1
-1
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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\"\\n157\\n147\\n207\\n227\\n227\\n\", \"\\n62\\n58\\n78\\n86\\n86\\n\"]}", "source": "taco"}
|
There are n cells, numbered 1,2,..., n from left to right. You have to place a robot at any cell initially. The robot must make exactly k moves.
In one move, the robot must move one cell to the left or right, provided that it doesn't move out of bounds. In other words, if the robot was in the cell i, it must move to either the cell i-1 or the cell i+1, as long as it lies between 1 and n (endpoints inclusive). The cells, in the order they are visited (including the cell the robot is placed), together make a good path.
Each cell i has a value a_i associated with it. Let c_0, c_1, ..., c_k be the sequence of cells in a good path in the order they are visited (c_0 is the cell robot is initially placed, c_1 is the cell where the robot is after its first move, and so on; more formally, c_i is the cell that the robot is at after i moves). Then the value of the path is calculated as a_{c_0} + a_{c_1} + ... + a_{c_k}.
Your task is to calculate the sum of values over all possible good paths. Since this number can be very large, output it modulo 10^9 + 7. Two good paths are considered different if the starting cell differs or there exists an integer i ∈ [1, k] such that the current cell of the robot after exactly i moves is different in those paths.
You must process q updates to a and print the updated sum each time. Each update changes the value of exactly one cell. See the input format and the sample input-output for more details.
Input
The first line of the input contains three space-separated integers n, k and q (2 ≤ n ≤ 5000; 1 ≤ k ≤ 5000; 1 ≤ q ≤ 2 ⋅ 10^5).
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
q lines follow. Each line contains two space-separated integers i and x (1 ≤ i ≤ n; 1 ≤ x ≤ 10^9) indicating that you must change the value of a_i to x.
Output
Print q integers. The i-th integer should be the sum of values over all good paths after the first i updates are performed. Since the answers may be large, print them modulo 10^9 + 7.
Examples
Input
5 1 5
3 5 1 4 2
1 9
2 4
3 6
4 6
5 2
Output
62
58
78
86
86
Input
5 2 5
3 5 1 4 2
1 9
2 4
3 6
4 6
5 2
Output
157
147
207
227
227
Input
4 40 6
92 21 82 46
3 56
1 72
4 28
1 97
2 49
2 88
Output
239185261
666314041
50729936
516818968
766409450
756910476
Note
In the first example, the good paths are (1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (4, 5), (5, 4).
Initially the values of a are [3, 5, 1, 4, 2]. After the first update, they become [9, 5, 1, 4, 2]. After the second update, they become [9, 4, 1, 4, 2], and so on.
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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2\\n5 1 1\\n1 6 5\\n6 1 2\\n7 1 1\\n1 8 1\\n8 1 1\\n1 9 2\\n9 1 1\\n1 10 8\\n10 1 2\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n1 6 7\\n1 7 7\\n1 8 7\\n1 9 7\\n1 10 7\\n\", \"-1\\n-1\\n11\\n1 2 1\\n2 1 11\\n1 3 2\\n3 1 1\\n1 4 2\\n4 1 1\\n5 1 1\\n1 2 8\\n1 3 8\\n1 4 8\\n1 5 8\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 2\\n1 2 4\\n1 3 4\\n1 4 4\\n-1\\n-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n1 5 3\\n\", \"8\\n2 1 1\\n1 3 1\\n3 1 1\\n1 4 3\\n4 1 2\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n1 5 3\\n\", \"8\\n2 1 1\\n1 3 1\\n3 1 1\\n1 4 3\\n4 1 2\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"27\\n1 2 1\\n2 1 4\\n1 3 2\\n3 1 3\\n1 4 1\\n4 1 2\\n1 5 3\\n5 1 2\\n1 6 5\\n6 1 2\\n1 7 5\\n7 1 1\\n1 8 1\\n8 1 1\\n1 9 2\\n9 1 1\\n1 10 3\\n10 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n1 6 7\\n1 7 7\\n1 8 7\\n1 9 7\\n1 10 7\\n\", \"-1\\n10\\n2 1 1\\n3 1 2\\n4 1 1\\n5 1 1\\n6 1 1\\n1 2 4\\n1 3 4\\n1 4 4\\n1 5 4\\n1 6 4\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 2\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 2\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 2\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 4\\n1 3 4\\n1 4 4\\n1 5 4\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 2\\n3 1 2\\n4 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 4\\n1 3 4\\n1 4 4\\n1 5 4\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 2\\n1 2 4\\n1 3 4\\n1 4 4\\n-1\\n-1\\n\", \"-1\\n\", \"-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 2\\n1 2 4\\n1 3 4\\n1 4 4\\n-1\\n-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n1 5 3\\n\", \"-1\\n\", \"-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 2\\n1 2 4\\n1 3 4\\n1 4 4\\n-1\\n-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n1 5 3\\n\", \"-1\\n\", \"8\\n1 2 1\\n2 1 1\\n1 3 1\\n3 1 2\\n4 1 2\\n1 2 4\\n1 3 4\\n1 4 4\\n-1\\n-1\\n\", \"-1\\n-1\\n11\\n2 1 4\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 3\\n5 1 1\\n1 2 3\\n1 3 3\\n1 4 3\\n1 5 3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"-1\\n\", \"-1\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\", \"8\\n2 1 8\\n1 3 2\\n3 1 2\\n1 4 2\\n4 1 5\\n1 2 10\\n1 3 10\\n1 4 10\\n-1\\n12\\n1 2 1\\n2 1 10\\n1 3 2\\n3 1 1\\n1 4 3\\n4 1 1\\n1 5 2\\n5 1 1\\n1 2 7\\n1 3 7\\n1 4 7\\n1 5 7\\n\"]}", "source": "taco"}
|
You are given an array a consisting of n positive integers, numbered from 1 to n. You can perform the following operation no more than 3n times:
1. choose three integers i, j and x (1 ≤ i, j ≤ n; 0 ≤ x ≤ 10^9);
2. assign a_i := a_i - x ⋅ i, a_j := a_j + x ⋅ i.
After each operation, all elements of the array should be non-negative.
Can you find a sequence of no more than 3n operations after which all elements of the array are equal?
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^4) — the number of elements in the array. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^5) — the elements of the array.
It is guaranteed that the sum of n over all test cases does not exceed 10^4.
Output
For each test case print the answer to it as follows:
* if there is no suitable sequence of operations, print -1;
* otherwise, print one integer k (0 ≤ k ≤ 3n) — the number of operations in the sequence. Then print k lines, the m-th of which should contain three integers i, j and x (1 ≤ i, j ≤ n; 0 ≤ x ≤ 10^9) for the m-th operation.
If there are multiple suitable sequences of operations, print any of them. Note that you don't have to minimize k.
Example
Input
3
4
2 16 4 18
6
1 2 3 4 5 6
5
11 19 1 1 3
Output
2
4 1 2
2 3 3
-1
4
1 2 4
2 4 5
2 3 3
4 5 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\": [\"1\\n2 3\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 5\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 5\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 3\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"2\\n1 3\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 4\\n2 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n4 1\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nRRBR\\nBRRR\", \"2\\n1 4\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 3\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 2\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 4\\n1 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n1 4\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 2\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 3\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBRGG\\nRRRB\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"1\\n4 2\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n5 4\\n2 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n4 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 6\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n1 4\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 3\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 5\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 2\\n4 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 1\\nGGRR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 2\\nGRRG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 0\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBGRG\\nRRRB\\nBRRR\", \"1\\n2 4\\nRGGR\\nGGRB\\nBRRR\\nRRBR\", \"1\\n4 4\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nBRGG\\nBRRR\\nRRRB\", \"2\\n4 6\\n1 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 1\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n1 3\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 2\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"2\\n2 0\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n5 3\\nGGRR\\nBGRG\\nRRRB\\nBRRR\", \"1\\n1 1\\nRRGG\\nBRGG\\nBRRR\\nRRRB\", \"1\\n2 1\\nGRGR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 0\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 4\\n1 0\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 5\\n0 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 2\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"2\\n1 3\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 4\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n2 2\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRBRR\", \"1\\n1 2\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 1\\nRRGG\\nBRGG\\nRRRB\\nBRRR\", \"2\\n1 4\\n3 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n4 1\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 3\\n4 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nGGRR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 1\\nGRRG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n4 3\\nRRGG\\nBGRG\\nRRRB\\nBRRR\", \"2\\n4 6\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n5 3\\nGGRR\\nBGRG\\nRRRB\\nRRRB\", \"1\\n1 1\\nRRGG\\nBRGG\\nRRRB\\nRRRB\", \"1\\n2 1\\nGRGR\\nBRGG\\nBRRR\\nBRRR\", \"2\\n2 0\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nGRGB\\nBRRR\\nBRRR\", \"1\\n3 2\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n1 4\\n2 0\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nGRGB\\nBRRR\\nBRRR\", \"2\\n2 4\\n3 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nGRBG\\nBRRR\\nBRRR\", \"1\\n2 1\\nRRGG\\nRGGB\\nRRRB\\nBRRR\", \"1\\n2 1\\nGRRG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n4 6\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nRRGG\\nGGRB\\nRRRB\\nRRRB\", \"1\\n4 1\\nGRGR\\nBRGG\\nBRRR\\nBRRR\", \"2\\n2 -1\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRGRG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 4\\nGGRR\\nGRGB\\nBRRR\\nRRRB\", \"2\\n2 4\\n0 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n3 1\\nRRGG\\nRGGB\\nRRRB\\nBRRR\", \"2\\n4 5\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nGGRR\\nGGRB\\nRRRB\\nRRRB\", \"2\\n3 -1\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRGRG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n2 4\\n-1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"2\\n2 4\\n-1 1\\nRRRR\\nRRGR\\nRRBR\\nRRRR\", \"2\\n2 2\\n-1 1\\nRRRR\\nRRGR\\nRRBR\\nRRRR\", \"1\\n2 3\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 4\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\"], \"outputs\": [\"6\\n\", \"3\\n\", \"5\\n\", \"12\\n\", \"9\\n\", \"16\\n\", \"8\\n\", \"10\\n\", \"4\\n\", \"13\\n\", \"7\\n\", \"11\\n\", \"14\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"3\\n\", \"5\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"9\\n\", \"3\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"8\\n\", \"16\\n\", \"8\\n\", \"9\\n\", \"5\\n\", \"9\\n\", \"5\\n\", \"12\\n\", \"9\\n\", \"9\\n\", \"10\\n\", \"8\\n\", \"16\\n\", \"11\\n\", \"7\\n\", \"16\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"4\\n\", \"16\\n\", \"10\\n\", \"8\\n\", \"9\\n\", \"8\\n\", \"8\\n\", \"11\\n\", \"11\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"10\\n\", \"8\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"16\\n\", \"10\\n\", \"6\\n\", \"16\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"5\\n\", \"7\\n\", \"11\\n\", \"11\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"8\\n\", \"7\\n\", \"6\\n\", \"10\\n\", \"6\\n\", \"4\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"7\\n\", \"5\", \"3\"]}", "source": "taco"}
|
Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to increase creativity by drawing pictures. Let's draw a pattern well using a square stamp.
I want to use stamps of various sizes to complete the picture of the red, green, and blue streets specified on the 4 x 4 squared paper. The stamp is rectangular and is used to fit the squares. The height and width of the stamp cannot be swapped.
The paper is initially uncolored. When you stamp on paper, the stamped part changes to the color of the stamp, and the color hidden underneath becomes completely invisible. Since the color of the stamp is determined by the ink to be applied, it is possible to choose the color of any stamp. The stamp can be stamped with a part protruding from the paper, and the protruding part is ignored.
It is possible to use one stamp multiple times. You may use the same stamp for different colors. Stamping is a rather nerve-wracking task, so I want to reduce the number of stamps as much as possible.
Input
N
H1 W1
...
HN WN
C1,1C1,2C1,3C1,4
C2,1C2,2C2,3C2,4
C3,1C3,2C3,3C3,4
C4,1C4,2C4,3C4,4
N is the number of stamps, and Hi and Wi (1 ≤ i ≤ N) are integers representing the vertical and horizontal lengths of the i-th stamp, respectively. Ci, j (1 ≤ i ≤ 4, 1 ≤ j ≤ 4) is a character that represents the color of the picture specified for the cells in the i-th row from the top and the j-th column from the left. Red is represented by `R`, green is represented by` G`, and blue is represented by `B`.
Satisfy 1 ≤ N ≤ 16, 1 ≤ Hi ≤ 4, 1 ≤ Wi ≤ 4. The same set as (Hi, Wi) does not appear multiple times.
Output
Print the minimum number of stamps that must be stamped to complete the picture on a single line.
Examples
Input
2
4 4
1 1
RRRR
RRGR
RBRR
RRRR
Output
3
Input
1
2 3
RRGG
BRGG
BRRR
BRRR
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\": [[\"aa_bb_cc_dd_bb_e\", \"bb\"], [\"aaabbbcccc\", \"bbb\"], [\"aaacccbbbcccc\", \"cc\"], [\"aaa\", \"aa\"], [\"aaa\", \"aa\", false], [\"aaabbbaaa\", \"bb\", false], [\"a\", \"\"], [\"\", \"a\"], [\"\", \"\"], [\"\", \"\", false]], \"outputs\": [[2], [1], [5], [2], [1], [1], [0], [0], [0], [0]]}", "source": "taco"}
|
Complete the solution so that it returns the number of times the search_text is found within the full_text.
```python
search_substr( fullText, searchText, allowOverlap = true )
```
so that overlapping solutions are (not) counted. If the searchText is empty, it should return `0`. Usage examples:
```python
search_substr('aa_bb_cc_dd_bb_e', 'bb') # should return 2 since bb shows up twice
search_substr('aaabbbcccc', 'bbb') # should return 1
search_substr( 'aaa', 'aa' ) # should return 2
search_substr( 'aaa', '' ) # should return 0
search_substr( 'aaa', 'aa', false ) # should return 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\": [\"82\\n\", \"720\\n\", \"1239\\n\", \"9999\\n\", \"4938\\n\", \"9562\\n\", \"6143\\n\", \"7274\\n\", \"30\\n\", \"3112\\n\", \"28\\n\", \"8865\\n\", \"5\\n\", \"2023\\n\", \"1936\\n\", \"9998\\n\", \"9798\\n\", \"4999\\n\", \"1\\n\", \"513\\n\", \"9146\\n\", \"9648\\n\", \"9409\\n\", \"1521\\n\", \"1434\\n\", \"6183\\n\", \"4116\\n\", \"9410\\n\", \"9973\\n\", \"56\\n\", \"8558\\n\", \"8363\\n\", \"101\\n\", \"3614\\n\", \"10000\\n\", \"6491\\n\", \"721\\n\", \"719\\n\", \"9408\\n\", \"6685\\n\", \"511\\n\", \"512\\n\", \"932\\n\", \"737\\n\", \"4311\\n\", \"4\\n\", \"9972\\n\", \"6230\\n\", \"4397\\n\", \"3809\\n\", \"2\\n\", \"9796\\n\", \"9974\\n\", \"6772\\n\", \"79\\n\", \"9797\\n\", \"5988\\n\", \"9060\\n\", \"113\\n\", \"1259\\n\", \"342\\n\", \"17554\\n\", \"7696\\n\", \"8547\\n\", \"8624\\n\", \"9145\\n\", \"23\\n\", \"4437\\n\", \"8\\n\", \"1560\\n\", \"9\\n\", \"2377\\n\", \"3495\\n\", \"10023\\n\", \"19176\\n\", \"6902\\n\", \"440\\n\", \"4798\\n\", \"14118\\n\", \"3762\\n\", \"1555\\n\", \"432\\n\", \"157\\n\", \"6342\\n\", \"2210\\n\", \"7136\\n\", \"91\\n\", \"12693\\n\", \"5179\\n\", \"111\\n\", \"2786\\n\", \"10010\\n\", \"1495\\n\", \"390\\n\", \"633\\n\", \"13962\\n\", \"3401\\n\", \"33\\n\", \"980\\n\", \"1479\\n\", \"745\\n\", \"4612\\n\", \"13\\n\", \"5460\\n\", \"7326\\n\", \"7306\\n\", \"2342\\n\", \"9210\\n\", \"7684\\n\", \"11237\\n\", \"20\\n\", \"1482\\n\", \"8289\\n\", \"3754\\n\", \"6\\n\", \"199\\n\", \"353\\n\", \"339\\n\", \"22919\\n\", \"10800\\n\", \"15329\\n\", \"8150\\n\", \"1798\\n\", \"44\\n\", \"7438\\n\", \"16\\n\", \"700\\n\", \"10\\n\", \"2977\\n\", \"5298\\n\", \"9991\\n\", \"27070\\n\", \"9816\\n\", \"875\\n\", \"9279\\n\", \"28128\\n\", \"4641\\n\", \"161\\n\", \"641\\n\", \"240\\n\", \"3902\\n\", \"1655\\n\", \"11568\\n\", \"48\\n\", \"16424\\n\", \"1538\\n\", \"110\\n\", \"4520\\n\", \"10110\\n\", \"853\\n\", \"618\\n\", \"716\\n\", \"1774\\n\", \"6344\\n\", \"64\\n\", \"649\\n\", \"756\\n\", \"341\\n\", \"7\\n\", \"3\\n\"], \"outputs\": [\"82 83 6806 \", \"720 721 519120 \", \"1239 1240 1536360 \", \"9999 10000 99990000 \", \"4938 4939 24388782 \", \"9562 9563 91441406 \", \"6143 6144 37742592 \", \"7274 7275 52918350 \", \"30 31 930 \", \"3112 3113 9687656 \", \"28 29 812 \", \"8865 8866 78597090 \", \"5 6 30 \", \"2023 2024 4094552 \", \"1936 1937 3750032 \", \"9998 9999 99970002 \", \"9798 9799 96010602 \", \"4999 5000 24995000 \", \"-1\\n\", \"513 514 263682 \", \"9146 9147 83658462 \", \"9648 9649 93093552 \", \"9409 9410 88538690 \", \"1521 1522 2314962 \", \"1434 1435 2057790 \", \"6183 6184 38235672 \", \"4116 4117 16945572 \", \"9410 9411 88557510 \", \"9973 9974 99470702 \", \"56 57 3192 \", \"8558 8559 73247922 \", \"8363 8364 69948132 \", \"101 102 10302 \", \"3614 3615 13064610 \", \"10000 10001 100010000 \", \"6491 6492 42139572 \", \"721 722 520562 \", \"719 720 517680 \", \"9408 9409 88519872 \", \"6685 6686 44695910 \", \"511 512 261632 \", \"512 513 262656 \", \"932 933 869556 \", \"737 738 543906 \", \"4311 4312 18589032 \", \"4 5 20 \", \"9972 9973 99450756 \", \"6230 6231 38819130 \", \"4397 4398 19338006 \", \"3809 3810 14512290 \", \"2 3 6 \", \"9796 9797 95971412 \", \"9974 9975 99490650 \", \"6772 6773 45866756 \", \"79 80 6320 \", \"9797 9798 95991006 \", \"5988 5989 35862132 \", \"9060 9061 82092660 \", \"113 114 12882\\n\", \"1259 1260 1586340\\n\", \"342 343 117306\\n\", \"17554 17555 308160470\\n\", \"7696 7697 59236112\\n\", \"8547 8548 73059756\\n\", \"8624 8625 74382000\\n\", \"9145 9146 83640170\\n\", \"23 24 552\\n\", \"4437 4438 19691406\\n\", \"8 9 72\\n\", \"1560 1561 2435160\\n\", \"9 10 90\\n\", \"2377 2378 5652506\\n\", \"3495 3496 12218520\\n\", \"10023 10024 100470552\\n\", \"19176 19177 367738152\\n\", \"6902 6903 47644506\\n\", \"440 441 194040\\n\", \"4798 4799 23025602\\n\", \"14118 14119 199332042\\n\", \"3762 3763 14156406\\n\", \"1555 1556 2419580\\n\", \"432 433 187056\\n\", \"157 158 24806\\n\", \"6342 6343 40227306\\n\", \"2210 2211 4886310\\n\", \"7136 7137 50929632\\n\", \"91 92 8372\\n\", \"12693 12694 161124942\\n\", \"5179 5180 26827220\\n\", \"111 112 12432\\n\", \"2786 2787 7764582\\n\", \"10010 10011 100210110\\n\", \"1495 1496 2236520\\n\", \"390 391 152490\\n\", \"633 634 401322\\n\", \"13962 13963 194951406\\n\", \"3401 3402 11570202\\n\", \"33 34 1122\\n\", \"980 981 961380\\n\", \"1479 1480 2188920\\n\", \"745 746 555770\\n\", \"4612 4613 21275156\\n\", \"13 14 182\\n\", \"5460 5461 29817060\\n\", \"7326 7327 53677602\\n\", \"7306 7307 53384942\\n\", \"2342 2343 5487306\\n\", \"9210 9211 84833310\\n\", \"7684 7685 59051540\\n\", \"11237 11238 126281406\\n\", \"20 21 420\\n\", \"1482 1483 2197806\\n\", \"8289 8290 68715810\\n\", \"3754 3755 14096270\\n\", \"6 7 42\\n\", \"199 200 39800\\n\", \"353 354 124962\\n\", \"339 340 115260\\n\", \"22919 22920 525303480\\n\", \"10800 10801 116650800\\n\", \"15329 15330 234993570\\n\", \"8150 8151 66430650\\n\", \"1798 1799 3234602\\n\", \"44 45 1980\\n\", \"7438 7439 55331282\\n\", \"16 17 272\\n\", \"700 701 490700\\n\", \"10 11 110\\n\", \"2977 2978 8865506\\n\", \"5298 5299 28074102\\n\", \"9991 9992 99830072\\n\", \"27070 27071 732811970\\n\", \"9816 9817 96363672\\n\", \"875 876 766500\\n\", \"9279 9280 86109120\\n\", \"28128 28129 791212512\\n\", \"4641 4642 21543522\\n\", \"161 162 26082\\n\", \"641 642 411522\\n\", \"240 241 57840\\n\", \"3902 3903 15229506\\n\", \"1655 1656 2740680\\n\", \"11568 11569 133830192\\n\", \"48 49 2352\\n\", \"16424 16425 269764200\\n\", \"1538 1539 2366982\\n\", \"110 111 12210\\n\", \"4520 4521 20434920\\n\", \"10110 10111 102222210\\n\", \"853 854 728462\\n\", \"618 619 382542\\n\", \"716 717 513372\\n\", \"1774 1775 3148850\\n\", \"6344 6345 40252680\\n\", \"64 65 4160\\n\", \"649 650 421850\\n\", \"756 757 572292\\n\", \"341 342 116622\\n\", \"7 8 56 \", \"3 4 12 \"]}", "source": "taco"}
|
Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction <image> as a sum of three distinct positive fractions in form <image>.
Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that <image>. Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
If there is no such answer, print -1.
Input
The single line contains single integer n (1 ≤ n ≤ 104).
Output
If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.
If there are multiple answers, print any of them.
Examples
Input
3
Output
2 7 42
Input
7
Output
7 8 56
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\": [\"(()((\\n\", \")(\\n\", \"(()())\\n\", \"()\\n\", \"()()()()()()()(\\n\", \"()\\n\", \"())((\\n\", \"))()((\\n\", \"(())(\\n\", \")))(((\\n\", \"(()()(\\n\", \"()))((\\n\", \"()(()(\\n\", \"((()()))()()()(\\n\", \"()(((\\n\", \"(())))\\n\", \"()()()()))()(((\\n\", \"()()()())(()(((\\n\", \")())(\\n\", \"((()(())()()()(\\n\", \")(()(())()()()(\\n\", \"()()()())(()(()\\n\", \"(()))\\n\", \"((()))\\n\", \"((()(())()))()(\\n\", \"()(())\\n\", \"((()()))()()))(\\n\", \")((()(\\n\", \"(()(()\\n\", \"))()()())(()(()\\n\", \"((()()\\n\", \"()()))())(()(((\\n\", \"))(()(\\n\", \"()())(\\n\", \"((()()))((())))\\n\", \"()((()\\n\", \")(()(())()()())\\n\", \"()()))())((((((\\n\", \"((()()))((()))(\\n\", \"(((((())()))()(\\n\", \"((())())((()))(\\n\", \"()))((())())(((\\n\", \"()()))()((()(((\\n\", \"(()))())((()))(\\n\", \"((()((()()))))(\\n\", \"()))((())()))((\\n\", \"()))))()((()(((\\n\", \"()))((()(()))((\\n\", \"()))))()((())((\\n\", \"(()))(()((()))(\\n\", \"(()))(()((())))\\n\", \"))))((()(()))((\\n\", \")()((\\n\", \")(((()\\n\", \"((()()))()((()(\\n\", \"()((()())(()(((\\n\", \")(()(())()()))(\\n\", \"()()()())((((()\\n\", \"((()(())()))(((\\n\", \"()))()()))()(((\\n\", \"((\\n\", \"))\\n\", \"))((((\\n\", \"(())((\\n\", \"((()(\\n\", \"(((())\\n\", \"())(((\\n\", \"(()(((\\n\", \"((()((\\n\", \"()(()\\n\", \"())()(\\n\", \"()()((\\n\", \"(()))(\\n\", \"()((((\\n\", \"((())(\\n\", \"()()(\\n\", \"((((((\\n\", \")(()(\\n\", \")))((\\n\", \")(((((\\n\", \"(())()\\n\", \"((((()\\n\", \"((()((()()))()(\\n\", \"))))((\\n\", \"(()()\\n\", \")()()(\\n\", \")((((\\n\", \")())))\\n\", \"(((()(\\n\", \")()(((\\n\", \"(((()\\n\", \"())))\\n\", \"))(((\\n\", \"(()((\\n\", \"(()())\\n\", \")(\\n\"], \"outputs\": [\"1\\n2\\n1 3 \\n\", \"0\\n\", \"1\\n4\\n1 2 5 6 \\n\", \"1\\n2\\n1 2 \\n\", \"1\\n8\\n1 3 5 7 8 10 12 14 \", \"1\\n2\\n1 2 \", \"1\\n2\\n1 3\\n\", \"1\\n2\\n3 4\\n\", \"1\\n4\\n1 2 3 4\\n\", \"0\\n\", \"1\\n4\\n1 2 3 5\\n\", \"1\\n2\\n1 4\\n\", \"1\\n2\\n1 5\\n\", \"1\\n8\\n1 2 3 5 8 10 12 14\\n\", \"1\\n2\\n1 2\\n\", \"1\\n4\\n1 2 5 6\\n\", \"1\\n8\\n1 3 5 7 8 9 10 12\\n\", \"1\\n6\\n1 3 5 8 9 12\\n\", \"1\\n2\\n2 4\\n\", \"1\\n10\\n1 2 3 5 6 7 8 10 12 14\\n\", \"1\\n8\\n2 3 5 6 8 10 12 14\\n\", \"1\\n8\\n1 3 5 7 8 9 12 15\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n6\\n1 2 3 4 5 6\\n\", \"1\\n10\\n1 2 3 5 6 8 10 11 12 14\\n\", \"1\\n4\\n1 3 5 6\\n\", \"1\\n8\\n1 2 3 5 10 12 13 14\\n\", \"1\\n2\\n2 5\\n\", \"1\\n4\\n1 2 3 6\\n\", \"1\\n6\\n3 5 7 9 12 15\\n\", \"1\\n4\\n1 2 4 6\\n\", \"1\\n6\\n1 3 7 8 9 12\\n\", \"1\\n2\\n3 5\\n\", \"1\\n4\\n1 3 4 5\\n\", \"1\\n8\\n1 2 3 5 12 13 14 15\\n\", \"1\\n2\\n1 6\\n\", \"1\\n8\\n2 3 5 6 10 12 14 15\\n\", \"1\\n4\\n1 3 8 9\\n\", \"1\\n8\\n1 2 3 5 8 12 13 14\\n\", \"1\\n12\\n1 2 3 4 5 6 7 8 10 11 12 14\\n\", \"1\\n8\\n1 2 3 6 8 12 13 14\\n\", \"1\\n8\\n1 5 6 7 8 9 11 12\\n\", \"1\\n4\\n1 3 8 12\\n\", \"1\\n6\\n1 2 6 12 13 14\\n\", \"1\\n12\\n1 2 3 5 6 7 8 10 11 12 13 14\\n\", \"1\\n8\\n1 5 6 7 9 11 12 13\\n\", \"1\\n4\\n1 7 8 12\\n\", \"1\\n8\\n1 5 6 7 8 11 12 13\\n\", \"1\\n4\\n1 7 12 13\\n\", \"1\\n8\\n1 2 6 7 8 12 13 14\\n\", \"1\\n8\\n1 2 6 7 12 13 14 15\\n\", \"1\\n6\\n5 6 7 11 12 13\\n\", \"1\\n2\\n2 3\\n\", \"1\\n2\\n2 6\\n\", \"1\\n8\\n1 2 3 5 7 8 10 14\\n\", \"1\\n8\\n1 3 4 5 6 8 9 12\\n\", \"1\\n8\\n2 3 5 6 10 12 13 14\\n\", \"1\\n6\\n1 3 5 8 9 15\\n\", \"1\\n10\\n1 2 3 5 6 7 8 10 11 12\\n\", \"1\\n6\\n1 5 7 9 10 12\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n4\\n1 2 3 4\\n\", \"1\\n2\\n1 4\\n\", \"1\\n4\\n1 2 5 6\\n\", \"1\\n2\\n1 3\\n\", \"1\\n2\\n1 3\\n\", \"1\\n2\\n1 4\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 4\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n2\\n1 2\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n2\\n1 4\\n\", \"0\\n\", \"1\\n2\\n2 4\\n\", \"0\\n\", \"0\\n\", \"1\\n4\\n1 2 4 6\\n\", \"1\\n2\\n1 6\\n\", \"1\\n10\\n1 2 3 5 6 8 10 11 12 14\\n\", \"0\\n\", \"1\\n4\\n1 2 3 5\\n\", \"1\\n2\\n2 5\\n\", \"0\\n\", \"1\\n2\\n2 6\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n2 3\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 5\\n\", \"0\\n\", \"1\\n2\\n1 3 \", \"1\\n4\\n1 2 5 6 \", \"0\"]}", "source": "taco"}
|
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by $n$ characters '(' or ')' is simple if its length $n$ is even and positive, its first $\frac{n}{2}$ characters are '(', and its last $\frac{n}{2}$ characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters $a$ is a subsequence of a string $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) characters.
-----Input-----
The only line of input contains a string $s$ ($1 \le |s| \le 1000$) formed by characters '(' and ')', where $|s|$ is the length of $s$.
-----Output-----
In the first line, print an integer $k$ — the minimum number of operations you have to apply. Then, print $2k$ lines describing the operations in the following format:
For each operation, print a line containing an integer $m$ — the number of characters in the subsequence you will remove.
Then, print a line containing $m$ integers $1 \le a_1 < a_2 < \dots < a_m$ — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest $k$, you may print any of them.
-----Examples-----
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
-----Note-----
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices $2$ and $3$, which results in the same final string.
In the second sample, it is already impossible to perform any 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
|
{"tests": "{\"inputs\": [\"1 2 3 4 5 6\\n3\\n4 5\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n1 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 3\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 2\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n2 3\\n4 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 6\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 4\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n1 4\\n6 2\", \"1 2 3 4 5 6\\n3\\n1 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n2\\n6 3\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 2\\n1 5\\n3 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 6\\n4 2\", \"1 2 3 4 5 6\\n2\\n6 3\\n1 4\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n2 4\\n6 2\", \"0 2 3 4 5 6\\n3\\n6 5\\n2 3\\n6 2\", \"1 2 3 4 5 12\\n3\\n4 2\\n1 3\\n3 2\", \"1 2 3 4 5 6\\n2\\n6 4\\n1 4\\n3 2\", \"1 2 3 4 5 12\\n3\\n3 2\\n1 3\\n3 2\", \"1 2 3 4 5 7\\n3\\n4 5\\n2 3\\n4 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 6\\n1 2\", \"1 2 3 7 5 6\\n3\\n1 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n2 4\\n4 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n4 6\\n1 2\", \"1 0 3 4 10 6\\n2\\n6 3\\n1 4\\n3 2\", \"1 2 3 8 5 6\\n3\\n6 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n4 6\\n6 2\", \"1 2 3 4 5 10\\n3\\n4 2\\n1 5\\n3 2\", \"1 2 3 7 5 6\\n3\\n1 5\\n2 3\\n1 2\", \"1 2 3 7 5 6\\n3\\n1 3\\n2 3\\n1 2\", \"1 2 3 4 7 6\\n1\\n6 3\\n1 4\\n3 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 6\\n4 1\", \"1 2 3 4 5 6\\n2\\n5 3\\n1 4\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 5\\n2 4\\n3 2\", \"1 2 3 4 5 7\\n3\\n3 5\\n2 3\\n4 2\", \"1 2 3 12 5 6\\n3\\n1 5\\n2 3\\n1 2\", \"1 2 3 4 5 6\\n3\\n3 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n4 2\\n1 3\\n1 2\", \"1 2 3 4 5 6\\n2\\n6 3\\n2 3\\n3 2\", \"1 2 3 4 5 6\\n2\\n6 3\\n1 2\\n3 2\", \"1 2 3 4 5 10\\n3\\n4 1\\n1 5\\n3 2\", \"1 2 3 4 10 6\\n2\\n2 3\\n1 4\\n3 2\", \"1 2 3 12 5 6\\n3\\n1 5\\n2 3\\n1 3\", \"1 2 3 4 5 6\\n3\\n6 3\\n2 3\\n3 2\", \"0 2 3 4 8 6\\n2\\n6 4\\n0 4\\n3 3\", \"1 2 3 4 5 6\\n3\\n6 3\\n2 6\\n3 2\", \"1 2 3 4 5 6\\n3\\n6 3\\n4 6\\n3 2\", \"1 2 3 4 5 6\\n2\\n4 5\\n1 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n1 3\\n5 4\", \"1 2 3 4 5 6\\n3\\n6 4\\n1 5\\n3 2\", \"1 2 3 4 5 16\\n3\\n3 2\\n1 3\\n3 2\", \"1 2 3 4 5 17\\n3\\n4 2\\n1 5\\n3 2\", \"1 2 3 4 5 6\\n2\\n1 3\\n1 3\\n0 2\", \"1 2 3 4 5 6\\n1\\n4 5\\n2 4\\n3 2\", \"1 2 3 7 5 10\\n3\\n2 3\\n2 3\\n1 2\", \"1 2 3 4 7 6\\n1\\n2 3\\n1 4\\n3 2\", \"1 2 3 4 7 6\\n1\\n6 4\\n0 4\\n3 1\", \"1 2 3 4 5 6\\n3\\n4 6\\n1 3\\n1 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n2 3\\n5 4\", \"1 2 3 4 9 6\\n2\\n1 3\\n1 3\\n0 2\", \"1 2 3 4 5 6\\n2\\n4 2\\n1 3\\n4 2\", \"1 2 3 8 5 6\\n3\\n6 5\\n2 6\\n6 2\", \"0 2 3 4 5 6\\n3\\n6 5\\n2 6\\n4 2\", \"1 2 3 4 5 12\\n3\\n3 2\\n1 3\\n3 1\", \"0 2 3 4 5 6\\n1\\n6 4\\n0 4\\n3 2\", \"1 2 3 4 5 6\\n2\\n1 5\\n1 3\\n6 2\", \"1 2 3 4 5 6\\n2\\n1 3\\n1 5\\n0 2\", \"1 2 3 4 0 6\\n3\\n6 3\\n2 4\\n3 2\", \"0 2 3 4 5 6\\n3\\n6 5\\n2 3\\n5 4\", \"1 2 3 4 9 6\\n2\\n1 3\\n2 3\\n0 2\", \"0 2 3 4 5 6\\n3\\n6 2\\n2 6\\n4 2\", \"1 2 3 7 5 11\\n3\\n1 5\\n2 3\\n1 3\", \"1 2 3 4 14 6\\n3\\n2 3\\n1 4\\n3 2\", \"1 2 3 4 8 6\\n3\\n6 4\\n1 4\\n3 2\", \"1 2 3 4 14 6\\n3\\n1 3\\n1 4\\n3 2\", \"1 2 3 4 14 0\\n3\\n1 3\\n1 4\\n3 2\", \"1 2 3 4 14 -1\\n3\\n1 3\\n1 4\\n3 2\", \"1 2 3 4 5 6\\n3\\n4 2\\n2 3\\n3 2\", \"1 2 3 4 5 6\\n3\\n6 4\\n1 3\\n3 1\", \"1 2 3 4 5 7\\n3\\n4 2\\n1 5\\n3 2\", \"1 2 3 4 5 7\\n3\\n3 5\\n2 1\\n4 2\", \"1 2 3 4 10 6\\n2\\n2 1\\n1 4\\n3 4\", \"1 2 3 4 5 6\\n2\\n4 5\\n2 3\\n6 2\", \"1 2 3 4 8 6\\n2\\n6 3\\n1 8\\n3 2\", \"1 2 3 4 0 6\\n3\\n6 3\\n2 3\\n3 1\", \"1 2 3 4 5 6\\n3\\n3 5\\n1 3\\n5 4\", \"1 2 3 4 9 6\\n2\\n1 3\\n1 2\\n0 2\", \"0 2 3 4 -1 6\\n3\\n6 3\\n2 3\\n3 2\", \"1 2 3 4 5 6\\n2\\n1 3\\n2 3\\n4 2\", \"1 2 3 4 14 6\\n2\\n2 6\\n1 4\\n3 2\", \"1 2 3 4 0 6\\n1\\n6 4\\n0 4\\n3 1\", \"1 2 3 4 8 6\\n3\\n6 3\\n1 4\\n1 2\", \"1 2 5 4 9 6\\n1\\n6 4\\n0 4\\n3 1\", \"1 2 3 4 14 6\\n3\\n1 3\\n1 4\\n1 2\", \"1 2 3 4 19 0\\n3\\n1 3\\n1 4\\n3 2\", \"1 2 3 4 5 6\\n3\\n3 5\\n1 3\\n1 4\", \"1 2 3 4 0 6\\n2\\n6 4\\n0 4\\n3 1\", \"1 2 3 4 7 11\\n2\\n2 4\\n1 4\\n3 2\", \"0 2 3 1 5 6\\n3\\n6 5\\n2 3\\n6 2\", \"1 2 3 4 5 6\\n3\\n6 5\\n1 3\\n3 2\"], \"outputs\": [\"6\\n5\\n6\\n\", \"6\\n5\\n4\\n\", \"6\\n1\\n4\\n\", \"3\\n1\\n4\\n\", \"2\\n5\\n6\\n\", \"1\\n5\\n6\\n\", \"6\\n1\\n1\\n\", \"3\\n3\\n4\\n\", \"5\\n5\\n6\\n\", \"6\\n2\\n4\\n\", \"4\\n1\\n4\\n\", \"2\\n5\\n\", \"1\\n4\\n6\\n\", \"3\\n3\\n1\\n\", \"2\\n2\\n\", \"6\\n6\\n4\\n\", \"3\\n0\\n4\\n\", \"1\\n5\\n12\\n\", \"5\\n2\\n\", \"12\\n5\\n12\\n\", \"7\\n1\\n1\\n\", \"3\\n3\\n3\\n\", \"7\\n1\\n7\\n\", \"6\\n6\\n1\\n\", \"3\\n2\\n3\\n\", \"0\\n0\\n\", \"3\\n1\\n8\\n\", \"3\\n2\\n4\\n\", \"1\\n4\\n10\\n\", \"7\\n1\\n3\\n\", \"5\\n1\\n3\\n\", \"2\\n\", \"3\\n3\\n5\\n\", \"6\\n2\\n\", \"6\\n6\\n6\\n\", \"1\\n1\\n1\\n\", \"12\\n1\\n3\\n\", \"1\\n1\\n4\\n\", \"1\\n5\\n3\\n\", \"2\\n1\\n\", \"2\\n3\\n\", \"5\\n4\\n10\\n\", \"1\\n2\\n\", \"12\\n1\\n5\\n\", \"2\\n1\\n6\\n\", \"8\\n2\\n\", \"2\\n3\\n6\\n\", \"2\\n2\\n6\\n\", \"6\\n5\\n\", \"3\\n5\\n1\\n\", \"5\\n4\\n6\\n\", \"16\\n5\\n16\\n\", \"1\\n4\\n17\\n\", \"5\\n5\\n\", \"6\\n\", \"1\\n1\\n3\\n\", \"1\\n\", \"7\\n\", \"2\\n5\\n3\\n\", \"3\\n1\\n1\\n\", \"9\\n9\\n\", \"1\\n5\\n\", \"3\\n3\\n8\\n\", \"3\\n3\\n0\\n\", \"12\\n5\\n2\\n\", \"5\\n\", \"4\\n5\\n\", \"5\\n4\\n\", \"2\\n6\\n6\\n\", \"3\\n0\\n0\\n\", \"9\\n1\\n\", \"4\\n3\\n0\\n\", \"7\\n1\\n5\\n\", \"1\\n2\\n6\\n\", \"8\\n2\\n6\\n\", \"14\\n2\\n6\\n\", \"14\\n2\\n0\\n\", \"14\\n2\\n-1\\n\", \"1\\n1\\n6\\n\", \"5\\n5\\n2\\n\", \"1\\n4\\n7\\n\", \"1\\n4\\n1\\n\", \"4\\n2\\n\", \"6\\n1\\n\", \"2\\n4\\n\", \"2\\n1\\n2\\n\", \"1\\n5\\n1\\n\", \"9\\n3\\n\", \"2\\n0\\n6\\n\", \"5\\n1\\n\", \"3\\n2\\n\", \"0\\n\", \"2\\n2\\n3\\n\", \"9\\n\", \"14\\n2\\n3\\n\", \"19\\n2\\n0\\n\", \"1\\n5\\n2\\n\", \"0\\n1\\n\", \"11\\n2\\n\", \"3\\n0\\n1\\n\", \"3\\n5\\n6\"]}", "source": "taco"}
|
Construct a dice from a given sequence of integers in the same way as Dice I.
You are given integers on the top face and the front face after the dice was rolled in the same way as Dice I. Write a program to print an integer on the right side face.
<image>
Constraints
* $0 \leq $ the integer assigned to a face $ \leq 100$
* The integers are all different
* $1 \leq q \leq 24$
Input
In the first line, six integers assigned to faces are given in ascending order of their corresponding labels. In the second line, the number of questions $q$ is given.
In the following $q$ lines, $q$ questions are given. Each question consists of two integers on the top face and the front face respectively.
Output
For each question, print the integer on the right side face.
Example
Input
1 2 3 4 5 6
3
6 5
1 3
3 2
Output
3
5
6
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\": [\"8 1 1\\n\", \"8 1 10\\n\", \"10 62 99\\n\", \"88 417 591\\n\", \"57 5289 8444\\n\", \"382 81437847 324871127\\n\", \"244 575154303 436759189\\n\", \"85 902510038 553915152\\n\", \"1926 84641582 820814219\\n\", \"3768 561740421 232937477\\n\", \"2313 184063453 204869248\\n\", \"35896 278270961 253614967\\n\", \"483867 138842067 556741142\\n\", \"4528217 187553422 956731625\\n\", \"10000000 1000000000 1\\n\", \"10000000 1 100\\n\", \"10000000 1 1000000000\\n\", \"10000000 1 1000\\n\", \"10000000 1 10\\n\", \"1 1 1\\n\", \"10000000 998 998\\n\", \"9999999 987654321 123456789\\n\", \"9999999 1 2\\n\", \"10000000 1 1\\n\", \"11478 29358 26962\\n\", \"4314870 1000000000 1\\n\", \"7186329 608148870 290497442\\n\", \"9917781 1 1\\n\", \"7789084 807239576 813643932\\n\", \"58087 1 100000000\\n\", \"9999991 2 3\\n\", \"1 1 1\\n\", \"3768 561740421 232937477\\n\", \"10000000 1 100\\n\", \"7789084 807239576 813643932\\n\", \"10000000 1 10\\n\", \"58087 1 100000000\\n\", \"10 62 99\\n\", \"9999999 987654321 123456789\\n\", \"35896 278270961 253614967\\n\", \"1926 84641582 820814219\\n\", \"10000000 1 1000\\n\", \"483867 138842067 556741142\\n\", \"2313 184063453 204869248\\n\", \"10000000 1 1\\n\", \"9999999 1 2\\n\", \"4314870 1000000000 1\\n\", \"85 902510038 553915152\\n\", \"11478 29358 26962\\n\", \"10000000 1 1000000000\\n\", \"57 5289 8444\\n\", \"244 575154303 436759189\\n\", \"10000000 1000000000 1\\n\", \"382 81437847 324871127\\n\", \"9917781 1 1\\n\", \"10000000 998 998\\n\", \"4528217 187553422 956731625\\n\", \"88 417 591\\n\", \"7186329 608148870 290497442\\n\", \"9999991 2 3\\n\", \"1 1 0\\n\", \"6304 561740421 232937477\\n\", \"39556 1 100000000\\n\", \"10 62 39\\n\", \"9999999 987654321 202833713\\n\", \"38618 278270961 253614967\\n\", \"1926 135244635 820814219\\n\", \"483867 138842067 234793352\\n\", \"2313 70978283 204869248\\n\", \"9999999 1 0\\n\", \"85 902510038 813358931\\n\", \"11478 5238 26962\\n\", \"57 3073 8444\\n\", \"127 575154303 436759189\\n\", \"382 107216562 324871127\\n\", \"7728959 1 1\\n\", \"4528217 268227006 956731625\\n\", \"175 417 591\\n\", \"1341311 608148870 290497442\\n\", \"9999991 2 2\\n\", \"12 1 10\\n\", \"8 1 2\\n\", \"6218 561740421 232937477\\n\", \"10 63 39\\n\", \"9999999 822479358 202833713\\n\", \"38618 278270961 407707735\\n\", \"1926 160311843 820814219\\n\", \"483867 138842067 4975010\\n\", \"2313 70978283 27345506\\n\", \"85 902510038 544684516\\n\", \"19729 5238 26962\\n\", \"20 3073 8444\\n\", \"245 575154303 436759189\\n\", \"382 113069268 324871127\\n\", \"1377545 1 1\\n\", \"1562474 268227006 956731625\\n\", \"175 19 591\\n\", \"1341311 608148870 63221163\\n\", \"1199303 2 2\\n\", \"6218 795896112 232937477\\n\", \"2 63 39\\n\", \"9999999 1516835495 202833713\\n\", \"1926 160311843 1074507089\\n\", \"137886 138842067 4975010\\n\", \"2918 70978283 27345506\\n\", \"85 902510038 249764288\\n\", \"19729 7634 26962\\n\", \"20 896 8444\\n\", \"245 386053070 436759189\\n\", \"2 1 0\\n\", \"39556 1 100100000\\n\", \"8 1 0\\n\", \"4 1 0\\n\", \"39556 1 100101000\\n\", \"52599 278270961 407707735\\n\", \"8 1 10\\n\", \"8 1 1\\n\"], \"outputs\": [\"4\\n\", \"8\\n\", \"384\\n\", \"4623\\n\", \"60221\\n\", \"2519291691\\n\", \"5219536421\\n\", \"6933531064\\n\", \"7184606427\\n\", \"5042211408\\n\", \"2969009745\\n\", \"5195579310\\n\", \"10712805143\\n\", \"21178755627\\n\", \"8000000023\\n\", \"1757\\n\", \"10000000\\n\", \"14224\\n\", \"214\\n\", \"1\\n\", \"30938\\n\", \"11728395036\\n\", \"54\\n\", \"31\\n\", \"556012\\n\", \"7000000022\\n\", \"12762929866\\n\", \"35\\n\", \"25165322688\\n\", \"58087\\n\", \"88\\n\", \"1\", \"5042211408\", \"1757\", \"25165322688\", \"214\", \"58087\", \"384\", \"11728395036\", \"5195579310\", \"7184606427\", \"14224\", \"10712805143\", \"2969009745\", \"31\", \"54\", \"7000000022\", \"6933531064\", \"556012\", \"10000000\", \"60221\", \"5219536421\", \"8000000023\", \"2519291691\", \"35\", \"30938\", \"21178755627\", \"4623\", \"12762929866\", \"88\", \"1\", \"5042211408\", \"39556\", \"241\", \"13554064288\", \"5752121232\", \"7918960102\", \"5337016872\", \"2340671213\", \"9\", \"8490193738\", \"348190\", \"49141\", \"4207622929\", \"2699742696\", \"30\", \"22353356572\", \"5631\", \"9458842060\", \"66\", \"12\", \"6\", \"5603951829\", \"243\", \"12067489621\", \"7934075978\", \"8169632182\", \"1066419659\", \"584713698\", \"6878147248\", \"364676\", \"32253\", \"5794690724\", \"2726374961\", \"27\", \"20439893322\", \"2037\", \"4913316480\", \"58\", \"6774730284\", \"102\", \"18316694854\", \"10199175142\", \"1056469639\", \"726670264\", \"5108625880\", \"392250\", \"17404\", \"4987579673\", \"1\", \"39556\", \"1\", \"1\", \"39556\", \"7934075978\", \"8\", \"4\"]}", "source": "taco"}
|
zscoder wants to generate an input file for some programming competition problem.
His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.
Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.
zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.
-----Input-----
The only line contains three integers n, x and y (1 ≤ n ≤ 10^7, 1 ≤ x, y ≤ 10^9) — the number of letters 'a' in the input file and the parameters from the problem statement.
-----Output-----
Print the only integer t — the minimum amount of time needed to generate the input file.
-----Examples-----
Input
8 1 1
Output
4
Input
8 1 10
Output
8
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\": [\"14 9\\n5 5 6 8 8 4 3 2 2 7 3 9 5 4\\n\", \"14 11\\n10 8 6 1 7 2 9 5 5 10 3 5 11 3\\n\", \"1 1\\n1\\n\", \"3 3\\n2 2 2\\n\", \"10 4\\n1 4 2 3 1 3 3 4 1 3\\n\", \"3 4\\n1 2 4\\n\", \"10 5\\n2 2 4 4 3 1 1 2 3 2\\n\", \"19 5\\n1 1 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 5 5\\n\", \"2 2\\n1 2\\n\", \"3 4\\n1 3 4\\n\", \"3 2\\n1 2 2\\n\", \"25 5\\n1 5 1 3 2 1 5 5 3 1 3 3 4 4 5 5 1 4 4 1 2 1 5 1 5\\n\", \"18 5\\n1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 5\\n\", \"19 5\\n2 5 1 3 4 2 3 5 1 3 2 1 4 2 1 3 3 4 5\\n\", \"3 2\\n1 1 2\\n\", \"3 3\\n1 2 3\\n\", \"30 12\\n7 2 12 5 9 9 8 10 7 10 5 4 5 8 4 4 10 11 3 8 7 8 3 2 1 6 3 9 7 1\\n\", \"5 5\\n1 1 4 2 2\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"2 1000000\\n1000000 1000000\\n\", \"3 1000000\\n1000000 1000000 1000000\\n\", \"1 1000000\\n1000000\\n\", \"14 11\\n10 8 6 1 7 2 9 3 5 10 3 5 11 3\\n\", \"3 3\\n1 2 2\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"10 5\\n2 2 6 4 3 1 1 2 3 1\\n\", \"14 15\\n5 5 6 8 8 4 3 2 2 7 3 9 5 4\\n\", \"19 5\\n1 1 2 2 4 2 3 3 3 3 3 3 3 4 4 4 4 5 5\\n\", \"25 5\\n1 5 1 5 2 1 5 5 3 1 3 3 4 4 5 5 1 4 4 1 2 1 5 1 5\\n\", \"18 5\\n1 1 2 2 2 4 3 3 3 3 3 3 4 4 4 4 5 5\\n\", \"30 12\\n7 2 12 5 9 9 8 10 7 10 5 4 5 8 4 4 10 11 3 8 7 8 3 2 1 6 3 6 7 1\\n\", \"10 4\\n1 4 2 3 1 3 3 6 1 3\\n\", \"10 5\\n2 2 4 4 3 1 1 2 3 1\\n\", \"2 2\\n1 1\\n\", \"3 4\\n1 6 4\\n\", \"2 1000000\\n0000000 1000000\\n\", \"10 6\\n2 3 3 3 4 4 4 5 5 4\\n\", \"12 6\\n1 5 3 3 3 4 3 9 3 2 3 3\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 2 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"3 2\\n1 2 4\\n\", \"3 2\\n1 4 2\\n\", \"19 5\\n2 5 1 3 4 2 3 5 1 3 2 1 4 2 1 1 3 4 5\\n\", \"3 3\\n1 1 2\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 9 6 6 8 8 6 2 6\\n\", \"14 11\\n10 8 6 1 7 2 9 3 5 6 3 5 11 3\\n\", \"10 4\\n1 4 2 3 2 3 3 6 1 3\\n\", \"2 4\\n1 2\\n\", \"3 7\\n1 6 4\\n\", \"100 10\\n7 4 1 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"10 5\\n2 2 6 4 3 2 1 2 3 1\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 5 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 2 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"19 5\\n1 1 2 2 4 2 3 3 3 3 3 3 3 4 4 4 2 5 5\\n\", \"3 4\\n1 4 2\\n\", \"19 5\\n2 5 1 3 4 2 3 5 1 3 2 1 4 2 1 1 3 2 5\\n\", \"30 12\\n7 2 12 5 9 9 8 10 7 10 5 4 5 8 4 4 10 11 3 8 7 8 3 2 2 6 3 6 7 1\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 2 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 9 6 6 8 8 6 2 6\\n\", \"14 11\\n10 8 6 1 7 2 9 3 5 1 3 5 11 3\\n\", \"2 4\\n1 1\\n\", \"100 10\\n7 4 1 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 4 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"10 5\\n2 2 6 4 1 2 1 2 3 1\\n\", \"100 10\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 5 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 2 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 5 4 10 4 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"19 10\\n1 1 2 2 4 2 3 3 3 3 3 3 3 4 4 4 2 5 5\\n\", \"3 1\\n1 4 2\\n\", \"30 12\\n7 2 12 5 9 9 8 10 7 10 5 4 5 8 4 4 10 11 3 8 5 8 3 2 2 6 3 6 7 1\\n\", \"100 10\\n7 4 1 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 6 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 4 5 6 1 8 10 4 10 5 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"10 5\\n2 2 6 4 2 2 1 2 3 1\\n\", \"19 10\\n1 1 1 2 4 2 3 3 3 3 3 3 3 4 4 4 2 5 5\\n\", \"30 12\\n7 1 12 5 9 9 8 10 7 10 5 4 5 8 4 4 10 11 3 8 5 8 3 2 2 6 3 6 7 1\\n\", \"10 5\\n2 2 6 4 1 2 1 2 1 1\\n\", \"19 10\\n1 1 1 2 4 2 3 1 3 3 3 3 3 4 4 4 2 5 5\\n\", \"30 12\\n7 1 12 5 9 17 8 10 7 10 5 4 5 8 4 4 10 11 3 8 5 8 3 2 2 6 3 6 7 1\\n\", \"10 5\\n2 2 6 4 1 2 1 1 1 1\\n\", \"19 10\\n1 1 1 2 2 2 3 1 3 3 3 3 3 4 4 4 2 5 5\\n\", \"30 12\\n7 1 12 5 9 17 8 10 7 10 5 4 5 8 4 4 10 11 3 8 8 8 3 2 2 6 3 6 7 1\\n\", \"30 12\\n7 1 12 5 9 17 8 10 7 10 5 4 5 8 4 4 10 11 3 8 8 14 3 2 2 6 3 6 7 1\\n\", \"10 6\\n2 3 3 3 4 4 4 5 5 6\\n\", \"13 5\\n1 1 5 1 2 3 3 2 4 2 3 4 5\\n\", \"12 6\\n1 5 3 3 3 4 3 5 3 2 3 3\\n\"], \"outputs\": [\"4\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"8\\n\", \"6\\n\", \"6\\n\", \"0\\n\", \"1\\n\", \"9\\n\", \"0\\n\", \"33\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"33\\n\", \"2\\n\", \"4\\n\", \"6\\n\", \"8\\n\", \"5\\n\", \"9\\n\", \"3\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"33\\n\", \"0\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"33\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"33\\n\", \"2\\n\", \"33\\n\", \"6\\n\", \"0\\n\", \"6\\n\", \"9\\n\", \"33\\n\", \"3\\n\", \"0\\n\", \"33\\n\", \"3\\n\", \"33\\n\", \"6\\n\", \"0\\n\", \"9\\n\", \"33\\n\", \"2\\n\", \"6\\n\", \"9\\n\", \"2\\n\", \"6\\n\", \"9\\n\", \"2\\n\", \"6\\n\", \"9\\n\", \"9\\n\", \"3\\n\", \"4\\n\", \"3\\n\"]}", "source": "taco"}
|
You are playing a game of Jongmah. You don't need to know the rules to solve this problem. You have n tiles in your hand. Each tile has an integer between 1 and m written on it.
To win the game, you will need to form some number of triples. Each triple consists of three tiles, such that the numbers written on the tiles are either all the same or consecutive. For example, 7, 7, 7 is a valid triple, and so is 12, 13, 14, but 2,2,3 or 2,4,6 are not. You can only use the tiles in your hand to form triples. Each tile can be used in at most one triple.
To determine how close you are to the win, you want to know the maximum number of triples you can form from the tiles in your hand.
Input
The first line contains two integers integer n and m (1 ≤ n, m ≤ 10^6) — the number of tiles in your hand and the number of tiles types.
The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ m), where a_i denotes the number written on the i-th tile.
Output
Print one integer: the maximum number of triples you can form.
Examples
Input
10 6
2 3 3 3 4 4 4 5 5 6
Output
3
Input
12 6
1 5 3 3 3 4 3 5 3 2 3 3
Output
3
Input
13 5
1 1 5 1 2 3 3 2 4 2 3 4 5
Output
4
Note
In the first example, we have tiles 2, 3, 3, 3, 4, 4, 4, 5, 5, 6. We can form three triples in the following way: 2, 3, 4; 3, 4, 5; 4, 5, 6. Since there are only 10 tiles, there is no way we could form 4 triples, so the answer is 3.
In the second example, we have tiles 1, 2, 3 (7 times), 4, 5 (2 times). We can form 3 triples as follows: 1, 2, 3; 3, 3, 3; 3, 4, 5. One can show that forming 4 triples is not possible.
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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|
Gerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.
One day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?
The formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of n marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least n marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want.
-----Input-----
The single line contains a single integer n (1 ≤ n ≤ 10^17).
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-----
In a single line print an integer: the maximum number of coins the unlucky buyer could have paid with.
-----Examples-----
Input
1
Output
1
Input
4
Output
2
-----Note-----
In the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.
In the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives.
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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\"5\\n19455868963/549972423\\n303236619504653/4855124198925\\n\", \"5\\n1377625934246/28748558475\\n303236619504653/4855124198925\\n\", \"5\\n1826/189\\n877318/35343\\n\", \"2\\n1826/189\\n8810/693\\n\", \"2\\n5\\n439331/27027\\n\", \"2\\n8810/693\\n19455868963/549972423\\n\", \"5\\n1826/189\\n1645249/81081\\n\", \"5\\n1826/189\\n21230945651546909948457797499670954/119209116549732434989049167756875\\n\", \"2\\n2\\n5\\n\", \"2\\n10/3\\n2997975588579466145916762078349601859974465077901/9437272446276300617211376799899847032332515625\\n\", \"2\\n10/3\\n223906399188563282369086366/1734960091324872338301375\\n\", \"5\\n2\\n877318/35343\\n\", \"10/3\\n8810/693\\n877318/35343\\n\", \"2\\n5\\n31989014885046101932963/328031781305515662375\\n\", \"2\\n1826/189\\n781771114/26189163\\n\", \"8810/693\\n781771114/26189163\\n260073418750644288862/2955241273022663625\\n\", \"8810/693\\n781771114/26189163\\n31989014885046101932963/328031781305515662375\\n\", 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\"10/3\\n2\\n3861289540035137932590423886961807813592751894315116939644306/8913121775113966157962800372668924735854723781840323828125\\n\", \"2\\n5\\n13427435743/324342711\\n\", \"5\\n10/3\\n540952945863433849/7675951358500425\\n\", \"5\\n2\\n3861289540035137932590423886961807813592751894315116939644306/8913121775113966157962800372668924735854723781840323828125\\n\", \"5\\n19455868963/549972423\\n20638876509950424295725838/174840939435839848045875\\n\", \"2\\n1826/189\\n1375672554597924028619713/12793239470915110832625\\n\", \"5\\n1826/189\\n13427435743/324342711\\n\", \"2\\n149/21\\n2997975588579466145916762078349601859974465077901/9437272446276300617211376799899847032332515625\\n\", \"2\\n10/3\\n5\\n\", \"149/21\\n2\\n877318/35343\\n\", \"1826/189\\n8810/693\\n877318/35343\\n\", \"2\\n439331/27027\\n31989014885046101932963/328031781305515662375\\n\", \"1826/189\\n781771114/26189163\\n260073418750644288862/2955241273022663625\\n\", \"8810/693\\n781771114/26189163\\n21230945651546909948457797499670954/119209116549732434989049167756875\\n\", \"1826/189\\n2\\n1375672554597924028619713/12793239470915110832625\\n\", \"5\\n1826/189\\n220557037392421755982518814001/1445537203362950452775645625\\n\", \"1826/189\\n10/3\\n1645249/81081\\n\", \"8810/693\\n877318/35343\\n19455868963/549972423\\n\", \"5\\n1826/189\\n20638876509950424295725838/174840939435839848045875\\n\", \"10/3\\n5\\n27552928801699870018553141565572285275417320742/97305498580828537620681150939914783014171875\\n\", \"1826/189\\n10/3\\n13427435743/324342711\\n\", \"439331/27027\\n877318/35343\\n1176971634399441794/14900376166500825\\n\", \"2\\n1826/189\\n877318/35343\\n\"]}", "source": "taco"}
|
Recently Johnny have learned bogosort sorting algorithm. He thought that it is too ineffective. So he decided to improve it. As you may know this algorithm shuffles the sequence randomly until it is sorted. Johnny decided that we don't need to shuffle the whole sequence every time. If after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if they are in the right places. For example, if the initial sequence is (3, 5, 1, 6, 4, 2) and after one shuffle Johnny gets (1, 2, 5, 4, 3, 6) he will fix 1, 2 and 6 and proceed with sorting (5, 4, 3) using the same algorithm. Johnny hopes that this optimization will significantly improve the algorithm. Help him calculate the expected amount of shuffles for the improved algorithm to sort the sequence of the first n natural numbers given that no elements are in the right places initially.
------ Input ------
The first line of input file is number t - the number of test cases. Each of the following t lines hold single number n - the number of elements in the sequence.
------ Constraints ------
1 ≤ t ≤ 150
2 ≤ n ≤ 150
------ Output ------
For each test case output the expected amount of shuffles needed for the improved algorithm to sort the sequence of first n natural numbers in the form of irreducible fractions.
----- Sample Input 1 ------
3
2
6
10
----- Sample Output 1 ------
2
1826/189
877318/35343
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, 200, 10], [123, 456, 5], [99, 501, 5], [99, 234, 1], [99, 234, 19], [99, 5001, 27], [99, 5001, 28], [2000, 7000, 3]], \"outputs\": [[[109, 190]], [[131, 410]], [[104, 500]], [[100, 100]], [[199, 199]], [[999, 4995]], [[1999, 4996]], [[2001, 3000]]]}", "source": "taco"}
|
# Task
You are given three integers `l, d and x`. Your task is:
```
• determine the minimal integer n
such that l ≤ n ≤ d, and the sum of its digits equals x.
• determine the maximal integer m
such that l ≤ m ≤ d, and the sum of its digits equals x.
```
It is guaranteed that such numbers always exist.
# Input/Output
- `[input]` integer `l`
- `[input]` integer `d`
`1 ≤ l ≤ d ≤ 10000.`
- `[input]` integer `x`
`1 ≤ x ≤ 36`
- `[output]` an integer array
Array of two elements, where the first element is `n`, and the second one is `m`.
# Example
For `l = 500, d = 505, x = 10`, the output should be `[505, 505]`.
For `l = 100, d = 200, x = 10`, the output should be `[109, 190]`.
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\": [\"4 3\\naaa\\nbbb\\nccb\\nddd\\n\", \"6 1\\na\\na\\nb\\nb\\nc\\nc\\n\", \"1 1\\na\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\niiillqqqqq\\njjjjjppwww\\n\", \"10 10\\naaaaaaaaaa\\nbbbbbbbbbb\\ncccccccccc\\ndddddddddd\\neeeeeeeeee\\nffffffffff\\ngggggggggg\\nhhhhhhhhhh\\niiiiiiiiii\\njjjjjjjjjj\\n\", \"10 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nbbbbpppkzv\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"9 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"10 10\\naaaaaaaaaa\\nbbbbbbbbbb\\ncccccccccc\\ndddddddddd\\neeeeeeeeee\\nffffffffff\\ngggggggggg\\nhhhhhhhhhh\\niiiiiiiiii\\njjjjjjjjjj\\n\", \"9 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 1\\na\\n\", \"10 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nbbbbpppkzv\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\niiillqqqqq\\njjjjjppwww\\n\", \"10 10\\naaaaaaaaaa\\nbbbbabbbbb\\ncccccccccc\\ndddddddddd\\neeeeeeeeee\\nffffffffff\\ngggggggggg\\nhhhhhhhhhh\\niiiiiiiiii\\njjjjjjjjjj\\n\", \"5 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"10 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nvzkpppbbbb\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\nihillqqqqq\\njjjjjppwww\\n\", \"6 1\\na\\na\\nb\\nb\\nb\\nc\\n\", \"10 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nvzkpppbbbb\\nbbbbpppbbv\\nippeerrsss\\nsssrreeppi\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"6 1\\na\\na\\na\\nb\\na\\nc\\n\", \"10 10\\naaaaaaaaaa\\nbbbbbbbbbb\\ncccccccccc\\ndddddddddd\\neeeeeeeeee\\nffffffffff\\nhggggggggg\\nhhhhhhhhhh\\niiiiiiiiii\\njjjjjjjjjj\\n\", \"9 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwwkwwwkw\\nwcccccww\\nwwwwwwww\\n\", \"8 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nbbbbpppkzv\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"10 10\\naaaaaaaaaa\\nbbbbabbbbb\\ncccccccccc\\ndddddddddd\\neeeeeeeeee\\nffffffffff\\ngggggggggg\\nhhhhhhhhhh\\niiiiiiiiii\\njjjjjjijjj\\n\", \"5 8\\nwmmmmrww\\nwwrmmmmw\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"10 10\\nitttrrrnnn\\nvdkpppbbbb\\nbbbbpppkzv\\nvzkpppbbbb\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffoqooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\nihillqqqqq\\njjjjjppwww\\n\", \"9 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggghxgww\\nssssmcww\\nxxxxzcww\\nwwkwwwkw\\nwcccccww\\nwwwwwwww\\n\", \"8 10\\nitttrrrnnn\\nbbbbpppkdv\\nbbbbpppkzv\\nbzbbpppkbv\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiieeeeeef\\nllorrrrvzz\\n\", \"5 8\\nwmmmmrww\\nwwrnmmmw\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"10 10\\nitttrrrnnn\\nvdkpppbbbb\\nbbbbpppkzv\\nvzkpppbbbb\\nbbbbpppbbv\\nippeerrsss\\nippeerrsss\\nibbeeeesss\\niiifeeeeee\\nllorrrrvzz\\n\", \"1 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"3 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\nihillqqqqq\\njjjjjppwww\\n\", \"6 1\\na\\na\\na\\nb\\nb\\nc\\n\", \"1 8\\nwmmmmrww\\nwmmmmrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwmmmmrww\\nwmmmnrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxgww\\ngwgxwggg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwgxxxxw\\ngwgxwggg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwgxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwhxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwhxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkww\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssrscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssrscmwv\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssrscmwv\\nxxxxzcww\\nwkwwwkwx\\nwbccccwv\\nwvwwwwww\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nffeffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\niiillqqqqq\\njjjjjppwww\\n\", \"1 1\\na\\na\\nb\\nb\\nc\\nc\\n\", \"1 8\\nwmmmmrww\\nrmmmmwww\\nwxxxxgww\\nggggxgww\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"3 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\nihillqqqqq\\njjjjppjwww\\n\", \"5 1\\na\\na\\nb\\nb\\nb\\nc\\n\", \"1 8\\nwmmmmrxw\\nwmmmmrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwmmmmrww\\nwmmmnrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccwcwc\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwvwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxwxgww\\ngwgxwggg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwgxxxxw\\ngwgxwggg\\nsrssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwwrnmmmw\\nwwgxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwwrnmmmw\\nwwhxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwwhxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwwkwwwkw\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwbccccww\\nwwwwwwwv\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwxwkwx\\nwbccccww\\nwwwwwwww\\n\", \"2 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwnmmnrww\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nstrscmwv\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nvwmcsrss\\nxxxxzcww\\nwkwwwkwx\\nwbccccwv\\nwvwwwwww\\n\", \"10 10\\naaaaarpppp\\nbbbbsssssu\\ncciiiiiiqq\\nddmmgggggg\\neeebbbbbbb\\nffeffooooq\\ngxxxxrrrrr\\nhhfuuuuuuu\\niiillqqqqq\\njjjjjppwww\\n\", \"3 10\\naaaaarpppp\\nbbbbsssssu\\nciiiiciiqq\\nddmmgggggg\\neeebbbbbbb\\nfffffqoooo\\ngxxxxrrrrr\\nhhfuuuuuuu\\nihillqqqqq\\njjjjppjwww\\n\", \"1 8\\nwmmmmrww\\nwmmmnrww\\nwxxxxgww\\nggwgxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccwcwc\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxgww\\ngggwxgwg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwwcccccw\\nwwwwvwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxwxgww\\ngwgxwggg\\nssssmcww\\nwxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwwrnmmmw\\nwwgxxxxw\\ngwgxwgfg\\nssssmcxw\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwwrnmmmw\\nwwhxxxxw\\ngwgxwgfg\\nsmssscww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwww\\n\", \"2 8\\nwrmmmmww\\nwmmmnrww\\nwwhxxxxw\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwwkwwwkw\\nwbccccww\\nwwwwwwww\\n\", \"1 8\\nwrmmmmww\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nssssmcww\\nxxxxzcww\\nwkwwwkww\\nwcccccww\\nwwwwwwwv\\n\", \"1 8\\nwrwmmmwm\\nwwrnmmnw\\nwxxxxhww\\ngwgxwgfg\\nsssscmww\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwlmmnrww\\nwxxxxhww\\ngwgxwgfg\\nstrscmwv\\nxxxxzcww\\nwkwwwkwx\\nwbccccww\\nwvwwwwww\\n\", \"1 8\\nwrwmmmwm\\nwmmmnrww\\nwxxxxhww\\ngwgxwgfg\\nvwmcsrss\\nxxxxzcww\\nwkwxwkwx\\nwbccccwv\\nwvwwwwww\\n\", \"6 1\\na\\na\\nb\\nb\\nc\\nc\\n\", \"4 3\\naaa\\nbbb\\nccb\\nddd\\n\"], \"outputs\": [\"6\\n\", \"1\\n\", \"0\\n\", \"138\\n\", \"440\\n\", \"14\\n\", \"45\\n\", \"440\\n\", \"45\\n\", \"0\\n\", \"14\\n\", \"138\\n\", \"381\\n\", \"13\\n\", \"24\\n\", \"135\\n\", \"0\\n\", \"50\\n\", \"2\\n\", \"411\\n\", \"45\\n\", \"3\\n\", \"353\\n\", \"14\\n\", \"37\\n\", \"126\\n\", \"38\\n\", \"5\\n\", \"15\\n\", \"39\\n\", \"0\\n\", \"13\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"135\\n\", \"0\\n\", \"0\\n\", \"13\\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\", \"135\\n\", \"14\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"6\\n\"]}", "source": "taco"}
|
Innokenty works at a flea market and sells some random stuff rare items. Recently he found an old rectangular blanket. It turned out that the blanket is split in $n \cdot m$ colored pieces that form a rectangle with $n$ rows and $m$ columns.
The colored pieces attracted Innokenty's attention so he immediately came up with the following business plan. If he cuts out a subrectangle consisting of three colored stripes, he can sell it as a flag of some country. Innokenty decided that a subrectangle is similar enough to a flag of some country if it consists of three stripes of equal heights placed one above another, where each stripe consists of cells of equal color. Of course, the color of the top stripe must be different from the color of the middle stripe; and the color of the middle stripe must be different from the color of the bottom stripe.
Innokenty has not yet decided what part he will cut out, but he is sure that the flag's boundaries should go along grid lines. Also, Innokenty won't rotate the blanket. Please help Innokenty and count the number of different subrectangles Innokenty can cut out and sell as a flag. Two subrectangles located in different places but forming the same flag are still considered different. [Image] [Image] [Image]
These subrectangles are flags. [Image] [Image] [Image] [Image] [Image] [Image]
These subrectangles are not flags.
-----Input-----
The first line contains two integers $n$ and $m$ ($1 \le n, m \le 1\,000$) — the number of rows and the number of columns on the blanket.
Each of the next $n$ lines contains $m$ lowercase English letters from 'a' to 'z' and describes a row of the blanket. Equal letters correspond to equal colors, different letters correspond to different colors.
-----Output-----
In the only line print the number of subrectangles which form valid flags.
-----Examples-----
Input
4 3
aaa
bbb
ccb
ddd
Output
6
Input
6 1
a
a
b
b
c
c
Output
1
-----Note----- [Image] [Image]
The selected subrectangles are flags in the first example.
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\": [\"6 5\\n1 2 200 10\\n1 4 400 15\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 5 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 400 22\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 22\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 41\\n1 3 250 22\\n2 4 100 10\\n4 5 1 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 71 22\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 22\\n2 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 3 300 30\\n2\\n2 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 41\\n1 3 250 22\\n2 4 100 10\\n4 5 150 20\\n3 3 335 30\\n2\\n1 5 0\\n1 2 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 400 15\\n1 3 250 25\\n1 4 100 10\\n4 5 150 20\\n2 3 95 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 41\\n1 3 250 22\\n2 4 100 10\\n2 5 150 20\\n3 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20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n2 4 400 15\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 5 80 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 7\\n1 2 200 11\\n1 4 103 43\\n2 3 250 0\\n2 5 100 10\\n4 5 178 20\\n3 3 300 30\\n2\\n2 5 0\\n1 5 0\\n0 0\", \"6 5\\n1 4 200 10\\n2 4 103 43\\n2 3 250 0\\n2 3 100 0\\n4 5 136 20\\n1 3 300 40\\n2\\n2 5 0\\n1 5 1\\n0 0\", \"6 6\\n1 4 200 10\\n1 4 158 35\\n2 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 3 300 30\\n2\\n3 4 1\\n1 5 1\\n0 0\", \"6 6\\n1 4 200 10\\n1 5 157 35\\n2 3 250 25\\n2 4 000 10\\n4 5 150 38\\n3 3 300 30\\n2\\n2 3 1\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 41\\n1 3 250 22\\n2 4 101 19\\n4 5 1 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 158 37\\n2 3 250 25\\n2 4 100 8\\n4 5 150 20\\n3 3 404 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 14\\n1 2 200 10\\n2 4 103 22\\n2 3 250 13\\n2 3 100 10\\n4 5 178 10\\n3 3 300 30\\n2\\n2 5 0\\n1 5 1\\n0 0\", \"6 7\\n1 2 200 10\\n2 5 103 43\\n2 3 250 0\\n2 3 100 10\\n4 5 178 20\\n3 3 369 30\\n2\\n2 5 0\\n1 3 1\\n0 0\", \"6 5\\n1 4 200 10\\n1 4 158 41\\n1 3 206 22\\n2 4 000 10\\n3 5 2 20\\n3 3 300 30\\n2\\n1 5 0\\n1 5 1\\n0 0\", \"6 7\\n1 2 77 11\\n1 4 103 43\\n2 3 250 0\\n2 5 100 10\\n4 5 178 20\\n3 3 300 30\\n2\\n2 5 0\\n1 5 0\\n0 0\", \"6 5\\n1 2 200 10\\n1 4 400 15\\n1 3 250 25\\n2 4 100 10\\n4 5 150 20\\n3 5 300 20\\n2\\n1 5 0\\n1 5 1\\n0 0\"], \"outputs\": [\"450\\n35\\n\", \"450\\n40\\n\", \"308\\n40\\n\", \"159\\n40\\n\", \"221\\n40\\n\", \"250\\n40\\n\", \"308\\n10\\n\", \"250\\n30\\n\", \"350\\n10\\n\", \"450\\n30\\n\", \"278\\n40\\n\", \"350\\n13\\n\", \"450\\n12\\n\", \"281\\n52\\n\", \"281\\n73\\n\", \"450\\n32\\n\", \"550\\n35\\n\", \"400\\n15\\n\", \"550\\n42\\n\", \"358\\n40\\n\", \"159\\n61\\n\", \"451\\n35\\n\", \"221\\n36\\n\", \"308\\n61\\n\", \"500\\n35\\n\", \"250\\n25\\n\", \"343\\n30\\n\", \"278\\n42\\n\", \"288\\n52\\n\", \"281\\n481\\n\", \"42\\n42\\n\", \"308\\n31\\n\", \"160\\n61\\n\", \"332\\n35\\n\", \"500\\n55\\n\", \"508\\n61\\n\", \"450\\n36\\n\", \"250\\n250\\n\", \"278\\n22\\n\", \"481\\n281\\n\", \"40\\n40\\n\", \"428\\n35\\n\", \"188\\n52\\n\", \"481\\n63\\n\", \"550\\n40\\n\", \"535\\n55\\n\", \"25\\n40\\n\", \"550\\n38\\n\", \"25\\n55\\n\", \"25\\n73\\n\", \"30\\n73\\n\", \"30\\n48\\n\", \"450\\n34\\n\", \"308\\n44\\n\", \"450\\n46\\n\", \"365\\n35\\n\", \"178\\n40\\n\", \"281\\n58\\n\", \"103\\n53\\n\", \"281\\n20\\n\", \"358\\n37\\n\", \"180\\n40\\n\", \"345\\n40\\n\", \"200\\n40\\n\", \"343\\n45\\n\", \"200\\n73\\n\", \"420\\n61\\n\", \"250\\n36\\n\", \"200\\n35\\n\", \"412\\n30\\n\", \"288\\n51\\n\", \"435\\n73\\n\", \"500\\n57\\n\", \"42\\n52\\n\", \"239\\n73\\n\", \"535\\n30\\n\", \"549\\n40\\n\", \"350\\n40\\n\", \"455\\n40\\n\", \"10\\n55\\n\", \"550\\n25\\n\", \"400\\n45\\n\", \"159\\n46\\n\", \"287\\n35\\n\", \"600\\n10\\n\", \"266\\n13\\n\", \"103\\n50\\n\", \"300\\n20\\n\", \"322\\n40\\n\", \"330\\n40\\n\", \"100\\n281\\n\", \"239\\n30\\n\", \"35\\n55\\n\", \"25\\n35\\n\", \"159\\n49\\n\", \"308\\n38\\n\", \"281\\n42\\n\", \"103\\n20\\n\", \"208\\n42\\n\", \"100\\n177\\n\", \"450\\n35\"]}", "source": "taco"}
|
Taro is planning a long trip by train during the summer vacation. However, in order for Taro, who is a high school student, to travel as far as possible during the summer vacation, which has only one month, he cannot make a good plan unless he finds the cheapest and the fastest way. Let's create a program to help Taro's plan so that he can enjoy a wonderful trip.
<image>
Create a program that outputs the minimum amount or the shortest time in response to inquiries by inputting track information and the number of stations.
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:
n m
a1 b1 cost1 time1
a2 b2 cost2 time2
::
an bn costn timen
k
p1 q1 r1
p2 q2 r2
::
pk qk rk
The first line gives the number of track information n (1 ≤ n ≤ 3000) and the number of stations m (1 ≤ m ≤ 100).
The following n lines give information on the i-th line. As information on each line, the numbers ai, bi (1 ≤ ai, bi ≤ m) of the two stations connecting the lines, the toll costi (1 ≤ costi ≤ 1000), and the travel time timei (1 ≤ timei ≤ 1000) are given. I will. However, each station shall be numbered in order from 1 to m. If ai and bi are connected by railroad tracks, both ai to bi and bi to ai can be moved at the same rate and time.
The following line is given the number of queries k (1 ≤ k ≤ 200). The next k line is given the i-th query. For each query, the departure station pi, the arrival station qi, and the type of value to output ri (0 or 1) are given. Inquiries must have a route.
The number of datasets does not exceed 50.
Output
Outputs the minimum amount or minimum time on one line for each data set. When ri is 0, the minimum amount is output, and when ri is 1, the minimum time is output.
Example
Input
6 5
1 2 200 10
1 4 400 15
1 3 250 25
2 4 100 10
4 5 150 20
3 5 300 20
2
1 5 0
1 5 1
0 0
Output
450
35
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, 4, 10], [4, 5, 4, 10], [0, 0, 4, 10], [3, 2, 4, 10], [3.9, 2, 4, 10], [5, 6, 4, 10], [3, 2, 4, 0], [3, 2, 2, 10]], \"outputs\": [[200], [200], [\"error\"], [80], [80], [\"error\"], [0], [60]]}", "source": "taco"}
|
A carpet shop sells carpets in different varieties. Each carpet can come in a different roll width and can have a different price per square meter.
Write a function `cost_of_carpet` which calculates the cost (rounded to 2 decimal places) of carpeting a room, following these constraints:
* The carpeting has to be done in one unique piece. If not possible, retrun `"error"`.
* The shop sells any length of a roll of carpets, but always with a full width.
* The cost has to be minimal.
* The length of the room passed as argument can sometimes be shorter than its width (because we define these relatively to the position of the door in the room).
* A length or width equal to zero is considered invalid, return `"error"` if it occurs.
INPUTS:
`room_width`, `room_length`, `roll_width`, `roll_cost` as floats.
OUTPUT:
`"error"` or the minimal cost of the room carpeting, rounded to two decimal places.
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\", \"AH KH QH TH JH\", \"KH 5S 3C 5C 7D\", \"QH QD 2S QC 2C\"], \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 6S 3C 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3C 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 6C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 5D 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3C 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 2C 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 5C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 4C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5D 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3D 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4C 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 5C 8D\\nQH QD 2S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 4C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 3D 5D 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 4C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4C 5C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 4C 8D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 6S 2D 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3C 5C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 4D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3D 5C 7D\\nQH QD 5S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 4C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 5D 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 7D\\nQH QC 2S QD 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 5C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nJH 4S 4D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5D 8D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 6D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 6D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 4C 8C\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nJH 5S 3C 5C 7D\\nQH QD 5S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 4C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 6C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 5C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3D 5D 8C\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 5C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7C\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 5D 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 4C 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 6D 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 6S 3D 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 4C 8D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nJH 6S 3C 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 2C 5C 8D\\nQH QD 2S QC 3C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 5D 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 4C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 4C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 5C 7C\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 4C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7D\\nQH QD 2S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 3D 6C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 5D 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 5C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 6C 7D\\nQH QD 4S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 6S 2C 5C 7D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 7C\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 2C 5C 8D\\nQH QD 2S QC 4C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 7C 7D\\nQH QD 4S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 8C\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 3S 2C 5C 8D\\nQH QD 2S QC 4C\", \"3\\nAH KH QH TH JH\\nJH 5S 3C 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 6D 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 4C 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 5D 4C 8C\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 4C 8C\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 6S 4D 6C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nJH 6S 3D 5D 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2C 5C 7D\\nQH QD 4S QC 2D\", \"3\\nAH KH QH TH JH\\nJH 5S 3D 5C 8C\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 8D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 4S 2C 4C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 4C 5C 8D\\nQH QD 2S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 4D 4C 8D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 6C 8D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 4D 6D 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 3C 4C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 2D 5C 7D\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 3D 5C 8C\\nQH QD 3S QC 2C\", \"3\\nAH KH QH TH JH\\nKH 5S 5D 4C 8D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 7S 4D 6C 7D\\nQH QD 3S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 6S 2C 5C 7D\\nQH QD 4S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 4S 2C 4C 8D\\nQH QD 2S QC 2D\", \"3\\nAH KH QH TH JH\\nKH 6S 3C 5D 7D\\nQH QD 4S QC 2C\", \"3\\nAH KH QH TH JH\\nJH 5S 3D 5C 7D\\nQH QD 4S QC 3C\", \"3\\nAH KH QH TH JH\\nKH 5S 3C 5C 7D\\nQH QD 2S QC 2C\"], \"outputs\": [[\"royal flush\", \"pair\", \"full house\"], \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nfull house\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\", \"royal flush\\nhigh card\\nthree of a kind\\n\", \"royal flush\\npair\\nthree of a kind\\n\", \"royal flush\\npair\\nfull house\\n\"]}", "source": "taco"}
|
In poker, you have 5 cards. There are 10 kinds of poker hands (from highest to lowest):
- royal flush - ace, king, queen, jack and ten, all in the same suit
- straight flush - five cards of the same suit in sequence, such
as 10,9,8,7,6 of clubs; ace can be counted both as the highest card or as the
lowest card - A,2,3,4,5 of hearts is a straight flush. But 4,3,2,A,K of hearts is not a straight flush - it's just a flush.
- four of a kind - four cards of the same rank, such as four kings.
- full house - three cards of one rank plus two cards of another rank
- flush - five cards of the same suit (but not a straight flush)
- straight - five cards in order - just like the straight flush, but mixed suits
- three of a kind - three cards of one rank and two other cards
- two pairs - two cards of one rank, two cards of another rank, and one more card
- pair - two cards of the same rank
- high card - none of the above
Write a program that will help you play poker by telling you what kind of hand you have.
-----Input-----
The first line of input contains the number of test cases (no more than 20). Each test case consists of one line - five space separated cards. Each card is represented by a two-letter (or digit) word. The first character is the rank (A,K,Q,J,T,9,8,7,6,5,4,3 or 2), the second character is the suit (S,H,D,C standing for spades, hearts, diamonds and clubs). The cards can be in any order (but they will not repeat).
-----Output-----
For each test case output one line describing the type of a hand, exactly like in the list above.
-----Example-----
Input:
3
AH KH QH TH JH
KH 5S 3C 5C 7D
QH QD 2S QC 2C
Output:
royal flush
pair
full house
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
|
{"tests": "{\"inputs\": [[\"a-(b)\"], [\"a-(-b)\"], [\"a+(b)\"], [\"a+(-b)\"], [\"(((((((((-((-(((n))))))))))))))\"], [\"(((a-((((-(-(f)))))))))\"], [\"((((-(-(-(-(m-g))))))))\"], [\"(((((((m-(-(((((t)))))))))))))\"], [\"-x\"], [\"-(-(x))\"], [\"-((-x))\"], [\"-(-(-x))\"], [\"-(-(x-y))\"], [\"-(x-y)\"], [\"x-(y+z)\"], [\"x-(y-z)\"], [\"x-(-y-z)\"], [\"x-(-((-((((-((-(-(-y)))))))))))\"], [\"u-(v-w+(x+y))-z\"], [\"x-(s-(y-z))-(a+b)\"], [\"u+(g+v)+(r+t)\"], [\"q+(s-(x-o))-(t-(w-a))\"], [\"u-(v-w-(x+y))-z\"], [\"v-(l+s)-(t+y)-(c+f)+(b-(n-p))\"]], \"outputs\": [[\"a-b\"], [\"a+b\"], [\"a+b\"], [\"a-b\"], [\"n\"], [\"a-f\"], [\"m-g\"], [\"m+t\"], [\"-x\"], [\"x\"], [\"x\"], [\"-x\"], [\"x-y\"], [\"-x+y\"], [\"x-y-z\"], [\"x-y+z\"], [\"x+y+z\"], [\"x-y\"], [\"u-v+w-x-y-z\"], [\"x-s+y-z-a-b\"], [\"u+g+v+r+t\"], [\"q+s-x+o-t+w-a\"], [\"u-v+w+x+y-z\"], [\"v-l-s-t-y-c-f+b-n+p\"]]}", "source": "taco"}
|
In this Kata, you will be given a mathematical string and your task will be to remove all braces as follows:
```Haskell
solve("x-(y+z)") = "x-y-z"
solve("x-(y-z)") = "x-y+z"
solve("u-(v-w-(x+y))-z") = "u-v+w+x+y-z"
solve("x-(-y-z)") = "x+y+z"
```
There are no spaces in the expression. Only two operators are given: `"+" or "-"`.
More examples in 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
|
{"tests": "{\"inputs\": [\"3 2\\n\", \"1 3\\n\", \"4 3\\n\", \"1000000000000000000 1000000000000000000\\n\", \"59 576460752303423489\\n\", \"1234567891234 100005\\n\", \"2 4\\n\", \"59 576460752303423488\\n\", \"2016 2016\\n\", \"2016 2017\\n\", \"468804735183774830 244864585447548924\\n\", \"172714899512474455 414514930706102803\\n\", \"876625063841174080 360793239109880865\\n\", \"70181875975239647 504898544415017211\\n\", \"364505998666117889 208660487087853057\\n\", \"648371335753080490 787441\\n\", \"841928147887146057 620004\\n\", \"545838312215845682 715670\\n\", \"473120513399321115 489435\\n\", \"17922687587622540 3728\\n\", \"211479504016655403 861717213151744108\\n\", \"718716873663426516 872259572564867078\\n\", \"422627037992126141 41909917823420958\\n\", \"616183854421159004 962643186273781485\\n\", \"160986032904427725 153429\\n\", \"88268234087903158 290389\\n\", \"58453009367192916 164246\\n\", \"565690379013964030 914981\\n\", \"269600543342663655 10645\\n\", 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"taco"}
|
ZS the Coder has recently found an interesting concept called the Birthday Paradox. It states that given a random set of 23 people, there is around 50% chance that some two of them share the same birthday. ZS the Coder finds this very interesting, and decides to test this with the inhabitants of Udayland.
In Udayland, there are 2^{n} days in a year. ZS the Coder wants to interview k people from Udayland, each of them has birthday in one of 2^{n} days (each day with equal probability). He is interested in the probability of at least two of them have the birthday at the same day.
ZS the Coder knows that the answer can be written as an irreducible fraction $\frac{A}{B}$. He wants to find the values of A and B (he does not like to deal with floating point numbers). Can you help him?
-----Input-----
The first and only line of the input contains two integers n and k (1 ≤ n ≤ 10^18, 2 ≤ k ≤ 10^18), meaning that there are 2^{n} days in a year and that ZS the Coder wants to interview exactly k people.
-----Output-----
If the probability of at least two k people having the same birthday in 2^{n} days long year equals $\frac{A}{B}$ (A ≥ 0, B ≥ 1, $\operatorname{gcd}(A, B) = 1$), print the A and B in a single line.
Since these numbers may be too large, print them modulo 10^6 + 3. Note that A and B must be coprime before their remainders modulo 10^6 + 3 are taken.
-----Examples-----
Input
3 2
Output
1 8
Input
1 3
Output
1 1
Input
4 3
Output
23 128
-----Note-----
In the first sample case, there are 2^3 = 8 days in Udayland. The probability that 2 people have the same birthday among 2 people is clearly $\frac{1}{8}$, so A = 1, B = 8.
In the second sample case, there are only 2^1 = 2 days in Udayland, but there are 3 people, so it is guaranteed that two of them have the same birthday. Thus, the probability is 1 and A = B = 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\": [\"6\\n7 2 3 1 5 6\\n\", \"10\\n424238336 649760493 681692778 714636916 719885387 804289384 846930887 957747794 596516650 189641422\\n\", \"50\\n804289384 846930887 681692778 714636916 957747794 424238336 719885387 649760493 596516650 189641422 25202363 350490028 783368691 102520060 44897764 967513927 365180541 540383427 304089173 303455737 35005212 521595369 294702568 726956430 336465783 861021531 59961394 89018457 101513930 125898168 131176230 145174068 233665124 278722863 315634023 369133070 468703136 628175012 635723059 653377374 656478043 801979803 859484422 914544920 608413785 756898538 734575199 973594325 149798316 38664371\\n\", \"1\\n1\\n\", \"2\\n1000000000 1000000000\\n\", \"5\\n1 2 3 4 1\\n\", \"10\\n1 2 3 4 5 5 6 7 8 9\\n\", \"5\\n1 1 1 1 1\\n\", \"5\\n1 1 2 3 4\\n\", \"5\\n1 2 3 1 6\\n\", \"1\\n42\\n\", \"5\\n1 2 42 3 4\\n\", \"5\\n1 5 9 6 10\\n\", \"5\\n5 2 3 4 5\\n\", \"3\\n2 1 3\\n\", \"5\\n1 2 3 3 4\\n\", \"8\\n1 2 3 4 1 5 6 7\\n\", 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1 3\\n\", \"3\\n1 1 2\\n\", \"6\\n7 2 12 4 5 6\\n\", \"6\\n1 2 2 3 4 5\\n\", \"2\\n1000000000 1000000000\\n\", \"10\\n1 2 3 4 5 5 6 7 8 9\\n\", \"1\\n42\\n\", \"4\\n5 1 2 3\\n\", \"5\\n1 1 2 3 4\\n\", \"5\\n1 2 3 4 5\\n\", \"5\\n1 2 42 3 4\\n\", \"9\\n1 2 3 4 5 42 7 8 9\\n\", \"7\\n11 2 1 2 13 4 14\\n\", \"5\\n1 2 4 4 5\\n\", \"10\\n1 2 3 4 100 6 7 8 9 10\\n\", \"6\\n1 2 3 100000 100 101\\n\", \"4\\n1 2 1 3\\n\", \"6\\n1 5 4 3 4 5\\n\", \"5\\n4 1 2 3 4\\n\", \"10\\n424238336 649760493 681692778 714636916 719885387 804289384 846930887 957747794 596516650 189641422\\n\", \"8\\n1 2 3 4 1 5 6 7\\n\", \"3\\n25 1 6\\n\", \"2\\n1 2\\n\", \"5\\n1 3 1 2 3\\n\", \"4\\n1 1 1 2\\n\", \"6\\n1 2 1 2 4 5\\n\", \"5\\n9 1 2 3 4\\n\", \"5\\n100 100 7 8 9\\n\", \"3\\n5 3 5\\n\", \"5\\n1 5 9 6 10\\n\", \"5\\n1 3 2 4 5\\n\", \"6\\n7 2 3 1 4 5\\n\", \"3\\n2 1 3\\n\", \"6\\n7 4 5 6 7 8\\n\", \"3\\n3 1 2\\n\", \"6\\n7 2 3 1 4 6\\n\", \"1\\n3\\n\", \"9\\n3 4 1 6 3 4 5 6 7\\n\", \"6\\n2 3 5 5 6 7\\n\", \"7\\n21 16 22 21 11 13 19\\n\", \"50\\n804289384 846930887 681692778 714636916 957747794 424238336 719885387 649760493 596516650 189641422 25202363 350490028 783368691 102520060 44897764 967513927 365180541 540383427 304089173 303455737 35005212 521595369 294702568 726956430 336465783 861021531 59961394 89018457 101513930 125898168 131176230 145174068 233665124 278722863 315634023 369133070 468703136 628175012 635723059 653377374 656478043 801979803 859484422 914544920 608413785 756898538 734575199 973594325 149798316 38664371\\n\", \"7\\n14 3 3 19 13 19 15\\n\", \"5\\n2 3 10 5 6\\n\", \"5\\n1 3 3 4 1\\n\", \"3\\n81 33 16\\n\", \"3\\n5 1 4\\n\", \"10\\n1 2 3 4 5 4 10 11 12 13\\n\", \"1\\n2\\n\", \"20\\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 3 4 5 6\\n\", \"9\\n1 2 3 5 5 42 7 8 9\\n\", \"10\\n1 2 3 4 100 6 7 9 9 10\\n\", \"50\\n804289384 846930887 681692778 714636916 957747794 424238336 719885387 649760493 596516650 189641422 25202363 350490028 783368691 102520060 44897764 967513927 365180541 540383427 304089173 303455737 6379420 521595369 294702568 726956430 336465783 861021531 59961394 89018457 101513930 125898168 131176230 145174068 233665124 278722863 315634023 369133070 468703136 628175012 635723059 653377374 656478043 801979803 859484422 914544920 608413785 756898538 734575199 973594325 149798316 38664371\\n\", \"5\\n1 2 1 4 1\\n\", \"4\\n1 5 0 4\\n\", \"10\\n1 1 5 3 2 9 8 7 7 6\\n\", \"5\\n2 4 7 6 13\\n\", \"5\\n1 2 5 3 6\\n\", \"2\\n2 2\\n\", \"4\\n1 4 2 4\\n\", \"5\\n2 2 3 3 4\\n\", \"5\\n1 2 3 1 10\\n\", \"6\\n2 2 2 6 4 5\\n\", \"5\\n1 5 2 3 4\\n\", \"4\\n4 3 1 1\\n\", \"10\\n17 99 23 72 78 36 9 43 95 9\\n\", \"4\\n2 1 2 3\\n\", \"4\\n3 3 2 4\\n\", \"3\\n7 3 5\\n\", \"5\\n1 1 2 1 1\\n\", \"5\\n5 2 3 1 5\\n\", \"3\\n100 2 10\\n\", \"3\\n5 1 1\\n\", \"3\\n1 1 0\\n\", \"6\\n7 2 13 4 5 6\\n\", \"10\\n1 2 3 4 5 5 8 7 8 9\\n\", \"1\\n51\\n\", \"5\\n1 1 2 3 2\\n\", \"5\\n1 2 3 2 5\\n\", \"5\\n1 2 42 4 4\\n\", \"7\\n11 2 1 0 13 4 14\\n\", \"5\\n1 2 5 4 5\\n\", \"6\\n1 2 3 100000 110 101\\n\", \"4\\n1 2 1 1\\n\", \"6\\n1 2 4 3 4 5\\n\", \"5\\n4 1 4 3 4\\n\", \"10\\n424238336 649760493 681692778 714636916 719885387 804289384 1387372535 957747794 596516650 189641422\\n\", \"8\\n1 2 3 4 1 5 6 2\\n\", \"3\\n25 1 9\\n\", \"2\\n1 4\\n\", \"5\\n2 3 1 2 3\\n\", \"4\\n1 1 2 2\\n\", \"5\\n110 100 7 8 9\\n\", \"5\\n1 5 9 6 13\\n\", \"5\\n1 1 2 4 5\\n\", \"6\\n7 4 3 1 4 5\\n\", \"3\\n2 2 3\\n\", \"1\\n5\\n\", \"9\\n3 4 1 6 3 4 1 6 7\\n\", \"6\\n2 3 5 5 6 10\\n\", \"7\\n21 16 22 16 11 13 19\\n\", \"7\\n14 3 3 25 13 19 15\\n\", \"6\\n7 2 3 1 5 5\\n\", \"5\\n2 3 5 5 6\\n\", \"5\\n1 3 3 4 0\\n\", \"3\\n109 33 16\\n\", \"5\\n2 2 1 4 1\\n\", \"4\\n2 5 0 4\\n\", \"10\\n1 1 5 3 2 9 8 7 1 6\\n\", \"5\\n2 5 7 6 13\\n\", \"10\\n1 2 3 4 5 4 15 11 12 13\\n\", \"1\\n4\\n\", \"5\\n1 2 5 3 10\\n\", \"4\\n1 4 2 0\\n\", \"5\\n2 2 3 3 5\\n\", \"20\\n1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 3 4 5 6\\n\", \"5\\n1 2 3 1 4\\n\", \"4\\n4 3 2 1\\n\", \"10\\n20 99 23 72 78 36 9 43 95 9\\n\", \"3\\n9 3 5\\n\", \"5\\n1 2 2 1 1\\n\", \"5\\n9 2 3 1 5\\n\", \"3\\n110 2 10\\n\", \"3\\n9 1 2\\n\", \"3\\n2 1 0\\n\", \"10\\n1 2 3 4 5 5 8 13 8 9\\n\", \"1\\n43\\n\", \"5\\n1 1 3 2 5\\n\", \"9\\n1 2 3 9 5 42 7 8 9\\n\", \"7\\n11 0 1 0 13 4 14\\n\", \"5\\n1 0 5 4 5\\n\", \"6\\n7 2 3 1 5 6\\n\"], \"outputs\": [\"5\\n\", \"9\\n\", \"19\\n\", \"1\\n\", \"2\\n\", \"5\\n\", \"6\\n\", \"2\\n\", \"5\\n\", \"5\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"5\\n\", \"7\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"3\\n\", \"6\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"10\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"10\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"6\\n\", \"7\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"9\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"10\\n\", \"1\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"2\\n\", \"6\\n\", \"1\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"5\\n\", \"5\\n\", \"10\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"9\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"7\\n\", \"6\\n\", \"4\\n\", \"19\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"10\\n\", \"1\\n\", \"7\\n\", \"6\\n\", \"8\\n\", \"19\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"2\\n\", \"5\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"5\\n\", \"7\\n\", \"1\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"8\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"3\\n\", \"1\\n\", \"5\\n\", \"6\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"7\\n\", \"1\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"7\\n\", \"4\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"8\\n\", \"1\\n\", \"4\\n\", \"6\\n\", \"4\\n\", \"4\\n\", \"5\\n\"]}", "source": "taco"}
|
DZY has a sequence a, consisting of n integers.
We'll call a sequence a_{i}, a_{i} + 1, ..., a_{j} (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
-----Input-----
The first line contains integer n (1 ≤ n ≤ 10^5). The next line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9).
-----Output-----
In a single line print the answer to the problem — the maximum length of the required subsegment.
-----Examples-----
Input
6
7 2 3 1 5 6
Output
5
-----Note-----
You can choose subsegment a_2, a_3, a_4, a_5, a_6 and change its 3rd element (that is a_4) to 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\": [\"2 2 1\\nH 1\\n\", \"200000 200000 1\\nH 1\\n\", \"2 2 2\\nH 1\\nV 1\\n\", \"10 10 10\\nV 6\\nH 8\\nV 4\\nV 8\\nH 2\\nH 5\\nV 9\\nH 7\\nH 3\\nV 7\\n\", \"2 2 1\\nV 1\\n\", \"2 2 2\\nV 1\\nH 1\\n\", \"2 4 1\\nH 2\\n\", \"2 3 1\\nH 1\\n\", \"5 15 10\\nH 8\\nH 9\\nV 1\\nH 2\\nH 6\\nH 4\\nH 1\\nV 2\\nH 13\\nV 3\\n\", \"15 5 10\\nV 13\\nV 10\\nV 3\\nH 2\\nV 9\\nV 7\\nV 2\\nH 1\\nV 4\\nH 3\\n\", \"200000 6228 1\\nH 1\\n\", \"2 4 1\\nH 3\\n\", \"15 5 10\\nV 13\\nV 6\\nV 3\\nH 2\\nV 9\\nV 7\\nV 2\\nH 1\\nV 4\\nH 3\\n\", \"200000 2774 1\\nH 1\\n\", \"200000 5462 1\\nH 1\\n\", \"200000 19026 1\\nH 1\\n\", \"4 2 2\\nH 1\\nV 1\\n\", \"5 25 10\\nH 8\\nH 9\\nV 1\\nH 2\\nH 6\\nH 4\\nH 1\\nV 2\\nH 13\\nV 3\\n\", \"6 3 4\\nH 2\\nV 2\\nV 3\\nV 1\\n\", \"7 6 5\\nH 4\\nV 2\\nV 5\\nH 2\\nV 1\\n\", \"200000 5462 1\\nH 2\\n\", \"3 2 2\\nH 1\\nV 1\\n\", \"7 6 5\\nH 3\\nV 2\\nV 5\\nH 2\\nV 1\\n\", \"200000 2085 1\\nH 2\\n\", \"7 6 5\\nH 3\\nV 2\\nV 3\\nH 2\\nV 1\\n\", \"10 10 10\\nV 6\\nH 8\\nV 4\\nV 8\\nH 1\\nH 5\\nV 9\\nH 7\\nH 3\\nV 7\\n\", \"3 2 2\\nV 1\\nH 1\\n\", \"7 6 5\\nH 4\\nV 3\\nV 6\\nH 2\\nV 1\\n\", \"200000 2774 1\\nH 2\\n\", \"200000 2012 1\\nH 1\\n\", \"7 8 5\\nH 3\\nV 2\\nV 5\\nH 2\\nV 1\\n\", \"3 3 2\\nV 1\\nH 1\\n\", \"200000 2774 1\\nH 4\\n\", \"1 4 1\\nH 1\\n\", \"10 19 10\\nV 6\\nH 8\\nV 4\\nV 8\\nH 2\\nH 5\\nV 9\\nH 7\\nH 3\\nV 7\\n\", \"2 7 1\\nH 3\\n\", \"10938 6228 1\\nH 1\\n\", \"15 5 10\\nV 13\\nV 6\\nV 3\\nH 4\\nV 9\\nV 7\\nV 2\\nH 1\\nV 4\\nH 3\\n\", \"200000 3332 1\\nH 1\\n\", \"147953 19026 1\\nH 1\\n\", \"6 4 1\\nH 2\\n\", \"7 5 5\\nH 3\\nV 2\\nV 3\\nH 2\\nV 1\\n\", \"4 2 2\\nV 1\\nH 1\\n\", \"2 8 1\\nH 1\\n\", \"2162 2774 1\\nH 2\\n\", \"1 7 1\\nH 3\\n\", \"1815 6228 1\\nH 1\\n\", \"15 5 10\\nV 13\\nV 6\\nV 3\\nH 4\\nV 12\\nV 7\\nV 2\\nH 1\\nV 4\\nH 3\\n\", \"2162 1984 1\\nH 2\\n\", \"3437 6228 1\\nH 1\\n\", \"2079 1984 1\\nH 2\\n\", \"3437 2017 1\\nH 1\\n\", \"3437 3355 1\\nH 1\\n\", \"5999 3355 1\\nH 1\\n\", \"5999 6446 1\\nH 1\\n\", \"5999 6446 1\\nH 2\\n\", \"5999 6446 1\\nH 3\\n\", \"5999 12644 1\\nH 2\\n\", \"3 4 1\\nH 2\\n\", \"3 2 2\\nH 1\\nV 2\\n\", \"7 6 5\\nH 3\\nV 2\\nV 3\\nH 1\\nV 1\\n\", \"2 4 1\\nH 1\\n\", \"2 8 1\\nH 2\\n\", \"2 5 1\\nH 2\\n\", \"4 3 4\\nH 2\\nV 2\\nV 3\\nV 1\\n\", \"7 6 5\\nH 4\\nV 3\\nV 5\\nH 2\\nV 1\\n\"], \"outputs\": [\"2\\n\", \"39999800000\\n\", \"2\\n1\\n\", \"60\\n48\\n32\\n32\\n24\\n12\\n12\\n12\\n8\\n8\\n\", \"2\\n\", \"2\\n1\\n\", \"4\\n\", \"4\\n\", \"40\\n40\\n32\\n24\\n24\\n24\\n24\\n18\\n12\\n8\\n\", \"65\\n50\\n35\\n21\\n18\\n12\\n12\\n12\\n9\\n6\\n\", \"1245400000\\n\", \"6\\n\", \"65\\n35\\n35\\n21\\n12\\n12\\n12\\n12\\n12\\n8\\n\", \"554600000\\n\", \"1092200000\\n\", \"3805000000\\n\", \"4\\n3\\n\", \"85\\n80\\n64\\n64\\n64\\n64\\n64\\n48\\n36\\n24\\n\", \"12\\n8\\n6\\n6\\n\", \"28\\n20\\n12\\n6\\n6\\n\", \"1092000000\\n\", \"3\\n2\\n\", \"21\\n15\\n9\\n9\\n9\\n\", \"416600000\\n\", \"21\\n15\\n12\\n12\\n12\\n\", \"60\\n48\\n32\\n32\\n28\\n16\\n16\\n16\\n8\\n8\\n\", \"4\\n2\\n\", \"28\\n16\\n12\\n6\\n6\\n\", \"554400000\\n\", \"402200000\\n\", \"35\\n25\\n15\\n15\\n15\\n\", \"6\\n4\\n\", \"554000000\\n\", \"3\\n\", \"114\\n66\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n\", \"8\\n\", \"68110926\\n\", \"65\\n35\\n35\\n28\\n16\\n16\\n16\\n12\\n12\\n8\\n\", \"666200000\\n\", \"2814805825\\n\", \"12\\n\", \"21\\n15\\n12\\n8\\n8\\n\", \"6\\n3\\n\", \"14\\n\", \"5993064\\n\", \"4\\n\", \"11302005\\n\", \"65\\n35\\n35\\n28\\n24\\n20\\n20\\n15\\n15\\n10\\n\", \"4285084\\n\", \"21402199\\n\", \"4120578\\n\", \"6928992\\n\", \"11527698\\n\", \"20120646\\n\", \"38663555\\n\", \"38657556\\n\", \"38651557\\n\", \"75839358\\n\", \"6\\n\", \"3\\n2\\n\", \"21\\n15\\n12\\n12\\n12\\n\", \"6\\n\", \"12\\n\", \"6\\n\", \"8\\n4\\n4\\n2\\n\", \"28\\n16\\n12\\n6\\n4\\n\"]}", "source": "taco"}
|
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm × h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.
In order not to waste time, he decided to practice the technique of carving. To do this, he makes vertical and horizontal cuts through the entire sheet. This process results in making smaller rectangular fragments of glass. Leonid does not move the newly made glass fragments. In particular, a cut divides each fragment of glass that it goes through into smaller fragments.
After each cut Leonid tries to determine what area the largest of the currently available glass fragments has. Since there appear more and more fragments, this question takes him more and more time and distracts him from the fascinating process.
Leonid offers to divide the labor — he will cut glass, and you will calculate the area of the maximum fragment after each cut. Do you agree?
Input
The first line contains three integers w, h, n (2 ≤ w, h ≤ 200 000, 1 ≤ n ≤ 200 000).
Next n lines contain the descriptions of the cuts. Each description has the form H y or V x. In the first case Leonid makes the horizontal cut at the distance y millimeters (1 ≤ y ≤ h - 1) from the lower edge of the original sheet of glass. In the second case Leonid makes a vertical cut at distance x (1 ≤ x ≤ w - 1) millimeters from the left edge of the original sheet of glass. It is guaranteed that Leonid won't make two identical cuts.
Output
After each cut print on a single line the area of the maximum available glass fragment in mm2.
Examples
Input
4 3 4
H 2
V 2
V 3
V 1
Output
8
4
4
2
Input
7 6 5
H 4
V 3
V 5
H 2
V 1
Output
28
16
12
6
4
Note
Picture for the first sample test:
<image> Picture for the second sample test: <image>
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\": [[50.0, 130.0, [[-1.0, 120.0], [-1.5, 120.0]]], [50.0, 110.0, [[1.0, 120.0], [1.5, 125.0]]], [50.0, 120.0, [[-1.0, 115.0], [-1.5, 110.0], [1.0, 130.0], [1.5, 130.0]]], [30.0, 100.0, [[-1.0, 110.0], [-0.7, 102.0], [-1.5, 108.0]]], [30.0, 130.0, [[1.0, 120.0], [0.7, 125.0], [1.5, 110.0]]], [50.0, 110.0, [[-1.0, 110.0], [0.5, 110.0], [1.0, 110.0], [1.5, 110.0]]], [50.0, 110.0, [[0.0, 110.0]]], [50.0, 130.0, []]], \"outputs\": [[2], [-2], [0], [0], [0], [0], [0], [0]]}", "source": "taco"}
|
# Back-Story
Every day I travel on the freeway.
When I am more bored than usual I sometimes like to play the following counting game I made up:
* As I join the freeway my count is ```0```
* Add ```1``` for every car that I overtake
* Subtract ```1``` for every car that overtakes me
* Stop counting when I reach my exit
What an easy game! What fun!
# Kata Task
You will be given
* The distance to my exit (km)
* How fast I am going (kph)
* Information about a lot of other cars
* Their time (relative to me) as I join the freeway. For example,
* ```-1.5``` means they already passed my starting point ```1.5``` minutes ago
* ```2.2``` means they will pass my starting point ```2.2``` minutes from now
* How fast they are going (kph)
Find what is my "score" as I exit the freeway!
# Notes
* Assume all cars travel at a constant speeds
Safety Warning
If you plan to play this "game" remember that it is not really a game. You are in a **real** car.
There may be a temptation to try to beat your previous best score.
Please don't do that...
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 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900EE\\n820R037\\n6 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\n994190562430809FDEDB\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99179A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900EE\\n820R037\\n6 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C8G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\n994190562430809FDEDB\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820703R\\n6 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7\\nJI03HE\\nID7722\\n0DA1AH\\n10C9G5\\n99078A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEHH\\nBDEDF909034265091498\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A80D0E\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n10C9G5\\n99078A\\nCA7EAI\\nAHLBEM\\n20 2\\nHHEDBC4321987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A800DE\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AI\\n10C9G5\\nA87099\\nCA7EAI\\nAHLBFM\\n20 2\\nHHEDBC4321987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R29A93\\n0E314A0\\n8A900DE\\nR307028\\n6 7\\nJI03HD\\nID7722\\n0DA1AH\\n30C9G5\\n99179A\\nCB7EAI\\nEHLBAM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8AE009E\\n820R037\\n6 7\\nEH30HJ\\nID7722\\n0DA1AH\\n30C8G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\n994190562430809FDEDB\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A900DE\\n820R/37\\n6 7\\nJH03HE\\n2277DI\\n0DA1AH\\n30C9G5\\n99971A\\nCE7AAI\\nAHLBEM\\n20 2\\nHGEDBC4321:87654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\nID7732\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nEHLBAM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0A413E0\\n8A900DE\\n820R047\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99279A\\nCB7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\nI277D2\\n0DA1AH\\n30C9G5\\nA17999\\nCA7EAI\\nAELBHM\\n20 2\\nA1234567891134CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R9A923\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nEH30IJ\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\nBDECF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8AE009E\\n820R037\\n6 7\\nEH30HJ\\nID7722\\n0DA1AH\\n30C8G5\\n9A9719\\nCA7FAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\n2276DI\\n0DA1AH\\n30C9G5\\n99970A\\nCE7AAI\\nAHMBEL\\n20 2\\nHGEDBC4321:87654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DD\\n820R137\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n5G9C03\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1236547891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A9E0E0\\n820R037\\n6 7\\nJH04HE\\nID7722\\n0DA1AH\\n5G8C03\\n99971A\\nCA7EAI\\nMEBLHA\\n20 2\\nHGEDBC4321987654321A\\n994190562430809FDEDB\\n0 0\", \"7 4\\n9R9A923\\n0E314A0\\n8A900DE\\n280R037\\n6 7\\nJI03HE\\nI7C722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDECF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n/E314A0\\n8A800DE\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n39C0G5\\n99178A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEHH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n00314AE\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\n1277DI\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAELBHM\\n20 2\\nHGEDBC4311987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0A413E0\\n8A800DE\\n820R037\\n6 7\\nJI03HE\\nI277D2\\n0DA1AH\\n30C9G5\\n99178A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEHH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\nED009@8\\n820R037\\n6 7\\nJI/3HD\\nID7722\\nHA1AD0\\n30C9G5\\n99169A\\nCB7EAI\\nAHLBEM\\n20 2\\nA1334567891234CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n/A413E0\\n8A900DE\\n820R037\\n6 7\\nEH30HK\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCF7AAI\\nAHLBEM\\n20 2\\nHGEDBC4821937654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A/\\n8A900DE\\n820R037\\n6 7\\nKH03HE\\nID9722\\n0DA1AH\\n30C9G5\\n99971A\\nCF7AAI\\nAHLCEM\\n20 2\\nHGEDBC4821937654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A/\\nED009A8\\n820R036\\n6 7\\nKH03HE\\nID7722\\n0DA1AH\\n30C9G5\\nA17999\\nCF7AAI\\nAHLCEM\\n20 2\\nHGEDBC4821937654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A800DE\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n20C9G5\\n99078A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEHH\\n994191562430909FDEDB\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A80D0E\\n820R037\\n6 7\\nJI03HE\\nID7722\\n0DA1AH\\n10C9G5\\n99078A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEHH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A9:3\\n0A413E0\\nED009A8\\n820R037\\n6 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nHGEDBC4321987654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJI03HD\\nID7722\\nHA1AD0\\n30C9G5\\n99179A\\nCB7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDFDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900EE\\n820R037\\n5 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C9G5\\n91979A\\nCA7EAJ\\n@HLBEM\\n20 2\\nHGEDB243219876543C1A\\n994190562430809FDEDB\\n0 0\", \"7 4\\n399A2R9\\n0E314A0\\n8A900DE\\n820R/37\\n6 7\\nJH03HE\\n2277DI\\nHA1AD0\\n30C9G5\\n99971A\\nCE7AAI\\nAHLBEM\\n20 2\\nHGEDBC4321:87654321A\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\nI277D2\\n0DA1AH\\n30C9G5\\nA1799:\\nCA7EAI\\nAELBHM\\n20 2\\nA1234567891134CBDEGH\\nBDEDF908034265091499\\n0 0\", \"7 4\\n9R2A993\\n0E314A0\\n8A900DE\\n820R037\\n6 7\\nJH03HE\\nID7722\\n0DA1AH\\n30C9G5\\n99971A\\nCA7EAI\\nAHLBEM\\n20 2\\nA1234567891234CBDEGH\\nBDEDF908034265091499\\n0 0\"], \"outputs\": [\"23900037\\n771971\\n908034265091499\\n\", \"23900037\\n771971\\n12345908034265091499\\n\", \"23900037\\n771971\\n994190562430809\\n\", \"23900037\\n771979\\n12345908034265091499\\n\", \"23900037\\n771871\\n994190562430809\\n\", \"908820703\\n771979\\n12345908034265091499\\n\", \"93900037\\n771971\\n12345908034265091499\\n\", \"23140937\\n771871\\n994190562430809\\n\", \"23140937\\n7718719\\n994190562430809\\n\", \"23900037\\n22771979\\n12345908034265091499\\n\", \"23900037\\n22771971\\n908034265091499\\n\", \"23140937\\n17718719\\n994190562430809\\n\", \"908820703\\n591979\\n12345908034265091499\\n\", \"23140837\\n17718719\\n994190562430809\\n\", \"2314903\\n591979\\n12345908034265091499\\n\", \"23800037\\n771979\\n12345908034265091499\\n\", \"23900037\\n771969\\n12345908034265091499\\n\", \"399390703\\n771979\\n12345908034265091499\\n\", \"2314903\\n771979\\n12345908034265091499\\n\", \"23140937\\n37718719\\n994190562430809\\n\", \"23900037\\n22771979\\n123499080342650\\n\", \"23900037\\n22771971\\n12345908034265091499\\n\", \"23900037\\n771971\\n12365908034265091499\\n\", \"23140037\\n771871\\n994190562430809\\n\", \"399490703\\n771979\\n12345908034265091499\\n\", \"23140928\\n7718719\\n994190562430809\\n\", \"23800037\\n771978\\n12345908034265091499\\n\", \"9003900037\\n771971\\n12345908034265091499\\n\", \"23140928\\n7718719\\n994190562420809\\n\", \"908820703\\n771919\\n12345908034265091499\\n\", \"2314903\\n97919\\n12345908034265091499\\n\", \"3993800037\\n771978\\n12345908034265091499\\n\", \"23900037\\n772205\\n12345908034265091499\\n\", \"9003900028\\n771971\\n12345908034265091499\\n\", \"23900037\\n771979\\n12365908034265091499\\n\", \"923900037\\n771979\\n12365908034265091499\\n\", \"3993800037\\n771978\\n994190562430809\\n\", \"23149037\\n771971\\n908034265091499\\n\", \"923900037\\n1771979\\n12365908034265091499\\n\", \"923140037\\n1771979\\n12365908034265091499\\n\", \"923140037\\n1771979\\n908034265091499\\n\", \"3993800037\\n771978\\n908034265091499\\n\", \"24900037\\n771971\\n908034265091499\\n\", \"23900037\\n771977\\n12345908034265091499\\n\", \"23140937\\n3771871\\n994190562430809\\n\", \"908820703\\n772205\\n12345908034265091499\\n\", \"908820\\n7718719\\n994190562430809\\n\", \"3993900037\\n22771971\\n908034265091499\\n\", \"23140937\\n13718719\\n994190562430809\\n\", \"23140837\\n177189\\n994190562430809\\n\", \"23900037\\n761971\\n994190562430809\\n\", \"24900037\\n771979\\n12345908034265091499\\n\", \"23900037\\n2771971\\n12345908034265091499\\n\", \"20900037\\n771971\\n908034265091499\\n\", \"93900037\\n771971\\n908034265091499\\n\", \"23900137\\n22771979\\n123499080342650\\n\", \"23900037\\n22771970\\n908034265091499\\n\", \"23140937\\n7722059\\n994190562430809\\n\", \"13900037\\n22771971\\n12345908034265091499\\n\", \"23900037\\n599971\\n12365908034265091499\\n\", \"23800037\\n771979\\n994190562430809\\n\", \"23140037\\n770871\\n994190562430809\\n\", \"9003900037\\n771971\\n908034265091499\\n\", \"23900037\\n771972\\n12365908034265091499\\n\", \"3994800037\\n771978\\n12345908034265091499\\n\", \"23900037\\n772205\\n13345908034265091499\\n\", \"23900037\\n3771971\\n908034265091499\\n\", \"24900037\\n771979\\n12365908034265091499\\n\", \"23900037\\n871971\\n908034265091499\\n\", \"23149037\\n7719999\\n908034265091499\\n\", \"3993800037\\n771978\\n994191562430809\\n\", \"3993800037\\n771978\\n12345909034265091498\\n\", \"399380\\n771978\\n908034265091499\\n\", \"3993800037\\n7719099\\n908034265091499\\n\", \"29140028\\n771979\\n12345908034265091499\\n\", \"3993140937\\n3771871\\n994190562430809\\n\", \"3993900\\n22771971\\n908034265091499\\n\", \"3993900037\\n771971\\n12345908034265091499\\n\", \"24900047\\n771979\\n12345908034265091499\\n\", \"23900037\\n27719999\\n12345908034265091499\\n\", \"93900037\\n3771971\\n908034265091499\\n\", \"23140937\\n37718719\\n908034265091499\\n\", \"23900037\\n22761970\\n908034265091499\\n\", \"23900137\\n599971\\n12365908034265091499\\n\", \"23140037\\n599971\\n994190562430809\\n\", \"93900037\\n399971\\n12345908034265091499\\n\", \"23800037\\n771078\\n12345908034265091499\\n\", \"9003900037\\n12771971\\n908034265091499\\n\", \"3994800037\\n2771978\\n12345908034265091499\\n\", \"23149037\\n772205\\n13345908034265091499\\n\", \"24900037\\n3771971\\n908034265091499\\n\", \"23900037\\n971971\\n908034265091499\\n\", \"23149036\\n7719999\\n908034265091499\\n\", \"3993800037\\n771978\\n994191562430909\\n\", \"399380\\n771978\\n12345908034265091499\\n\", \"24139037\\n771971\\n908034265091499\\n\", \"3993900037\\n772205\\n12345908034265091499\\n\", \"23900037\\n771979\\n994190562430809\\n\", \"3993900\\n399971\\n908034265091499\\n\", \"23900037\\n2771999\\n12345908034265091499\\n\", \"23900037\\n771971\\n12345908034265091499\"]}", "source": "taco"}
|
Your job is to find out the secret number hidden in a matrix, each of whose element is a digit ('0'-'9') or a letter ('A'-'Z'). You can see an example matrix in Figure 1.
<image>
Figure 1: A Matrix
The secret number and other non-secret ones are coded in a matrix as sequences of digits in a decimal format. You should only consider sequences of digits D1 D2 ... Dn such that Dk+1 (1 <= k < n) is either right next to or immediately below Dk in the matrix. The secret you are seeking is the largest number coded in this manner.
Four coded numbers in the matrix in Figure 1, i.e., 908820, 23140037, 23900037, and 9930, are depicted in Figure 2. As you may see, in general, two or more coded numbers may share a common subsequence. In this case, the secret number is 23900037, which is the largest among the set of all coded numbers in the matrix.
<image>
Figure 2: Coded Numbers
In contrast, the sequences illustrated in Figure 3 should be excluded: 908A2 includes a letter; the fifth digit of 23149930 is above the fourth; the third digit of 90037 is below right of the second.
<image>
Figure 3: Inappropriate Sequences
Write a program to figure out the secret number from a given matrix.
Input
The input consists of multiple data sets, each data set representing a matrix. The format of each data set is as follows.
> W H
> C11C12 ... C1W
> C21C22 ... C2W
> ...
> CH1CH2 ... CHW
>
In the first line of a data set, two positive integers W and H are given. W indicates the width (the number of columns) of the matrix, and H indicates the height (the number of rows) of the matrix. W+H is less than or equal to 70.
H lines follow the first line, each of which corresponds to a row of the matrix in top to bottom order. The i-th row consists of W characters Ci1Ci2 ... CiW in left to right order. You may assume that the matrix includes at least one non-zero digit.
Following the last data set, two zeros in a line indicate the end of the input.
Output
For each data set, print the secret number on a line. Leading zeros should be suppressed.
Example
Input
7 4
9R2A993
0E314A0
8A900DE
820R037
6 7
JH03HE
ID7722
0DA1AH
30C9G5
99971A
CA7EAI
AHLBEM
20 2
A1234567891234CBDEGH
BDEDF908034265091499
0 0
Output
23900037
771971
12345908034265091499
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\": [\"14 8\\n1 2\\n2 7\\n3 4\\n6 3\\n5 7\\n3 8\\n6 8\\n11 12\\n\", \"200000 3\\n7 9\\n9 8\\n4 5\\n\", \"3 1\\n1 3\\n\", \"200000 1\\n1 200000\\n\", \"500 5\\n100 300\\n200 400\\n420 440\\n430 450\\n435 460\\n\", \"500 5\\n100 300\\n200 400\\n420 440\\n430 450\\n435 460\\n\", \"200000 1\\n1 200000\\n\", \"3 1\\n1 3\\n\", \"974 5\\n100 300\\n200 400\\n420 440\\n430 450\\n435 460\\n\", \"5 1\\n1 3\\n\", \"974 5\\n100 300\\n200 400\\n420 440\\n374 450\\n435 460\\n\", \"974 5\\n100 300\\n200 400\\n420 440\\n559 450\\n435 460\\n\", \"974 5\\n100 300\\n200 735\\n420 440\\n559 450\\n435 460\\n\", \"974 5\\n100 473\\n200 400\\n420 440\\n430 450\\n435 460\\n\", \"14 8\\n1 2\\n2 7\\n2 4\\n7 3\\n5 7\\n3 8\\n6 8\\n11 12\\n\", \"974 5\\n100 548\\n200 400\\n420 440\\n374 450\\n435 460\\n\", \"974 5\\n100 300\\n200 791\\n420 440\\n559 450\\n435 460\\n\", \"974 5\\n100 300\\n200 458\\n420 440\\n559 450\\n435 460\\n\", \"974 5\\n100 548\\n200 400\\n420 440\\n374 450\\n435 662\\n\", 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|
You're given an undirected graph with $n$ nodes and $m$ edges. Nodes are numbered from $1$ to $n$.
The graph is considered harmonious if and only if the following property holds: For every triple of integers $(l, m, r)$ such that $1 \le l < m < r \le n$, if there exists a path going from node $l$ to node $r$, then there exists a path going from node $l$ to node $m$.
In other words, in a harmonious graph, if from a node $l$ we can reach a node $r$ through edges ($l < r$), then we should able to reach nodes $(l+1), (l+2), \ldots, (r-1)$ too.
What is the minimum number of edges we need to add to make the graph harmonious?
-----Input-----
The first line contains two integers $n$ and $m$ ($3 \le n \le 200\ 000$ and $1 \le m \le 200\ 000$).
The $i$-th of the next $m$ lines contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \neq v_i$), that mean that there's an edge between nodes $u$ and $v$.
It is guaranteed that the given graph is simple (there is no self-loop, and there is at most one edge between every pair of nodes).
-----Output-----
Print the minimum number of edges we have to add to the graph to make it harmonious.
-----Examples-----
Input
14 8
1 2
2 7
3 4
6 3
5 7
3 8
6 8
11 12
Output
1
Input
200000 3
7 9
9 8
4 5
Output
0
-----Note-----
In the first example, the given graph is not harmonious (for instance, $1 < 6 < 7$, node $1$ can reach node $7$ through the path $1 \rightarrow 2 \rightarrow 7$, but node $1$ can't reach node $6$). However adding the edge $(2, 4)$ is sufficient to make it harmonious.
In the second example, the given graph is already harmonious.
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 a set of n points on the plane. A line containing the origin is called good, if projection of the given set to this line forms a symmetric multiset of points. Find the total number of good lines.
Multiset is a set where equal elements are allowed.
Multiset is called symmetric, if there is a point P on the plane such that the multiset is centrally symmetric in respect of point P.
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 2000) — the number of points in the set.
Each of the next n lines contains two integers x_{i} and y_{i} ( - 10^6 ≤ x_{i}, y_{i} ≤ 10^6) — the coordinates of the points. It is guaranteed that no two points coincide.
-----Output-----
If there are infinitely many good lines, print -1.
Otherwise, print single integer — the number of good lines.
-----Examples-----
Input
3
1 2
2 1
3 3
Output
3
Input
2
4 3
1 2
Output
-1
-----Note-----
Picture to the first sample test:
[Image]
In the second sample, any line containing the origin is good.
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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|
Consider a sequence of n numbers using integers from 0 to 9 k1, k2, ..., kn. Read the positive integers n and s,
k1 + 2 x k2 + 3 x k3 + ... + n x kn = s
Create a program that outputs how many rows of n numbers such as. However, the same number does not appear more than once in one "n sequence of numbers".
Input
The input consists of multiple datasets. For each dataset, n (1 ≤ n ≤ 10) and s (0 ≤ s ≤ 10,000) are given on one line, separated by blanks.
The number of datasets does not exceed 100.
Output
For each dataset, print the number of combinations in which the sum of n integers is s on one line.
Example
Input
3 10
3 1
Output
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.
| 0.875
|
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\"5\\n2\\n01\\n10\\n5\\n01001\\n11001\\n2\\n01\\n01\\n10\\n1110011011\\n1000110100\\n1\\n0\\n0\\n\", \"5\\n2\\n01\\n10\\n5\\n01011\\n10100\\n1\\n01\\n01\\n10\\n0110001011\\n1000110101\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n01011\\n11100\\n1\\n01\\n01\\n10\\n0110001011\\n1000110100\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n01001\\n11100\\n1\\n01\\n01\\n10\\n0110011011\\n1000110100\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n01011\\n11110\\n1\\n01\\n01\\n10\\n0110011011\\n1010110100\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n00011\\n11010\\n2\\n01\\n01\\n10\\n1110011011\\n1000110100\\n1\\n0\\n0\\n\", \"5\\n2\\n01\\n10\\n5\\n01001\\n11000\\n1\\n01\\n01\\n10\\n1110011011\\n1000110100\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n01001\\n11000\\n2\\n01\\n01\\n10\\n0010011011\\n1000110000\\n1\\n0\\n1\\n\", \"5\\n2\\n01\\n10\\n5\\n01011\\n11110\\n2\\n01\\n01\\n10\\n0110011011\\n1000110100\\n1\\n1\\n0\\n\", \"5\\n2\\n01\\n10\\n5\\n01011\\n11100\\n2\\n01\\n01\\n10\\n0110011011\\n1000110100\\n1\\n0\\n1\\n\"], \"outputs\": [\"3 1 2 1 \\n3 1 5 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 4 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 4 3 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 4 3 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 8 7 1 4 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n5 1 10 8 7 1 \\n0 \\n\", \"3 1 2 1 \\n7 1 5 1 4 1 3 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 1 7 5 4 1 3 2 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n5 1 10 8 7 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 4 2 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 8 7 1 4 1 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n5 1 10 8 7 4 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 4 1 2 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 4 3 1 2 \\n0 \\n9 1 10 8 1 6 4 1 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n4 5 1 4 2 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n11 1 10 8 7 1 4 1 3 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n6 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n6 5 1 4 1 3 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n11 1 10 8 7 6 1 5 4 1 3 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 4 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n2 1 5 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n11 1 10 8 7 6 1 5 4 1 3 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 4 3 1 2 \\n0 \\n9 1 10 8 7 1 4 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 1 7 5 4 1 3 2 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n4 10 8 7 3 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 3 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n6 5 1 4 1 3 2 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n9 1 10 1 7 5 4 1 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n7 1 10 8 7 6 1 5 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n5 1 10 8 7 3 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 1 7 5 4 1 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n4 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 3 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n9 1 10 1 9 1 8 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 8 1 6 4 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n9 1 10 1 9 1 8 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 8 7 1 5 1 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 4 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n4 10 9 2 1 \\n0 \\n\", \"3 1 2 1 \\n1 2 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n9 1 10 8 7 1 4 1 2 1 \\n1 1 \\n\", \"1 1 \\n3 1 5 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 3 1 2 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 4 3 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 3 1 2 \\n0 \\n11 1 10 8 7 6 1 5 4 1 3 1 \\n0 \\n\", \"3 1 2 1 \\n6 1 5 3 1 2 1 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n11 1 10 8 7 6 1 5 4 1 3 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 4 3 \\n0 \\n4 10 8 7 3 \\n0 \\n\", \"3 1 2 1 \\n4 5 4 1 2 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n9 1 10 1 7 5 4 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n7 1 10 5 4 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 3 \\n0 \\n9 1 10 8 1 6 4 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 4 1 \\n0 \\n9 1 10 1 9 1 8 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n1 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n7 1 9 8 1 5 3 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n9 1 10 8 7 1 4 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 1 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 4 1 2 \\n0 \\n5 1 10 8 7 3 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 1 \\n0 \\n6 10 8 7 1 2 1 \\n0 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n6 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 1 3 2 \\n0 \\n9 1 10 1 9 1 8 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n5 1 5 4 1 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\", \"3 1 2 1 \\n3 1 5 2 \\n0 \\n7 1 10 8 7 1 2 1 \\n1 1 \\n\"]}", "source": "taco"}
|
This is the easy version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved.
There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix.
For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001.
Your task is to transform the string a into b in at most 3n operations. It can be proved that it is always possible.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 3t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 1000) — the length of the binary strings.
The next two lines contain two binary strings a and b of length n.
It is guaranteed that the sum of n across all test cases does not exceed 1000.
Output
For each test case, output an integer k (0≤ k≤ 3n), followed by k integers p_1,…,p_k (1≤ p_i≤ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation.
Example
Input
5
2
01
10
5
01011
11100
2
01
01
10
0110011011
1000110100
1
0
1
Output
3 1 2 1
6 5 2 5 3 1 2
0
9 4 1 2 10 4 1 2 1 5
1 1
Note
In the first test case, we have 01→ 11→ 00→ 10.
In the second test case, we have 01011→ 00101→ 11101→ 01000→ 10100→ 00100→ 11100.
In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged.
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\": [\"?&?&?|?|?&?\", \"?|?&?|?&?&?\", \"?&?&?|?&?|?\", \"?&?|?|?&?&?\", \"?|?|?&?&?&?\", \"?&?&?&?|?|?\", \"?|?&?&?|?&?\", \"?&?|?&?&?|?\", \"?|?|?&?&??&\", \"?|?&?&?&?|?\", \"?|?&?|?&??&\", \"?&?|?|?&??&\", \"?|?|?&??&?&\", \"?|?|?&?&?&?\", \"?&?&?&?|?|?\", \"?|?&?&?|?&?\", \"?&?|?&?&?|?\", \"?&?&?|?|?&?\", \"?&?|?|?&?&?\", \"?|?&?&?&?|?\", \"?&?&?|?&?|?\", \"?|?&?|?&?&?\", \"?|?|?&?&??&\", \"?|?&?|?&??&\", \"?&?|?|?&??&\", \"?&?|?&?|?&?\"], \"outputs\": [\"3 2\\n\", \"3 1\\n\", \"3 3\\n\", \"3 2\\n\", \"3 1\\n\", \"3 2\\n\", \"3 1\\n\", \"3 2\\n\", \"3 1\\n\", \"3 1\\n\", \"3 1\\n\", \"3 2\\n\", \"3 1\\n\", \"3 1\\n\", \"3 2\\n\", \"3 1\\n\", \"3 2\\n\", \"3 2\\n\", \"3 2\\n\", \"3 1\\n\", \"3 3\\n\", \"3 1\\n\", \"3 1\\n\", \"3 1\\n\", \"3 2\\n\", \"3 2\"]}", "source": "taco"}
|
C: Short-circuit evaluation
problem
Naodai-kun and Hokkaido University-kun are playing games. Hokkaido University first generates the following logical formula represented by BNF.
<formula> :: = <or-expr>
<or-expr> :: = <and-expr>
| <or-expr> "|" <and-expr>
<and-expr> :: = <term>
| <and-expr> "&" <term>
<term> :: = "(" <or-expr> ")" | "?"
`&` represents the logical product, `|` represents the logical sum, and `&` is evaluated before `|`.
Naodai reads this formula from the left (as a string), and when he finds a `?`, He does the following:
* If it is certain that the evaluation result of the formula does not change regardless of whether the `?` Is `0` or` 1`, read it without doing anything.
* If not, pay 1 yen to Hokkaido University and replace the `?` With `0` or` 1`.
The logical expression is evaluated as follows. It is a so-called ordinary formula.
(0 &?) == 0
(1 & 0) == 0
(1 & 1) == 1
(0 | 0) == 0
(0 | 1) == 1
(1 |?) == 1
What is the minimum amount Naodai has to pay to finalize the evaluation result of a well-formed formula? Obtain the evaluation result depending on whether it is set to `0` or` 1`.
Input format
A formula that follows the BNF above is given in one line.
Constraint
The length of the formula does not exceed 2 \ times 10 ^ 5.
Output format
Output the minimum amount required to make the evaluation result `0`,` 1`, separated by blanks.
Input example 1
? &? |? &? |? &?
Output example 1
3 2
If you want to make it `0`, rewrite it with` 0 0 0` to make it `0 &? | 0 &? | 0 &?`, If you want to make it `1`, rewrite it with` 1 1` and make it `1 & 1 |? &? |? & It is best to use? `.
Input example 2
? &? &? |? &? &?
Output example 2
twenty three
They are `0 &? &? | 0 &? &?` And `1 & 1 & 1 |? &? &?`, Respectively.
Input example 3
(? |? |?) &? &? &? &? |? &? |? &?
Output example 3
4 4
Example
Input
?&?|?&?|?&?
Output
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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{"tests": "{\"inputs\": [\"1\\nx eazqyp pnop pngtg ye obmpngt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye obmpngt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye onmpbgt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye pnmobgt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pngtg yd pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pngth yd pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pngth yd pnmobgt xmybp rm wgyl\", \"1\\nx pyqzae pnop pngth yd pnmobgt xmybp rm wgzl\", \"1\\nx eazqyp pnop pngth yd pnmobgt xmybp rm wgzl\", \"1\\nx eazqyp pnop pngth yd pnmobgt xmyap rm wgzl\", \"1\\nx eazqyp pnop pngtg yd pnmobgt xmyap rm wgzl\", \"1\\ny eazqyp pnop pngtg ey obmpngt xmybp mr lygw\", \"1\\ny eazqyp pnop pngtg ye obmpngt xmybp mr lygx\", \"1\\nx pyqzae pnop pngtg ye tgnpmbo xmybp mr lygw\", \"1\\nx pyqzae pnop pngug ye onmpbgt xmybp mr lygw\", \"1\\nx pyqzae pnop ongtg ye pnmobgt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye pnmobgt xmybp sm lygw\", \"1\\nx eazqyp pnop pngth yd pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pmgth yd pnmobgt xmybp rm wgyl\", \"1\\nx pyqzae pnop pngth yd pnmobgt xmybp rl wgzl\", \"1\\nw eazqyp pnop pngth yd pnmobgt xmyap rm wgzl\", \"1\\nx eazqyp pnop pngtg yd pnmobgt xmyap rm wfzl\", \"1\\ny eazqyp pnop pngtg ey obmpngt xmybp mr wygl\", \"1\\ny eazqyp pnop pngtg ye obmpngt xnybp mr lygx\", \"1\\nx pyqzae pnop pngtg xe tgnpmbo xmybp mr lygw\", \"1\\nx pyqzae pnop pngug ye onmpbgt xmybp mr wgyl\", \"1\\nx pyqzae pnop ongtg ye tgbomnp xmybp mr lygw\", \"1\\nx pyqzae pnop pnggt ye pnmobgt xmybp sm lygw\", \"1\\nx eazqyp pnop pngth zd pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pmgth yd pnmobgt xmybp rm wgzl\", \"1\\nx pyqzae pnop pngth dy pnmobgt xmybp rl wgzl\", \"1\\ny eazqyp pnop pngtg ey obmpngt xmybp mr vygl\", \"1\\ny eazqyp pnop pngtg ye tgnpmbo xnybp mr lygx\", \"1\\nx pyqzae pnop pngtg xe tgnpmao xmybp mr lygw\", \"1\\nx pyqzae pnop qngug ye onmpbgt xmybp mr wgyl\", \"1\\nw pyqzae pnop ongtg ye tgbomnp xmybp mr lygw\", \"1\\ny pyqzae pnop pmgth yd pnmobgt xmybp rm wgzl\", \"1\\nx pyqzae pnop pngth dx pnmobgt xmybp rl wgzl\", \"1\\ny eazqyp pnop pnftg ey obmpngt xmybp mr vygl\", \"1\\ny eazqyp pnop pngtg ze tgnpmbo xnybp mr lygx\", \"1\\nx pyqzae pnop qngug ye onmpagt xmybp mr wgyl\", \"1\\nw pyqzae pnop ongtg ye tgbomnp xmybp mr lygx\", \"1\\ny pyqzae pnop pmgth ye pnmobgt xmybp rm wgzl\", \"1\\ny eazqyp pnop pnftg ey obmpngt xmybp mr vygk\", \"1\\ny eazqyp pnop pngtg ze tgnqmbo xnybp mr lygx\", \"1\\nw pyqzae pnop qngug ye onmpagt xmybp mr wgyl\", \"1\\nw pyqzae pnop nogtg ye tgbomnp xmybp mr lygx\", \"1\\ny pyqzae pnop pmgth ye pnmobgt xmybp mr wgzl\", \"1\\ny eazqyp pnop pnftg ey obmpngu xmybp mr vygk\", \"1\\nw pyqzae pnop qngug ey onmpagt xmybp mr wgyl\", \"1\\nw pyqzae pnop qngug ey onmpagt xmybp mr wgzl\", \"1\\nw pyqzae pnop qngug ey onmpbgt xmybp mr wgzl\", \"1\\nw pyqzae pnop gugnq ey onmpbgt xmybp mr wgzl\", \"1\\nw eazqyp pnop gugnq ey onmpbgt xmybp mr wgzl\", \"1\\nx eazqyp pnop gugnq ey onmpbgt xmybp mr wgzl\", \"1\\nx eazqyp pnop gugnq ey onmpbgt xmybp mr wlzg\", \"1\\ny eazqyp pnop pngtg ye obmpngt xmybp mr lgyw\", \"1\\nx eazqyp pnop pogtg ye obmpngt xmybp mr lygw\", \"1\\nx pyqzae pnop pmgtg ye obmpngt xmybp mr lygw\", \"1\\nx pyqzae pnop pngtg ye onmpbgt xmybp rm lygw\", \"1\\nx pyqzae pnop pngtg ye pnmobgt xmybp ms lygw\", \"1\\nx pyqzae pnop pngtg ye pnmobgt xmxbp rm lygw\", \"1\\nx pyqzae pnop qngtg yd pnmobgt xmybp rm lygw\", \"1\\nx pyqzae pnop pngth dy pnmobgt xmybp rm wgyl\", \"1\\nx pyqzae pnop pngth yd pnmobgt xmybp rm gwzl\", \"1\\nx eazqyp pnop pngth yd pnmobgt xmybp rm wfzl\", \"1\\nx eazqyp pnop pngth xd pnmobgt xmyap rm wgzl\", \"1\\nx eazqyp pnop pngtg yd pnmobgt xmyap mr wgzl\", \"1\\ny eazqyp pnop pngtg ex obmpngt xmybp mr lygw\", \"1\\ny eazqyp pnop pngtg ye tgnpmbo xmybp mr lygx\", \"1\\nx pyqzae pnop pngtg ye tgnpmbo xmybp mq lygw\", \"1\\nx pyqzae pnop pngug ye onmpbgt xmybp lr lygw\", \"1\\nx pyqzae pnop ongtg ye pnmobgt xnybp mr lygw\", \"1\\nx eazqyp pnop pngtg ye pnmobgt xmybp sm lygw\", \"1\\nx pyqzae pnop qngth yd pnmobgt xmybp rl wgzl\", \"1\\nv eazqyp pnop pngth yd pnmobgt xmyap rm wgzl\", \"1\\ny eazqyp pnop pngtg ey obmpngt xmybo mr wygl\", \"1\\ny eazqyp pnop pngtg ye obmpngt xnybp lr lygx\", \"1\\nx pyqzae pnop pngtg xe tgnpmbo ymybp mr lygw\", \"1\\nx pyqzae pnop pngug ye tgbpmno xmybp mr wgyl\", \"1\\nx pyqzae pnop ongtg ye tgbomnp pbymx mr lygw\", \"1\\nx pyqzae pnop pnggt ye pnmobgt xmybp ms lygw\", \"1\\nx eazqyp pnop pngth dz pnmobgt xmybp rm lygw\", \"1\\nx pyqz`e pnop pmgth yd pnmobgt xmybp rm wgzl\", \"1\\nx pyqzae pnop pngth dy pnmobgt xmybp rm wgzl\", \"1\\ny eazqyp pnop pngtg ey obmpngt xmybp mr vxgl\", \"1\\ny eazqyp pnop pngtg ye tgnpmbo xnybp mr lzgx\", \"1\\nx pyqzae pnop pngtg xe tgnpmao xmybp rm lygw\", \"1\\nx pyqzae pnop qngug ey onmpbgt xmybp mr wgyl\", \"1\\nw ayqzpe pnop ongtg ye tgbomnp xmybp mr lygw\", \"1\\ny pyqzae pnop pmgth yd pnmobgt xmybp mr wgzl\", \"1\\nx pyqzae pnop pngth dx pnmobht xmybp rl wgzl\", \"1\\ny eazqyp pnop pnftg ey obmpngt xmybp mr gyvl\", \"1\\ny eayqzp pnop pngtg ze tgnpmbo xnybp mr lygx\", \"1\\nx pyqzae pnop gugnq ye onmpagt xmybp mr wgyl\", \"1\\nx pyqzae pnop ongtg ye tgbomnp xmybp mr lygx\", \"1\\ny pyqzae pnop pmgth ye pnmobgt xnybp rm wgzl\", \"1\\ny eazqyp pnop pngtg ze tgnqmbo xnzbp mr lygx\", \"1\\nw pyqzae pnop qggun ye onmpagt xmybp mr wgyl\", \"1\\ny eazqyp pnop pngtg ye obmpngt xmybp mr lygw\"], \"outputs\": [\"p submit that there is another point of view\\n\", \"p timbus that there is another point of view\\n\", \"p timbus that there is ahotner point of view\\n\", \"p timbus that there is thoaner point of view\\n\", \"p timbus that there is thoaner point fo view\\n\", \"p timbus that there iz thoaner point fo view\\n\", \"p timbus that therx iz thoaner point fo view\\n\", \"p timbus that therx iz thoaner point fo weiv\\n\", \"p timbus that therx iz thoaner point fo webv\\n\", \"p submit that therx iz thoaner point fo webv\\n\", \"p submit that therx iz thoaner poiut fo webv\\n\", \"p submit that there iz thoaner poiut fo webv\\n\", \"i submit that there si another point of view\\n\", \"i submit that there is another point of viep\\n\", \"p timbus that there is rehtona point of view\\n\", \"p timbus that theke is ahotner point of view\\n\", \"p timbus that ahere is thoaner point of view\\n\", \"p timbus that there is thoaner point yo view\\n\", \"p submit that therx iz thoaner point fo view\\n\", \"p timbus that toerx iz thoaner point fo weiv\\n\", \"p timbus that therx iz thoaner point fv webv\\n\", \"w submit that therx iz thoaner poiut fo webv\\n\", \"p submit that there iz thoaner poiut fo wlbv\\n\", \"i submit that there si another point of wiev\\n\", \"i submit that there is another phint of viep\\n\", \"p timbus that there ps rehtona point of view\\n\", \"p timbus that theke is ahotner point of weiv\\n\", \"p timbus that ahere is renaoht point of view\\n\", \"p timbus that theer is thoaner point yo view\\n\", \"p submit that therx bz thoaner point fo view\\n\", \"p timbus that toerx iz thoaner point fo webv\\n\", \"p timbus that therx zi thoaner point fv webv\\n\", \"i submit that there si another point of diev\\n\", \"i submit that there is rehtona phint of viep\\n\", \"p timbus that there ps rehtoua point of view\\n\", \"p timbus that mheke is ahotner point of weiv\\n\", \"w timbus that ahere is renaoht point of view\\n\", \"i timbus that toerx iz thoaner point fo webv\\n\", \"p timbus that therx zp thoaner point fv webv\\n\", \"i submit that thlre si another point of diev\\n\", \"i submit that there bs rehtona phint of viep\\n\", \"p timbus that mheke is ahotuer point of weiv\\n\", \"w timbus that ahere is renaoht point of viep\\n\", \"i timbus that toerx is thoaner point fo webv\\n\", \"i submit that thlre si another point of diec\\n\", \"i submit that there bs rehmona phint of viep\\n\", \"w timbus that mheke is ahotuer point of weiv\\n\", \"w timbus that haere is renaoht point of viep\\n\", \"i timbus that toerx is thoaner point of webv\\n\", \"i submit that thlre si anothek point of diec\\n\", \"w timbus that mheke si ahotuer point of weiv\\n\", \"w timbus that mheke si ahotuer point of webv\\n\", \"w timbus that mheke si ahotner point of webv\\n\", \"w timbus that ekehm si ahotner point of webv\\n\", \"w submit that ekehm si ahotner point of webv\\n\", \"p submit that ekehm si ahotner point of webv\\n\", \"p submit that ekehm si ahotner point of wvbe\\n\", \"i submit that there is another point of veiw\\n\", \"p submit that taere is another point of view\\n\", \"p timbus that toere is another point of view\\n\", \"p timbus that there is ahotner point fo view\\n\", \"p timbus that there is thoaner point oy view\\n\", \"p timbus that there is thoaner popnt fo view\\n\", \"p timbus that mhere iz thoaner point fo view\\n\", \"p timbus that therx zi thoaner point fo weiv\\n\", \"p timbus that therx iz thoaner point fo ewbv\\n\", \"p submit that therx iz thoaner point fo wlbv\\n\", \"p submit that therx pz thoaner poiut fo webv\\n\", \"p submit that there iz thoaner poiut of webv\\n\", \"i submit that there sp another point of view\\n\", \"i submit that there is rehtona point of viep\\n\", \"p timbus that there is rehtona point om view\\n\", \"p timbus that theke is ahotner point vf view\\n\", \"p timbus that ahere is thoaner phint of view\\n\", \"p submit that there is thoaner point yo view\\n\", \"p timbus that mherx iz thoaner point fv webv\\n\", \"d submit that therx iz thoaner poiut fo webv\\n\", \"i submit that there si another poina of wiev\\n\", \"i submit that there is another phint vf viep\\n\", \"p timbus that there ps rehtona ioint of view\\n\", \"p timbus that theke is rentoha point of weiv\\n\", \"p timbus that ahere is renaoht tniop of view\\n\", \"p timbus that theer is thoaner point oy view\\n\", \"p submit that therx zb thoaner point fo view\\n\", \"p timb`s that toerx iz thoaner point fo webv\\n\", \"p timbus that therx zi thoaner point fo webv\\n\", \"i submit that there si another point of dpev\\n\", \"i submit that there is rehtona phint of vbep\\n\", \"p timbus that there ps rehtoua point fo view\\n\", \"p timbus that mheke si ahotner point of weiv\\n\", \"w uimbts that ahere is renaoht point of view\\n\", \"i timbus that toerx iz thoaner point of webv\\n\", \"p timbus that therx zp thoanxr point fv webv\\n\", \"i submit that thlre si another point of eidv\\n\", \"i suimbt that there bs rehtona phint of viep\\n\", \"p timbus that ekehm is ahotuer point of weiv\\n\", \"p timbus that ahere is renaoht point of viep\\n\", \"i timbus that toerx is thoaner phint fo webv\\n\", \"i submit that there bs rehmona phbnt of viep\\n\", \"w timbus that meekh is ahotuer point of weiv\\n\", \"i submit that there is another point of view\"]}", "source": "taco"}
|
One of the simple ciphers is the affine cipher. First, replace the letters a to z with the numbers a = 0, b = 1, c = 2, ..., x = 23, y = 24, z = 25 and 0 to 25. Then replace the original alphabet with the following formula.
$ F (\ gamma) = (\ alpha \ cdot \ gamma + \ beta) $ mod $ 26 $
However, mod 26 represents the remainder after dividing by 26. For example, when $ \ alpha = 3, \ beta = 2 $, the alphabet'a'(= 0) is $ F (0) = (3 \ cdot 0 + 2) $ mod $ 26 = 2 $ and'c In', the alphabet'n'(= 13) is replaced with'p' at $ F (13) = (3 \ cdot 13 + 2) $ mod $ 26 = 15 $. At this time, it is assumed that $ \ alpha $ and $ \ beta $ are carefully selected so that $ F (\ gamma) $ is always associated with $ \ gamma $ on a one-to-one basis ($ \ alpha). As long as $ and 26 are relatively prime). $ F ('a') = 7, F ('n') = 7 $, as in $ \ alpha = 4, \ beta = 7 $, and'a'and'n' are the same'h' It will not be replaced by. Also, non-alphabetic characters are not replaced.
Create a program that outputs the encrypted character string decrypted into the original text. In the original text, as a keyword
that
this
It is assumed that one of the above is always included.
Input
Given multiple datasets. The first line gives the number of datasets $ n $ ($ n \ leq 30 $). It is followed by $ n $ rows of data. Each dataset is given an encrypted sentence of up to 256 characters consisting of lowercase letters and blanks on one line.
Output
For each dataset, output the decrypted original text on one line.
Example
Input
1
y eazqyp pnop pngtg ye obmpngt xmybp mr lygw
Output
i submit that there is another point of view
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\": [\"O O .\\n O O . .\\n. . . . .\\n . . . .\\n . O .\\n\", \". . O\\n . O O .\\nO . O . O\\n O O O O\\n . . O\\n\", \". . .\\n . O . .\\n. O O . .\\n . . O .\\n . O .\\n\", \"O O O\\n O O . O\\nO . O O O\\n O . O O\\n O O .\\n\", \"O O O\\n O O . O\\nO . O O O\\n O O O O\\n . O O\\n\", \"O O O\\n O . O .\\nO . . O O\\n O . O O\\n O O O\\n\", \"O O O\\n O O O O\\nO . O O .\\n . O O O\\n O O O\\n\", \"O O O\\n . O . O\\nO O O O .\\n . . O .\\n O . O\\n\", \". . O\\n O . O .\\n. . O . .\\n . O . .\\n O . .\\n\", \". . .\\n . . . .\\n. O . O .\\n . O O .\\n O . .\\n\", \"O O O\\n O O O O\\nO O O O O\\n O O O O\\n O O O\\n\", \"O . O\\n O O O O\\nO O . O O\\n . O O .\\n . . .\\n\", \"O . O\\n O . O .\\nO . O . .\\n O O . .\\n O O O\\n\", \". . .\\n . O O O\\nO O O O O\\n O O O O\\n . O .\\n\", \". O O\\n . . O .\\n. . . . .\\n . . . .\\n . . .\\n\", \"O O O\\n O . O .\\n. . . O O\\n O O O O\\n O O O\\n\", \". . .\\n . O O .\\nO . . O .\\n . . . O\\n . . O\\n\", \"O . .\\n O O . .\\n. . . . .\\n O . O .\\n . O .\\n\", \"O O O\\n O O O O\\n. O O O .\\n . O O .\\n . . .\\n\", \". . .\\n . . O O\\n. . O . O\\n . . O .\\n . O .\\n\", \". O .\\n O O . O\\nO . O O O\\n O O O O\\n O O O\\n\", \". . O\\n . . . O\\n. . . O .\\n . . O .\\n . O .\\n\", \"O O O\\n . O . O\\nO O O O .\\n . . . .\\n . . .\\n\", \"O O O\\n O O O O\\nO O O O O\\n O O O O\\n . . .\\n\", \"O . .\\n . O O O\\n. O . . .\\n . . . .\\n . . .\\n\", \". O O\\n O O O O\\nO O O O O\\n O O O .\\n . . .\\n\", \". . .\\n O O O .\\nO O . O .\\n O . O .\\n . O .\\n\", \"O O O\\n O O . O\\n. O . O O\\n O O . O\\n O O O\\n\", \"O . O\\n . . . .\\nO . O . O\\n . . . .\\n O . O\\n\", \"O . O\\n O O O O\\n. O . O O\\n O O . .\\n O O O\\n\", \"O O O\\n O . . O\\nO . . . O\\n O . . O\\n O O O\\n\", \". . .\\n O . . O\\n. . . . .\\n O . . O\\n O O O\\n\", \"O O O\\n O O . O\\nO O . O O\\n O . O O\\n O O O\\n\", \"O O O\\n O O O O\\nO O . O O\\n O . O O\\n O O .\\n\", \". O O\\n . O . O\\n. . . . .\\n . . . .\\n . . O\\n\", \"O . O\\n O O O O\\nO O O O O\\n . O O .\\n O O O\\n\", \". O O\\n O O O O\\nO . O O .\\n O O . .\\n . . .\\n\", \". . .\\n O . . O\\n. O . O .\\n . O O .\\n . O .\\n\", \"O O O\\n O . O O\\nO O O . O\\n O O O O\\n O O O\\n\", \". . O\\n . O . O\\n. . O O .\\n . . O .\\n . . .\\n\", \"O O O\\n . O O .\\nO O . O O\\n O . O .\\n O . .\\n\", \". O O\\n . O O O\\n. . O . .\\n O O . .\\n O O O\\n\", \"O O O\\n O O O O\\n. O . O O\\n O . . .\\n O O .\\n\", \". O O\\n O O . O\\nO . O O .\\n O O . O\\n . O O\\n\", \". O O\\n O . O O\\nO O . O O\\n . O O O\\n O O O\\n\", \". . .\\n O . . O\\n. . O . .\\n . . O .\\n . O .\\n\", \". . .\\n . . O .\\n. O . O .\\n O . . .\\n . . .\\n\", \". O .\\n . . O .\\n. O O . .\\n O . O .\\n . O .\\n\", \". . .\\n . . . O\\n. . . O O\\n . . O O\\n . O O\\n\", \"O . O\\n . O O O\\n. . . . O\\n O O O O\\n . . O\\n\", \". . .\\n . O . .\\n. . . O .\\n . O . .\\n . . .\\n\", \"O O O\\n O O O O\\nO O O O .\\n . . . .\\n O O .\\n\", \"O O O\\n O O O O\\nO O . O O\\n O O O O\\n O O O\\n\", \". O .\\n O . . .\\nO O O O .\\n O O O O\\n . . O\\n\", \"O O .\\n O . O .\\nO O O O O\\n O O O O\\n . . O\\n\", \"O O O\\n O O O O\\nO O O O O\\n O . O O\\n O O O\\n\", \". . .\\n . . . .\\nO . O . .\\n O O . .\\n O . .\\n\", \". O O\\n O O . O\\nO O . O .\\n . . . .\\n . . .\\n\", \"O . O\\n O O O .\\n. O O O .\\n . O O .\\n O O O\\n\", \"O O O\\n O O O O\\nO . . . O\\n O . . O\\n O . .\\n\", \"O O O\\n . O O O\\nO . . . O\\n O O . O\\n . O O\\n\", \"O O O\\n O O . O\\nO O . O .\\n . . O .\\n O . O\\n\", \". . .\\n O O O .\\n. O O O .\\n O . O O\\n O O O\\n\", \"O O O\\n O . . O\\n. O O O .\\n . . . O\\n O O O\\n\", \". O O\\n O . O O\\nO O . . .\\n . . . .\\n O O O\\n\", \"O O O\\n O O O O\\nO O O O .\\n O O O .\\n . . .\\n\", \". . .\\n . . . .\\n. . . . .\\n . . O .\\n . . .\\n\", \"O O O\\n O O O .\\nO O O O O\\n O O O O\\n . O O\\n\", \". O O\\n . O . .\\nO . O O .\\n O O . O\\n . . O\\n\", \". O O\\n . O . O\\n. O . . .\\n . . . .\\n . . .\\n\", \". . .\\n . O O O\\n. O O . .\\n O . . .\\n O O .\\n\", \". . .\\n . . . .\\n. . . . .\\n O . . .\\n . . O\\n\", \"O O O\\n O O O O\\nO O O O O\\n O O O O\\n . O O\\n\", \"O O O\\n O O O .\\nO O O O O\\n O O O O\\n O O O\\n\", \"O O O\\n O . . O\\nO O O O O\\n O . . .\\n O . .\\n\", \". O O\\n . O O O\\n. . O O O\\n . . . .\\n . . .\\n\", \". . O\\n O . O O\\nO O . . .\\n . . . .\\n . . .\\n\", \"O O O\\n O O O O\\n. . O . .\\n O . . O\\n O O O\\n\", \". . .\\n . . . O\\n. . . O .\\n O . O .\\n . O .\\n\", \". . .\\n . . O .\\n. . O O .\\n . . . .\\n . . .\\n\"], \"outputs\": [\"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Karlsson\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Lillebror\\n\", \"Karlsson\\n\", \"Lillebror\\n\"]}", "source": "taco"}
|
Karlsson has visited Lillebror again. They found a box of chocolates and a big whipped cream cake at Lillebror's place. Karlsson immediately suggested to divide the sweets fairly between Lillebror and himself. Specifically, to play together a game he has just invented with the chocolates. The winner will get the cake as a reward.
The box of chocolates has the form of a hexagon. It contains 19 cells for the chocolates, some of which contain a chocolate. The players move in turns. During one move it is allowed to eat one or several chocolates that lay in the neighboring cells on one line, parallel to one of the box's sides. The picture below shows the examples of allowed moves and of an unacceptable one. The player who cannot make a move loses.
<image>
Karlsson makes the first move as he is Lillebror's guest and not vice versa. The players play optimally. Determine who will get the cake.
Input
The input data contains 5 lines, containing 19 words consisting of one symbol. The word "O" means that the cell contains a chocolate and a "." stands for an empty cell. It is guaranteed that the box contains at least one chocolate. See the examples for better understanding.
Output
If Karlsson gets the cake, print "Karlsson" (without the quotes), otherwise print "Lillebror" (yet again without the quotes).
Examples
Input
. . .
. . O .
. . O O .
. . . .
. . .
Output
Lillebror
Input
. . .
. . . O
. . . O .
O . O .
. O .
Output
Karlsson
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\": [\"6 9\\n9 9 9 9 9 9\\n\", \"3 2\\n6 2 6\\n\", \"2 1\\n1 2\\n\", \"1 1\\n500000\\n\", \"1 500000\\n500000\\n\", \"9 2\\n1 2 1 2 1 2 1 3 3\\n\", \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 3 1 4 2 2 3 4 2 4 2\\n\", \"18 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"18 1\\n2 2 2 2 1 1 1 1 2 1 2 2 1 2 2 2 2 2\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 3 2\\n\", \"18 1\\n3 3 1 3 1 1 3 4 2 2 2 1 2 1 4 1 4 3\\n\", \"18 2\\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 1\\n\", \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 4 1 3\\n\", \"18 3\\n7 3 5 7 5 4 4 1 2 6 5 5 6 6 6 3 1 1\\n\", \"18 1\\n8 2 3 1 8 3 3 2 7 5 8 2 7 1 4 3 1 3\\n\", \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 3 8 4 4 6 3 7\\n\", \"18 4\\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\", \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 2 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\\n\", \"11 4\\n1 4 3 4 3 3 4 1 1 3 4\\n\", \"13 4\\n1 4 3 4 3 3 4 1 1 3 4 3 4\\n\", \"1 500000\\n500000\\n\", \"18 4\\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\", \"1 1\\n500000\\n\", \"9 2\\n1 2 1 2 1 2 1 3 3\\n\", \"2 1\\n1 2\\n\", \"18 1\\n2 2 2 2 1 1 1 1 2 1 2 2 1 2 2 2 2 2\\n\", \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 4 1 3\\n\", \"18 1\\n3 3 1 3 1 1 3 4 2 2 2 1 2 1 4 1 4 3\\n\", \"18 2\\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 1\\n\", \"18 3\\n7 3 5 7 5 4 4 1 2 6 5 5 6 6 6 3 1 1\\n\", \"13 4\\n1 4 3 4 3 3 4 1 1 3 4 3 4\\n\", \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 3 8 4 4 6 3 7\\n\", \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 3 1 4 2 2 3 4 2 4 2\\n\", \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 2 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\\n\", \"18 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"18 1\\n8 2 3 1 8 3 3 2 7 5 8 2 7 1 4 3 1 3\\n\", \"11 4\\n1 4 3 4 3 3 4 1 1 3 4\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 3 2\\n\", \"1 316327\\n500000\\n\", \"18 5\\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\", \"9 2\\n1 2 1 2 1 2 1 3 0\\n\", \"18 1\\n3 3 1 3 1 1 3 4 2 2 3 1 2 1 4 1 4 3\\n\", \"18 2\\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\", \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 3 2 4 4 6 3 7\\n\", \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 2\\n\", \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 5 2\\n\", \"3 2\\n6 2 0\\n\", \"9 2\\n2 2 1 2 1 2 1 3 0\\n\", \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 1 4\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 1\\n\", \"2 0\\n1 2\\n\", \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 1 1 3\\n\", \"13 4\\n1 4 3 4 3 3 4 1 1 1 4 3 4\\n\", \"18 1\\n8 2 3 1 7 3 3 2 7 5 8 2 7 1 4 3 1 3\\n\", \"11 4\\n1 4 3 4 3 3 4 2 1 3 4\\n\", \"6 9\\n9 9 1 9 9 9\\n\", \"18 5\\n1 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\", \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 4 4 5 6 1 1 3\\n\", \"18 1\\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\\n\", \"18 2\\n5 0 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\", \"13 4\\n1 4 3 4 2 3 4 1 1 1 4 3 4\\n\", \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\", \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 3\\n\", \"18 1\\n8 2 3 1 7 3 3 2 7 5 8 2 7 2 4 3 1 3\\n\", \"11 8\\n1 4 3 4 3 3 4 2 1 3 4\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 2\\n\", \"6 9\\n9 9 1 18 9 9\\n\", \"18 5\\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\", \"9 2\\n2 2 1 2 2 2 1 3 0\\n\", \"18 0\\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\\n\", \"18 2\\n5 0 4 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\", \"13 7\\n1 4 3 4 2 3 4 1 1 1 4 3 4\\n\", \"18 1\\n3 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\", \"18 1\\n8 2 3 1 7 2 3 2 7 5 8 2 7 2 4 3 1 3\\n\", \"11 8\\n1 4 3 4 3 3 4 4 1 3 4\\n\", \"6 9\\n9 9 1 18 3 9\\n\", \"18 5\\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 6\\n\", \"9 2\\n2 3 1 2 2 2 1 3 0\\n\", \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\", \"13 7\\n1 4 3 4 2 3 4 1 1 1 5 3 4\\n\", \"18 1\\n2 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\", \"18 1\\n8 2 3 1 7 2 3 2 7 5 8 4 7 2 4 3 1 3\\n\", \"11 8\\n1 4 3 4 3 3 2 4 1 3 4\\n\", \"18 2\\n3 3 2 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\\n\", \"6 9\\n9 9 1 18 3 13\\n\", \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 6 6 5 9 6\\n\", \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 6 2\\n\", \"13 7\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\", \"18 1\\n2 4 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\\n\", \"11 8\\n1 0 3 4 3 3 2 4 1 3 4\\n\", \"18 2\\n3 3 3 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\\n\", \"6 9\\n9 9 1 18 3 7\\n\", \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 5 9 6\\n\", \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 5 2 3 6 2\\n\", \"13 3\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\", \"18 1\\n2 0 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\\n\", \"11 8\\n1 0 3 4 3 3 2 4 1 0 4\\n\", \"18 2\\n3 3 3 2 3 2 0 2 2 2 3 0 1 3 3 3 5 1\\n\", \"6 9\\n9 9 1 1 3 7\\n\", \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 4 9 6\\n\", \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 3 6 2\\n\", \"13 3\\n1 4 3 5 2 3 4 1 1 1 5 3 3\\n\", \"11 14\\n1 0 3 4 3 3 2 4 1 0 4\\n\", \"18 2\\n3 3 3 2 3 2 0 2 2 2 6 0 1 3 3 3 5 1\\n\", \"18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 4 9 6\\n\", \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n\", \"13 5\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\", \"18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 6 9 6\\n\", \"18 2\\n5 0 1 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n\", \"3 2\\n6 2 6\\n\", \"6 9\\n9 9 9 9 9 9\\n\"], \"outputs\": [\"6\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"5\\n\", \"12\\n\", \"18\\n\", \"12\\n\", \"11\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"19\\n\", \"6\\n\", \"7\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"5\\n\", \"2\\n\", \"12\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"7\\n\", \"4\\n\", \"12\\n\", \"19\\n\", \"18\\n\", \"5\\n\", \"6\\n\", \"11\\n\", \"1\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"7\\n\", \"3\\n\", \"12\\n\", \"19\\n\", \"10\\n\", \"2\\n\", \"5\\n\", \"20\\n\", \"9\\n\", \"1\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"8\\n\", \"4\\n\", \"12\\n\", \"5\\n\", \"4\\n\", \"10\\n\", \"5\\n\", \"5\\n\", \"6\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"10\\n\", \"3\\n\", \"5\\n\", \"7\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"3\\n\", \"5\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"9\\n\", \"4\\n\", \"4\\n\", \"7\\n\", \"7\\n\", \"3\\n\", \"8\\n\", \"4\\n\", \"8\\n\", \"5\\n\", \"4\\n\", \"7\\n\", \"2\\n\", \"6\\n\"]}", "source": "taco"}
|
You are given array $a$ of length $n$. You can choose one segment $[l, r]$ ($1 \le l \le r \le n$) and integer value $k$ (positive, negative or even zero) and change $a_l, a_{l + 1}, \dots, a_r$ by $k$ each (i.e. $a_i := a_i + k$ for each $l \le i \le r$).
What is the maximum possible number of elements with value $c$ that can be obtained after one such operation?
-----Input-----
The first line contains two integers $n$ and $c$ ($1 \le n \le 5 \cdot 10^5$, $1 \le c \le 5 \cdot 10^5$) — the length of array and the value $c$ to obtain.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 5 \cdot 10^5$) — array $a$.
-----Output-----
Print one integer — the maximum possible number of elements with value $c$ which can be obtained after performing operation described above.
-----Examples-----
Input
6 9
9 9 9 9 9 9
Output
6
Input
3 2
6 2 6
Output
2
-----Note-----
In the first example we can choose any segment and $k = 0$. The array will stay same.
In the second example we can choose segment $[1, 3]$ and $k = -4$. The array will become $[2, -2, 2]$.
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
|
{"tests": "{\"inputs\": [\"5\\n0 0\\n0 1\\n1 1\\n1 -1\\n2 2\\n\", \"5\\n0 0\\n1 0\\n2 1\\n1 1\\n2 3\\n\", \"1\\n-1000000000 1000000000\\n\", \"5\\n2 -1\\n-4 1\\n0 -9\\n5 -9\\n9 -10\\n\", \"5\\n6 1\\n10 5\\n10 -2\\n-2 -10\\n-4 -9\\n\", \"5\\n-10 3\\n4 -5\\n-9 5\\n-5 -3\\n-4 -6\\n\", \"5\\n2 9\\n-1 -4\\n-3 -8\\n-4 8\\n7 2\\n\", \"10\\n315 202\\n315 203\\n315 204\\n-138 -298\\n-136 -295\\n-134 -292\\n-132 -289\\n-130 -286\\n-128 -283\\n-126 -280\\n\", \"10\\n416 -473\\n-162 491\\n-164 488\\n-170 479\\n-166 485\\n-172 476\\n416 -475\\n416 -474\\n-168 482\\n-160 494\\n\", \"6\\n0 0\\n1 1\\n0 1\\n1 0\\n0 2\\n2 0\\n\", \"5\\n3 3\\n6 3\\n0 0\\n10 0\\n-10 0\\n\", \"1\\n0 0\\n\", \"10\\n0 0\\n1 0\\n0 1\\n0 2\\n2 0\\n3 0\\n0 3\\n0 4\\n4 0\\n0 -10000000\\n\", \"6\\n0 0\\n0 1\\n0 2\\n1 1\\n1 2\\n2 1\\n\", \"6\\n0 -1\\n1 -1\\n3 3\\n2 0\\n-2 -2\\n1 -2\\n\", \"5\\n1000000000 1000000000\\n999999999 999999999\\n999999999 999999998\\n-1000000000 1000000000\\n-1000000000 999999999\\n\", \"5\\n0 0\\n1 0\\n0 1\\n1 1\\n-1 1\\n\", \"6\\n0 0\\n0 1\\n0 -1\\n1 1\\n1 -1\\n2 -1\\n\", \"4\\n0 0\\n0 1\\n1 0\\n1 1\\n\", \"6\\n0 0\\n1 0\\n2 1\\n1 1\\n0 1\\n6 0\\n\", \"10\\n536870912 536870912\\n268435456 368435456\\n268435456 168435456\\n1 3\\n2 4\\n3 5\\n4 6\\n5 7\\n6 8\\n7 9\\n\", \"5\\n0 0\\n0 1\\n100 100\\n100 99\\n100 98\\n\", \"8\\n0 0\\n1 0\\n2 1\\n1 1\\n0 1\\n6 0\\n5 0\\n7 0\\n\", \"5\\n0 0\\n2 0\\n1 1\\n0 2\\n5 1\\n\", \"7\\n0 0\\n4 0\\n1 1\\n2 2\\n3 1\\n5 1\\n6 2\\n\", \"6\\n1 1\\n2 2\\n3 2\\n4 1\\n5 2\\n6 1\\n\", \"8\\n0 0\\n1 0\\n2 0\\n3 0\\n0 1\\n1 1\\n2 1\\n3 1\\n\", \"12\\n0 0\\n1 1\\n2 2\\n3 3\\n10 11\\n20 11\\n30 11\\n40 11\\n-1 1\\n-2 2\\n-3 3\\n-4 4\\n\", \"6\\n0 0\\n165580141 267914296\\n331160282 535828592\\n267914296 433494437\\n535828592 866988874\\n433494437 701408733\\n\", \"5\\n-1000000000 -1000000000\\n-588442013 -868997024\\n-182303377 -739719081\\n-999999999 -999999999\\n229254610 -608716105\\n\", \"5\\n-1000000000 -1000000000\\n229254610 -608716105\\n-588442013 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|
You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.
You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?
-----Input-----
The first line contains one integer n (1 ≤ n ≤ 10^5) — the number of points you are given.
Then n lines follow, each line containing two integers x_{i} and y_{i} (|x_{i}|, |y_{i}| ≤ 10^9)— coordinates of i-th point. All n points are distinct.
-----Output-----
If it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.
-----Examples-----
Input
5
0 0
0 1
1 1
1 -1
2 2
Output
YES
Input
5
0 0
1 0
2 1
1 1
2 3
Output
NO
-----Note-----
In the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points. [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
|
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\"10000110030\\n\", \"15\\n\", \"5121000005\\n\", \"10\\n\", \"3011100103\\n\", \"5010275490\\n\", \"21\\n\", \"17\\n\", \"7\\n\", \"15\\n\", \"6\\n\"]}", "source": "taco"}
|
You invited $n$ guests to dinner! You plan to arrange one or more circles of chairs. Each chair is going to be either occupied by one guest, or be empty. You can make any number of circles.
Your guests happen to be a little bit shy, so the $i$-th guest wants to have a least $l_i$ free chairs to the left of his chair, and at least $r_i$ free chairs to the right. The "left" and "right" directions are chosen assuming all guests are going to be seated towards the center of the circle. Note that when a guest is the only one in his circle, the $l_i$ chairs to his left and $r_i$ chairs to his right may overlap.
What is smallest total number of chairs you have to use?
-----Input-----
First line contains one integer $n$ — number of guests, ($1 \leqslant n \leqslant 10^5$).
Next $n$ lines contain $n$ pairs of space-separated integers $l_i$ and $r_i$ ($0 \leqslant l_i, r_i \leqslant 10^9$).
-----Output-----
Output a single integer — the smallest number of chairs you have to use.
-----Examples-----
Input
3
1 1
1 1
1 1
Output
6
Input
4
1 2
2 1
3 5
5 3
Output
15
Input
1
5 6
Output
7
-----Note-----
In the second sample the only optimal answer is to use two circles: a circle with $5$ chairs accomodating guests $1$ and $2$, and another one with $10$ chairs accomodationg guests $3$ and $4$.
In the third sample, you have only one circle with one person. The guest should have at least five free chairs to his left, and at least six free chairs to his right to the next person, which is in this case the guest herself. So, overall number of chairs should be at least 6+1=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\": [\"1 1\\n0 0\\n2 3\\n\", \"2 3\\n1 6\\n6 1\\n10 1\\n1 10\\n7 7\\n\", \"1 2\\n0 0\\n0 0\\n0 0\\n\", \"7 3\\n0 8\\n3 8\\n2 7\\n0 10\\n5 5\\n7 0\\n3 5\\n6 6\\n3 11\\n11 5\\n\", \"1 1\\n0 0\\n0 0\\n\", \"2 1\\n0 0\\n0 0\\n0 0\\n\", \"1 1\\n279 365\\n566 88\\n\", \"1 2\\n244 520\\n590 781\\n867 704\\n\", \"2 1\\n469 963\\n697 509\\n456 80\\n\", \"1 1\\n0 0\\n0 0\\n\", \"1 1\\n279 365\\n566 88\\n\", \"1 2\\n244 520\\n590 781\\n867 704\\n\", \"2 1\\n469 963\\n697 509\\n456 80\\n\", \"1 1\\n0 0\\n1000000 1000000\\n\", \"2 1\\n0 0\\n0 0\\n0 0\\n\", \"1 1\\n2 0\\n1000000 1000000\\n\", \"1 2\\n244 520\\n590 781\\n994 704\\n\", \"2 1\\n469 963\\n697 711\\n456 80\\n\", \"1 1\\n3 0\\n1000000 1000000\\n\", \"7 3\\n0 8\\n3 8\\n2 7\\n0 10\\n5 5\\n7 0\\n3 5\\n6 1\\n3 11\\n11 5\\n\", \"2 3\\n0 6\\n6 1\\n10 1\\n1 10\\n7 7\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 10\\n7 7\\n\", \"1 2\\n244 520\\n590 781\\n442 1058\\n\", \"1 2\\n244 520\\n404 781\\n442 1058\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 4\\n6 7\\n\", \"1 2\\n35 520\\n404 781\\n442 1058\\n\", \"1 2\\n35 520\\n349 781\\n366 1058\\n\", \"1 2\\n35 75\\n683 781\\n366 1058\\n\", \"1 2\\n35 100\\n532 781\\n366 1058\\n\", \"1 1\\n1 0\\n1000000 1000000\\n\", \"1 1\\n5 0\\n1000000 1000000\\n\", \"1 2\\n311 520\\n590 781\\n442 1058\\n\", \"1 2\\n8 520\\n404 781\\n442 1058\\n\", \"1 2\\n35 520\\n727 781\\n442 1058\\n\", \"1 2\\n54 520\\n349 781\\n442 1058\\n\", \"1 2\\n244 520\\n590 781\\n442 704\\n\", \"2 1\\n469 452\\n697 711\\n456 80\\n\", \"7 3\\n0 8\\n3 8\\n2 7\\n0 10\\n5 5\\n7 0\\n3 5\\n6 0\\n3 11\\n11 5\\n\", \"2 1\\n469 452\\n697 711\\n521 80\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 4\\n7 7\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 6\\n6 7\\n\", \"1 2\\n35 520\\n349 781\\n442 1058\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 4\\n6 11\\n\", \"1 2\\n35 75\\n349 781\\n366 1058\\n\", \"1 2\\n35 100\\n683 781\\n366 1058\\n\", \"1 2\\n35 100\\n532 781\\n336 1058\\n\", \"1 2\\n35 100\\n532 781\\n350 1058\\n\", \"1 1\\n279 365\\n566 70\\n\", \"1 2\\n244 520\\n590 781\\n867 2\\n\", \"2 1\\n469 1407\\n697 509\\n456 80\\n\", \"2 3\\n1 6\\n6 1\\n10 1\\n1 12\\n7 7\\n\", \"1 2\\n1 0\\n0 0\\n0 0\\n\", \"1 2\\n218 520\\n590 781\\n994 704\\n\", \"7 3\\n0 8\\n3 8\\n2 7\\n0 10\\n5 5\\n7 0\\n3 7\\n6 1\\n3 11\\n11 5\\n\", \"1 2\\n244 520\\n531 781\\n442 704\\n\", \"2 1\\n469 452\\n1222 711\\n456 80\\n\", \"2 1\\n469 819\\n697 711\\n521 80\\n\", \"2 3\\n0 12\\n6 1\\n10 0\\n1 4\\n7 7\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n2 4\\n6 7\\n\", \"2 3\\n0 12\\n6 1\\n10 1\\n1 4\\n6 14\\n\", \"1 2\\n35 51\\n349 781\\n366 1058\\n\", \"1 2\\n35 101\\n532 781\\n336 1058\\n\", \"7 3\\n0 8\\n3 8\\n2 7\\n0 10\\n5 5\\n7 0\\n3 5\\n6 6\\n3 11\\n11 5\\n\", \"2 3\\n1 6\\n6 1\\n10 1\\n1 10\\n7 7\\n\", \"1 1\\n0 0\\n2 3\\n\", \"1 2\\n0 0\\n0 0\\n0 0\\n\"], \"outputs\": [\"3\\n\", \"4\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"262\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"262\\n\", \"0\\n\", \"1000001\\n\", \"1\\n\", \"999999\\n\", \"262\\n\", \"0\\n\", \"999998\\n\", \"6\\n\", \"4\\n\", \"3\\n\", \"347\\n\", \"199\\n\", \"2\\n\", \"408\\n\", \"332\\n\", \"649\\n\", \"498\\n\", \"1000000\\n\", \"999996\\n\", \"280\\n\", \"435\\n\", \"539\\n\", \"389\\n\", \"262\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"408\\n\", \"2\\n\", \"332\\n\", \"649\\n\", \"498\\n\", \"498\\n\", \"0\\n\", \"262\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"262\\n\", \"6\\n\", \"262\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"332\\n\", \"498\\n\", \"6\\n\", \"4\\n\", \"3\\n\", \"1\\n\"]}", "source": "taco"}
|
There are $n$ robbers at coordinates $(a_1, b_1)$, $(a_2, b_2)$, ..., $(a_n, b_n)$ and $m$ searchlight at coordinates $(c_1, d_1)$, $(c_2, d_2)$, ..., $(c_m, d_m)$.
In one move you can move each robber to the right (increase $a_i$ of each robber by one) or move each robber up (increase $b_i$ of each robber by one). Note that you should either increase all $a_i$ or all $b_i$, you can't increase $a_i$ for some points and $b_i$ for some other points.
Searchlight $j$ can see a robber $i$ if $a_i \leq c_j$ and $b_i \leq d_j$.
A configuration of robbers is safe if no searchlight can see a robber (i.e. if there is no pair $i,j$ such that searchlight $j$ can see a robber $i$).
What is the minimum number of moves you need to perform to reach a safe configuration?
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n, m \leq 2000$): the number of robbers and the number of searchlight.
Each of the next $n$ lines contains two integers $a_i$, $b_i$ ($0 \leq a_i, b_i \leq 10^6$), coordinates of robbers.
Each of the next $m$ lines contains two integers $c_i$, $d_i$ ($0 \leq c_i, d_i \leq 10^6$), coordinates of searchlights.
-----Output-----
Print one integer: the minimum number of moves you need to perform to reach a safe configuration.
-----Examples-----
Input
1 1
0 0
2 3
Output
3
Input
2 3
1 6
6 1
10 1
1 10
7 7
Output
4
Input
1 2
0 0
0 0
0 0
Output
1
Input
7 3
0 8
3 8
2 7
0 10
5 5
7 0
3 5
6 6
3 11
11 5
Output
6
-----Note-----
In the first test, you can move each robber to the right three times. After that there will be one robber in the coordinates $(3, 0)$.
The configuration of the robbers is safe, because the only searchlight can't see the robber, because it is in the coordinates $(2, 3)$ and $3 > 2$.
In the second test, you can move each robber to the right two times and two times up. After that robbers will be in the coordinates $(3, 8)$, $(8, 3)$.
It's easy the see that the configuration of the robbers is safe.
It can be proved that you can't reach a safe configuration using no more than $3$ moves.
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\": [\"4 5 1 1 2\\n1 3 5 7\\n1 2 3 9 10\\n\", \"2 2 4 4 2\\n1 10\\n10 20\\n\", \"4 3 2 3 1\\n1 999999998 999999999 1000000000\\n3 4 1000000000\\n\", \"1 1 1 1 1\\n1\\n2\\n\", \"5 10 20 10 3\\n7 9 18 19 20\\n3 6 7 8 9 10 14 15 16 17\\n\", \"10 5 17 10 3\\n6 7 8 10 15 16 17 19 20 21\\n1 5 8 16 17\\n\", \"10 11 4 5 10\\n1 2 3 4 5 6 7 8 9 10\\n16 17 18 19 20 21 22 23 24 25 26\\n\", \"2 2 1 1 1\\n1 2\\n3 4\\n\", \"2 2 10 10 1\\n1 2\\n3 4\\n\", \"2 2 10 10 1\\n1 2\\n11 12\\n\", \"2 2 10 10 2\\n1 2\\n11 12\\n\", \"5 3 1 1 4\\n1 2 3 4 5\\n4 100 1000\\n\", \"2 1 2 1 1\\n1 2\\n5\\n\", \"2 2 1 1 1\\n1 2\\n1 3\\n\", \"1 5 1 1 1\\n1\\n10 11 12 13 14\\n\", \"3 3 1 1 1\\n1 2 3\\n2 15 16\\n\", \"2 2 1 1 1\\n1 5\\n2 3\\n\", \"2 2 2 1 1\\n1 4\\n3 4\\n\", \"3 3 1 1 1\\n1 10 100\\n2 3 4\\n\", \"5 12 50 1 4\\n1 2 3 4 5\\n1 2 3 4 5 6 7 8 9 10 100 1000\\n\", \"4 7 10 10 3\\n1 2 3 100\\n20 30 40 50 60 70 80\\n\", \"3 4 1 1 2\\n1 2 3\\n1 2 3 4\\n\", \"2 2 1 1 1\\n2 3\\n1 4\\n\", \"3 3 2 1 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1 2\\n1 2 3\\n1 2 3 4\\n\", \"10 11 4 5 10\\n1 2 3 4 5 6 7 8 9 10\\n16 17 18 19 20 21 22 23 24 25 26\\n\", \"2 2 1 1 1\\n1 2\\n3 5\\n\", \"2 2 1 1 1\\n2 5\\n1 4\\n\", \"3 3 1 2 1\\n1 2 3\\n2 15 16\\n\", \"10 11 4 5 3\\n1 2 3 4 5 6 7 8 9 10\\n16 17 18 19 20 21 22 23 24 25 26\\n\", \"4 3 2 3 1\\n1 999999998 999999999 1000010000\\n3 4 1000000000\\n\", \"3 3 1 3 1\\n1 2 3\\n2 15 16\\n\", \"4 7 10 10 2\\n2 2 3 100\\n20 30 40 50 60 70 80\\n\", \"2 2 0 1 1\\n1 4\\n3 4\\n\", \"2 2 0 1 0\\n1 0\\n3 4\\n\", \"2 2 1 1 1\\n1 2\\n1 4\\n\", \"5 3 1 1 4\\n1 2 3 4 5\\n8 100 1000\\n\", \"2 2 2 1 2\\n1 4\\n3 4\\n\", \"2 2 10 17 2\\n1 2\\n11 12\\n\", \"1 1 1 1 2\\n1\\n2\\n\", \"2 0 2 1 1\\n1 2\\n5\\n\", \"10 5 17 10 3\\n6 7 8 10 15 16 17 19 12 21\\n1 5 8 16 17\\n\", \"5 10 20 10 3\\n7 9 18 19 24\\n3 6 7 8 9 10 14 15 16 17\\n\", \"3 3 1 1 1\\n0 10 100\\n2 3 4\\n\", \"2 2 10 10 2\\n1 2\\n7 12\\n\", \"2 2 10 10 1\\n1 2\\n1 4\\n\", \"1 5 1 1 1\\n1\\n12 11 12 13 14\\n\", \"5 12 50 1 4\\n1 0 3 4 5\\n1 2 3 4 5 6 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11 4 5 3\\n1 4 0 4 5 6 7 8 9 10\\n15 17 18 19 20 21 34 23 24 25 43\\n\", \"0 0 2 1 1\\n3 2\\n6\\n\", \"10 5 17 19 3\\n6 3 5 18 15 16 34 19 12 21\\n2 5 8 16 17\\n\", \"5 10 20 4 3\\n8 9 18 19 24\\n3 6 7 8 2 10 20 15 16 17\\n\", \"2 2 14 3 4\\n1 1\\n7 23\\n\", \"1 1 1 1 1\\n1\\n12 11 1 6 14\\n\", \"2 2 4 4 2\\n1 10\\n10 20\\n\", \"4 5 1 1 2\\n1 3 5 7\\n1 2 3 9 10\\n\", \"4 3 2 3 1\\n1 999999998 999999999 1000000000\\n3 4 1000000000\\n\"], \"outputs\": [\"11\\n\", \"-1\\n\", \"1000000003\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"5\\n\", \"-1\\n\", \"22\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"16\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"5\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"5\\n\", \"-1\\n\", \"16\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"22\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\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\", 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\"-1\\n\", \"-1\\n\", \"-1\\n\", \"11\\n\", \"1000000003\\n\"]}", "source": "taco"}
|
Arkady bought an air ticket from a city A to a city C. Unfortunately, there are no direct flights, but there are a lot of flights from A to a city B, and from B to C.
There are $n$ flights from A to B, they depart at time moments $a_1$, $a_2$, $a_3$, ..., $a_n$ and arrive at B $t_a$ moments later.
There are $m$ flights from B to C, they depart at time moments $b_1$, $b_2$, $b_3$, ..., $b_m$ and arrive at C $t_b$ moments later.
The connection time is negligible, so one can use the $i$-th flight from A to B and the $j$-th flight from B to C if and only if $b_j \ge a_i + t_a$.
You can cancel at most $k$ flights. If you cancel a flight, Arkady can not use it.
Arkady wants to be in C as early as possible, while you want him to be in C as late as possible. Find the earliest time Arkady can arrive at C, if you optimally cancel $k$ flights. If you can cancel $k$ or less flights in such a way that it is not possible to reach C at all, print $-1$.
-----Input-----
The first line contains five integers $n$, $m$, $t_a$, $t_b$ and $k$ ($1 \le n, m \le 2 \cdot 10^5$, $1 \le k \le n + m$, $1 \le t_a, t_b \le 10^9$) — the number of flights from A to B, the number of flights from B to C, the flight time from A to B, the flight time from B to C and the number of flights you can cancel, respectively.
The second line contains $n$ distinct integers in increasing order $a_1$, $a_2$, $a_3$, ..., $a_n$ ($1 \le a_1 < a_2 < \ldots < a_n \le 10^9$) — the times the flights from A to B depart.
The third line contains $m$ distinct integers in increasing order $b_1$, $b_2$, $b_3$, ..., $b_m$ ($1 \le b_1 < b_2 < \ldots < b_m \le 10^9$) — the times the flights from B to C depart.
-----Output-----
If you can cancel $k$ or less flights in such a way that it is not possible to reach C at all, print $-1$.
Otherwise print the earliest time Arkady can arrive at C if you cancel $k$ flights in such a way that maximizes this time.
-----Examples-----
Input
4 5 1 1 2
1 3 5 7
1 2 3 9 10
Output
11
Input
2 2 4 4 2
1 10
10 20
Output
-1
Input
4 3 2 3 1
1 999999998 999999999 1000000000
3 4 1000000000
Output
1000000003
-----Note-----
Consider the first example. The flights from A to B depart at time moments $1$, $3$, $5$, and $7$ and arrive at B at time moments $2$, $4$, $6$, $8$, respectively. The flights from B to C depart at time moments $1$, $2$, $3$, $9$, and $10$ and arrive at C at time moments $2$, $3$, $4$, $10$, $11$, respectively. You can cancel at most two flights. The optimal solution is to cancel the first flight from A to B and the fourth flight from B to C. This way Arkady has to take the second flight from A to B, arrive at B at time moment $4$, and take the last flight from B to C arriving at C at time moment $11$.
In the second example you can simply cancel all flights from A to B and you're done.
In the third example you can cancel only one flight, and the optimal solution is to cancel the first flight from A to B. Note that there is still just enough time to catch the last flight from B to C.
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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|
The only difference between easy and hard versions is constraints.
Now elections are held in Berland and you want to win them. More precisely, you want everyone to vote for you.
There are $n$ voters, and two ways to convince each of them to vote for you. The first way to convince the $i$-th voter is to pay him $p_i$ coins. The second way is to make $m_i$ other voters vote for you, and the $i$-th voter will vote for free.
Moreover, the process of such voting takes place in several steps. For example, if there are five voters with $m_1 = 1$, $m_2 = 2$, $m_3 = 2$, $m_4 = 4$, $m_5 = 5$, then you can buy the vote of the fifth voter, and eventually everyone will vote for you. Set of people voting for you will change as follows: ${5} \rightarrow {1, 5} \rightarrow {1, 2, 3, 5} \rightarrow {1, 2, 3, 4, 5}$.
Calculate the minimum number of coins you have to spend so that everyone votes for you.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 5000$) — the number of test cases.
The first line of each test case contains one integer $n$ ($1 \le n \le 5000$) — the number of voters.
The next $n$ lines contains the description of voters. $i$-th line contains two integers $m_i$ and $p_i$ ($1 \le p_i \le 10^9, 0 \le m_i < n$).
It is guaranteed that the sum of all $n$ over all test cases does not exceed $5000$.
-----Output-----
For each test case print one integer — the minimum number of coins you have to spend so that everyone votes for you.
-----Example-----
Input
3
3
1 5
2 10
2 8
7
0 1
3 1
1 1
6 1
1 1
4 1
4 1
6
2 6
2 3
2 8
2 7
4 4
5 5
Output
8
0
7
-----Note-----
In the first test case you have to buy vote of the third voter. Then the set of people voting for you will change as follows: ${3} \rightarrow {1, 3} \rightarrow {1, 2, 3}$.
In the second example you don't need to buy votes. The set of people voting for you will change as follows: ${1} \rightarrow {1, 3, 5} \rightarrow {1, 2, 3, 5} \rightarrow {1, 2, 3, 5, 6, 7} \rightarrow {1, 2, 3, 4, 5, 6, 7}$.
In the third test case you have to buy votes of the second and the fifth voters. Then the set of people voting for you will change as follows: ${2, 5} \rightarrow {1, 2, 3, 4, 5} \rightarrow {1, 2, 3, 4, 5, 6}$.
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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\"1000000000 6 999999904 272656295\\n\", \"1000000000 999999946 60 715189365\\n\", \"1000000000 999999916 61 857945620\\n\", \"1000000000 999999946 85 423654797\\n\", \"1000000000 999999938 65 384381709\\n\", \"1000000000 999999957 30 891773002\\n\", \"548813503 532288332 26800940 350552333\\n\", \"847251738 695702891 698306947 648440371\\n\", \"891773002 152235342 682786380 386554406\\n\", \"812168727 57791401 772019566 644719499\\n\", \"71036059 25478942 38920202 19135721\\n\", \"549 198 8 262611\\n\", \"848 409 661 620581\\n\", \"892 364 824 53858\\n\", \"813 154 643 141422\\n\", \"72 40 68 849\\n\", \"958 768 649 298927\\n\", \"800 305 317 414868\\n\", \"721 112 687 232556\\n\", \"522 228 495 74535\\n\", \"737 231 246 79279\\n\", \"6 4 3 36\\n\", \"9 3 8 55\\n\", \"9 4 3 73\\n\", \"9 8 2 50\\n\", \"1 1 1 1\\n\", \"10 7 2 7\\n\", \"8 2 6 20\\n\", \"8 1 2 64\\n\", \"6 1 4 15\\n\", \"8 8 3 1\\n\", \"1000000000 63 65 384381709\\n\", \"9 4 3 10\\n\", \"847251738 695702891 698306947 648440371\\n\", \"958 768 649 298927\\n\", \"8 2 6 10\\n\", \"9 8 2 50\\n\", \"1000000000 55 999999916 423654797\\n\", \"8 8 3 1\\n\", \"8 1 2 10\\n\", \"1000000000 6 999999904 272656295\\n\", \"1000000000 999999938 65 384381709\\n\", \"737 231 246 79279\\n\", \"9 4 3 73\\n\", \"1000000000 999999916 999999940 857945620\\n\", \"548813503 532288332 26800940 350552333\\n\", \"813 154 643 141422\\n\", \"522 228 495 74535\\n\", \"891773002 152235342 682786380 386554406\\n\", \"1000000000 999999946 85 423654797\\n\", \"1000000000 55 85 423654797\\n\", \"1000000000 63 999999936 384381709\\n\", \"1000000000 85 999999940 857945620\\n\", \"10 7 2 7\\n\", \"1000000000 999999946 999999916 423654797\\n\", \"721 112 687 232556\\n\", \"1000000 948438 69861 89178\\n\", \"1000000000 999999957 30 891773002\\n\", \"9 8 2 10\\n\", \"549 198 8 262611\\n\", \"1000000000 81587964 595232616 623563697\\n\", \"812168727 57791401 772019566 644719499\\n\", \"71036059 25478942 38920202 19135721\\n\", \"1000000 951981 612086 60277\\n\", \"1000000000 999999946 60 715189365\\n\", \"1000000000 999999916 61 857945620\\n\", \"72 40 68 849\\n\", \"1000000000 44 999999971 891773002\\n\", \"1000000000 999999946 999999941 715189365\\n\", \"1000000000 504951981 646612086 602763371\\n\", \"8 2 6 20\\n\", \"6 4 3 36\\n\", \"9 3 8 55\\n\", \"6 1 4 10\\n\", \"892 364 824 53858\\n\", \"1000000000 999999938 999999936 384381709\\n\", \"848 409 661 620581\\n\", \"800 305 317 414868\\n\", \"1000000000 44 30 891773002\\n\", \"1000000000 6 97 272656295\\n\", \"6 1 4 15\\n\", \"1000000000 55 999999941 715189365\\n\", \"1000000000 55 60 715189365\\n\", \"1000000000 85 61 857945620\\n\", \"1 1 1 1\\n\", \"1000000 587964 232616 62357\\n\", \"8 1 2 64\\n\", \"1000000000 63 44 384381709\\n\", \"9 4 3 1\\n\", \"892989837 695702891 698306947 648440371\\n\", \"8 4 6 10\\n\", \"9 8 2 14\\n\", \"1000000000 999999938 81 384381709\\n\", \"737 425 246 79279\\n\", \"9 4 4 73\\n\", \"1000000000 999999916 988822957 857945620\\n\", \"548813503 532288332 31573577 350552333\\n\", \"813 290 643 141422\\n\", \"522 228 495 123033\\n\", \"891773002 152235342 682786380 675857690\\n\", \"1000000000 999999946 62 423654797\\n\", \"1000000000 80 85 423654797\\n\", \"1000000000 21 999999936 384381709\\n\", \"1000000000 1 999999940 857945620\\n\", \"1000000000 999999946 999999916 121316995\\n\", \"1082 112 687 232556\\n\", \"1000000 948438 137570 89178\\n\", \"1000000000 999999957 39 891773002\\n\", \"549 198 8 238671\\n\", \"1000000000 81587964 434149922 623563697\\n\", \"62451920 25478942 38920202 19135721\\n\", \"1000000000 999999946 96 715189365\\n\", \"1000000000 999999916 61 799796081\\n\", \"72 40 68 640\\n\", \"1000000000 44 897925036 891773002\\n\", \"1000000000 999999946 999999941 133981546\\n\", \"1000000000 739789895 646612086 602763371\\n\", \"1215 364 824 53858\\n\", \"941 409 661 620581\\n\", \"1427 305 317 414868\\n\", \"1000000000 6 97 243307060\\n\", \"1000000000 73 999999941 715189365\\n\", \"1000000000 55 25 715189365\\n\", \"1000000000 130 61 857945620\\n\", \"1000000 587964 169783 62357\\n\", \"8 1 3 64\\n\", \"1000000000 63 44 607398780\\n\", \"892989837 695702891 698306947 155313074\\n\", \"12 1 2 16\\n\", \"1001000000 999999938 81 384381709\\n\", \"9 6 3 73\\n\", \"813 290 190 141422\\n\", \"891773002 152235342 682786380 23800420\\n\", \"1000000000 357399792 62 423654797\\n\", \"12 1 2 10\\n\", \"10 7 1 7\\n\", \"8 2 6 12\\n\", \"6 4 5 36\\n\", \"10 1 4 15\\n\", \"9 5 8 10\\n\", \"8 5 6 10\\n\", \"18 8 2 14\\n\", \"737 438 246 79279\\n\", \"876662179 532288332 31573577 350552333\\n\", \"9 3 8 10\\n\", \"6 4 3 1\\n\"], \"outputs\": [\"0\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"174\\n\", \"177\\n\", \"211\\n\", \"17360\\n\", \"17657\\n\", \"37707\\n\", \"41279\\n\", \"28970\\n\", \"27600\\n\", \"42159\\n\", \"23250\\n\", \"37707\\n\", \"41279\\n\", \"28970\\n\", \"27600\\n\", \"37707\\n\", \"41279\\n\", \"28970\\n\", \"27600\\n\", \"42159\\n\", \"23250\\n\", \"37707\\n\", \"41279\\n\", \"28970\\n\", \"27600\\n\", \"42159\\n\", \"13239\\n\", \"18006\\n\", \"13902\\n\", \"17954\\n\", \"3093\\n\", \"635\\n\", \"771\\n\", \"183\\n\", \"299\\n\", \"25\\n\", \"431\\n\", \"489\\n\", \"556\\n\", \"249\\n\", \"199\\n\", \"6\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"13\\n\", \"3\\n\", \"0\\n\", \"27600\\n\", \"2\\n\", \"18006\\n\", \"431\\n\", \"2\\n\", \"7\\n\", \"28970\\n\", \"0\\n\", \"3\\n\", \"23250\\n\", \"27600\\n\", \"199\\n\", \"8\\n\", \"41279\\n\", \"13239\\n\", \"299\\n\", \"249\\n\", \"13902\\n\", \"28970\\n\", \"28970\\n\", \"27600\\n\", \"41279\\n\", \"2\\n\", \"28970\\n\", \"556\\n\", \"211\\n\", \"42159\\n\", \"2\\n\", \"635\\n\", \"17657\\n\", \"17954\\n\", \"3093\\n\", \"174\\n\", \"37707\\n\", \"41279\\n\", \"25\\n\", \"42159\\n\", \"37707\\n\", \"17360\\n\", \"3\\n\", \"6\\n\", \"7\\n\", \"3\\n\", \"183\\n\", \"27600\\n\", \"771\\n\", \"489\\n\", \"42159\\n\", \"23250\\n\", \"3\\n\", \"37707\\n\", \"37707\\n\", \"41279\\n\", \"0\\n\", \"177\\n\", \"13\\n\", \"27621\\n\", \"0\\n\", \"18006\\n\", \"2\\n\", \"3\\n\", \"27584\\n\", \"199\\n\", \"7\\n\", \"29206\\n\", \"13239\\n\", \"276\\n\", \"341\\n\", \"18383\\n\", \"28993\\n\", \"28945\\n\", \"27642\\n\", \"41362\\n\", \"15438\\n\", \"396\\n\", \"211\\n\", \"42150\\n\", \"578\\n\", \"17657\\n\", \"3093\\n\", \"37671\\n\", \"39850\\n\", \"22\\n\", \"29819\\n\", \"16256\\n\", \"17360\\n\", \"164\\n\", \"636\\n\", \"489\\n\", \"21958\\n\", \"37689\\n\", \"37741\\n\", \"41234\\n\", \"177\\n\", \"12\\n\", \"34748\\n\", \"8812\\n\", \"4\\n\", \"19525\\n\", \"8\\n\", \"272\\n\", \"3450\\n\", \"20522\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"7\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"199\\n\", \"13239\\n\", \"2\\n\", \"0\\n\"]}", "source": "taco"}
|
Mr. Bender has a digital table of size n × n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy.
We'll consider the table rows numbered from top to bottom from 1 to n, and the columns — numbered from left to right from 1 to n. Initially there is exactly one switched on cell with coordinates (x, y) (x is the row number, y is the column number), and all other cells are switched off. Then each second we switch on the cells that are off but have the side-adjacent cells that are on.
For a cell with coordinates (x, y) the side-adjacent cells are cells with coordinates (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1).
In how many seconds will Mr. Bender get happy?
-----Input-----
The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 10^9; 1 ≤ x, y ≤ n; c ≤ n^2).
-----Output-----
In a single line print a single integer — the answer to the problem.
-----Examples-----
Input
6 4 3 1
Output
0
Input
9 3 8 10
Output
2
-----Note-----
Initially the first test has one painted cell, so the answer is 0. In the second test all events will go as is shown on the figure. [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\": [\"xoxoxoxoxoxoxo\", \"oxoxowoxoxoxox\", \"oxoxowoooxoxxx\", \"xxxoxooowoxoxo\", \"xoxoxooxwoxoxo\", \"xoxoyoxoxoxoxo\", \"xxxoxoooooxwxo\", \"xoxowooxwoxoxo\", \"oxoxoxoxoyoxox\", \"xoxoxoxoxoyoxo\", \"xxxoxooovoxoxo\", \"xoxowooxwoxowo\", \"oxoxoyoxoyoxox\", \"oxoyoxoxoxoxox\", \"oxoxovoooxoxxx\", \"xoxowooywoxowo\", \"oxxowooywoxowo\", \"owoxowyoowoxxo\", \"owoyowyoowoxxo\", \"oxxowooywoyowo\", \"oxoxoxoxowoxox\", \"xoxoxoxoyoxoxo\", \"oxoxowxooxoxox\", \"xoyoxoxoyoxoxo\", \"oxwxoooooxoxxx\", \"xoxovooxwoxoxo\", \"oxoyoxoooxxxox\", \"xoxxwooowoxowo\", \"xoxoyoxoyoxoxo\", \"owoxowyoowoxox\", \"oxxowooowoxowy\", \"owoyowyoowowxo\", \"xoxowoxoxoxoxo\", \"oxowowxooxoxox\", \"xoyoxoooyxxoxo\", \"xxxovooowoxoxo\", \"oooyoxoxoxxxox\", \"owoxowooowxxox\", \"xoxowoozwoxowo\", \"wxxowoooooxowy\", \"owoyowyoowowyo\", \"xoxxwoxoxoooxo\", \"oyowowxooxoxox\", \"xoooxoooyxxyxo\", \"oxxovxoowoxoxo\", \"oooyoyoxoxxxox\", \"xoxxwooowowowo\", \"owoxowzoowoxox\", \"oxxowowoooxowy\", \"oywowooywoyowo\", \"xoyxwoxoxoooxo\", \"xoxxxoxoyoyooo\", \"xoxxxooowowowo\", \"owoxowzooxoxox\", \"ywoxooowowoxxo\", \"oooyooyxoxxxox\", \"xoxxxoooxowowo\", \"owzxowoooxoxox\", \"oooyooywoxxxox\", \"owowoxoooxxxox\", \"xoxoxooowoxzwo\", \"oooyooyooxxxwx\", \"owowoxooowxxox\", \"xoxzxooowoxowo\", \"ooxyooyooxoxwx\", \"xoxxwoooxowowo\", \"xoxzooxowoxowo\", \"ooxyooxooxoywx\", \"xoxzooxowooxwo\", \"xwyoxooxooyxoo\", \"owxoowoxoozxox\", \"ooxyooyooxoywx\", \"xwyoxooyooyxoo\", \"xwooxooyoyyxoo\", \"xwooxoozoyyxoo\", \"ooxyyozooxoowx\", \"oxoxoxoxoxowox\", \"oxoxovoxoxoxox\", \"oxoxoxoooxoxxx\", \"oxxoxooxwoxoxo\", \"xoooyoxxxoxoxo\", \"oxxxoooooxowxx\", \"oooxoxoxxyoxox\", \"ooxoxoxxxoyoxo\", \"oxoxovoooxowxx\", \"xwxowooxwoxooo\", \"oxowoyoxoyoxox\", \"oxoyoxoxxooxox\", \"owoxovoooxoxxx\", \"oxxowooyvoxowo\", \"owoxowyoowoxyo\", \"oxxowoozwoyowo\", \"oxoxoyoxoxoxox\", \"oooxowxooxxxox\", \"xoyoxoxoyoxxoo\", \"oxoxoowooxoxxx\", \"oxoxowxoovoxox\", \"yoxowoxoxoxoxo\", \"xoxoxooxwowoxo\", \"xoyoyoooyxxoxo\", \"oxoxoxoxoxoxox\", \"xxxxxxxx\"], \"outputs\": [\"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\", \"NO\"]}", "source": "taco"}
|
Takahashi is competing in a sumo tournament. The tournament lasts for 15 days, during which he performs in one match per day. If he wins 8 or more matches, he can also participate in the next tournament.
The matches for the first k days have finished. You are given the results of Takahashi's matches as a string S consisting of `o` and `x`. If the i-th character in S is `o`, it means that Takahashi won the match on the i-th day; if that character is `x`, it means that Takahashi lost the match on the i-th day.
Print `YES` if there is a possibility that Takahashi can participate in the next tournament, and print `NO` if there is no such possibility.
Constraints
* 1 \leq k \leq 15
* S is a string of length k consisting of `o` and `x`.
Input
Input is given from Standard Input in the following format:
S
Output
Print `YES` if there is a possibility that Takahashi can participate in the next tournament, and print `NO` otherwise.
Examples
Input
oxoxoxoxoxoxox
Output
YES
Input
xxxxxxxx
Output
NO
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\": [\"3 3\\n\", \"4 2\\n\", \"5 5\\n\", \"6 4\\n\", \"100 1\\n\", \"76 48\\n\", \"100 90\\n\", \"90 100\\n\", \"1 98\\n\", \"1 100\\n\", \"56 98\\n\", \"89 89\\n\", \"18 94\\n\", \"84 27\\n\", \"1 1\\n\", \"1 2\\n\", \"2 1\\n\", \"1 34\\n\", \"46 2\\n\", \"99 3\\n\", \"10 100\\n\", \"100 100\\n\", \"1 4\\n\", \"100 100\\n\", \"1 2\\n\", \"10 100\\n\", \"1 34\\n\", \"1 100\\n\", \"90 100\\n\", \"1 4\\n\", \"89 89\\n\", \"6 4\\n\", \"1 98\\n\", \"99 3\\n\", \"1 1\\n\", \"46 2\\n\", \"84 27\\n\", \"5 5\\n\", \"76 48\\n\", \"2 1\\n\", \"56 98\\n\", \"100 90\\n\", \"18 94\\n\", \"100 1\\n\", \"100 101\\n\", \"2 2\\n\", \"0 100\\n\", \"1 32\\n\", \"1 110\\n\", \"22 100\\n\", \"1 7\\n\", \"89 36\\n\", \"2 4\\n\", \"1 188\\n\", \"53 3\\n\", \"8 2\\n\", \"83 2\\n\", \"168 27\\n\", \"6 5\\n\", \"31 48\\n\", \"2 0\\n\", \"56 106\\n\", \"110 90\\n\", \"18 99\\n\", \"101 1\\n\", \"4 1\\n\", \"3 5\\n\", \"100 001\\n\", \"1 3\\n\", \"1 0\\n\", \"0 101\\n\", \"22 000\\n\", \"0 7\\n\", \"89 42\\n\", \"0 4\\n\", \"1 359\\n\", \"78 3\\n\", \"8 3\\n\", \"142 2\\n\", \"168 12\\n\", \"2 5\\n\", \"45 48\\n\", \"112 106\\n\", \"010 90\\n\", \"18 8\\n\", \"101 2\\n\", \"3 1\\n\", \"3 10\\n\", \"100 011\\n\", \"1 6\\n\", \"0 001\\n\", \"0 3\\n\", \"89 33\\n\", \"-1 4\\n\", \"1 442\\n\", \"54 3\\n\", \"6 3\\n\", \"147 2\\n\", \"279 12\\n\", \"2 6\\n\", \"45 38\\n\", \"112 176\\n\", \"010 162\\n\", \"22 8\\n\", \"101 4\\n\", \"3 2\\n\", \"1 10\\n\", \"110 001\\n\", \"1 5\\n\", \"0 010\\n\", \"3 000\\n\", \"9 33\\n\", \"0 2\\n\", \"1 852\\n\", \"20 3\\n\", \"6 2\\n\", \"188 2\\n\", \"374 12\\n\", \"3 6\\n\", \"45 19\\n\", \"136 176\\n\", \"011 162\\n\", \"22 13\\n\", \"101 0\\n\", \"3 4\\n\", \"1 19\\n\", \"010 001\\n\", \"4 000\\n\", \"9 34\\n\", \"1 430\\n\", \"20 0\\n\", \"-1 5\\n\", \"188 0\\n\", \"259 12\\n\", \"3 7\\n\", \"45 37\\n\", \"136 10\\n\", \"001 162\\n\", \"33 13\\n\", \"100 0\\n\", \"2 7\\n\", \"0 19\\n\", \"010 101\\n\", \"1 011\\n\", \"4 2\\n\", \"3 3\\n\"], \"outputs\": [\"GBGBGB\\n\", \"BGBGBB\\n\", \"GBGBGBGBGB\\n\", \"BGBGBGBGBB\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GB\\n\", \"GBG\\n\", \"BGB\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"GBGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"GBG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGG\\n\", \"GBGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"BGBGBGBGBB\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", 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\"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBBBBBBBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBB\\n\", \"GBGBGBGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGGG\\n\", \"G\\n\", \"GGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGB\\n\", \"GBGGGGGGGGG\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGG\\n\", \"GGGGGGGGGG\\n\", \"BBB\\n\", \"GBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBB\\n\", \"BGBGBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBB\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBG\\n\", \"GBGGGGGGGGGGGGGGGGGG\\n\", \"BGBBBBBBBBB\\n\", \"BBBB\\n\", \"GBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BBBBBBBBBBBBBBBBBBBB\\n\", \"GGGGGG\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBB\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGGGG\\n\", \"GGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGG\\n\", \"BGBGBB\\n\", \"GBGBGB\\n\"]}", "source": "taco"}
|
There are n boys and m girls studying in the class. They should stand in a line so that boys and girls alternated there as much as possible. Let's assume that positions in the line are indexed from left to right by numbers from 1 to n + m. Then the number of integers i (1 ≤ i < n + m) such that positions with indexes i and i + 1 contain children of different genders (position i has a girl and position i + 1 has a boy or vice versa) must be as large as possible.
Help the children and tell them how to form the line.
-----Input-----
The single line of the input contains two integers n and m (1 ≤ n, m ≤ 100), separated by a space.
-----Output-----
Print a line of n + m characters. Print on the i-th position of the line character "B", if the i-th position of your arrangement should have a boy and "G", if it should have a girl.
Of course, the number of characters "B" should equal n and the number of characters "G" should equal m. If there are multiple optimal solutions, print any of them.
-----Examples-----
Input
3 3
Output
GBGBGB
Input
4 2
Output
BGBGBB
-----Note-----
In the first sample another possible answer is BGBGBG.
In the second sample answer BBGBGB is also optimal.
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 1 3 4\\n1 2 5\\n2 3 9\\n2 4 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 9\\n2 4 5\\n1 3 3\\n1 4 8\\n0 0 0 0 0\", \"6 5 1 3 4\\n1 2 5\\n4 3 5\\n2 3 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 5\\n2 4 5\\n1 3 8\\n2 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n0 2 5\\n2 3 9\\n2 4 5\\n1 2 3\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n0 2 5\\n2 3 9\\n2 4 5\\n1 2 3\\n1 2 8\\n0 0 0 0 0\", \"6 5 1 3 4\\n1 2 7\\n2 0 5\\n2 3 5\\n1 3 8\\n2 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 4\\n2 1 5\\n1 3 8\\n1 4 1\\n0 0 0 0 0\", \"6 5 1 3 4\\n1 2 5\\n3 3 5\\n2 3 5\\n1 3 8\\n1 4 11\\n0 0 0 0 0\", \"6 5 1 1 4\\n1 2 7\\n2 0 11\\n2 3 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"7 5 1 3 4\\n1 2 5\\n3 6 9\\n2 4 5\\n1 3 18\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 9\\n2 4 5\\n1 3 3\\n1 4 4\\n0 0 0 0 0\", \"6 5 1 3 4\\n1 2 5\\n4 3 7\\n2 3 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 5\\n2 4 5\\n1 3 8\\n2 4 0\\n0 0 0 0 0\", \"4 5 1 3 4\\n0 2 5\\n2 3 9\\n2 4 5\\n1 2 3\\n1 2 16\\n0 0 0 0 0\", \"6 5 1 3 4\\n1 2 8\\n2 0 5\\n2 3 5\\n1 4 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n-1 4 5\\n2 3 9\\n3 4 6\\n2 2 3\\n1 2 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 5\\n2 4 5\\n1 3 1\\n2 4 0\\n0 0 0 0 0\", \"4 5 1 4 4\\n1 2 5\\n2 3 5\\n2 4 5\\n1 3 1\\n2 4 0\\n0 0 0 0 0\", \"4 5 1 3 4\\n0 2 5\\n2 3 12\\n3 4 5\\n2 2 3\\n1 2 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n-1 2 5\\n2 3 9\\n3 4 7\\n2 2 3\\n1 2 8\\n0 0 0 0 0\", \"4 5 1 3 3\\n1 0 5\\n1 0 5\\n2 1 5\\n1 3 1\\n1 4 8\\n0 0 0 0 0\", \"6 5 1 2 4\\n1 2 5\\n4 3 5\\n2 3 0\\n1 3 8\\n1 4 24\\n0 0 0 0 0\", \"7 5 1 3 4\\n1 2 10\\n3 6 0\\n2 4 5\\n1 3 2\\n1 4 12\\n0 0 0 0 0\", \"7 5 1 3 3\\n1 2 10\\n3 6 0\\n2 4 5\\n1 3 2\\n1 4 8\\n0 0 0 0 0\", \"4 5 2 4 4\\n1 2 5\\n2 2 5\\n2 4 5\\n2 3 1\\n2 4 0\\n0 0 0 0 0\", \"6 5 1 2 4\\n1 2 5\\n4 3 5\\n2 3 -1\\n1 3 8\\n1 4 36\\n0 0 0 0 0\", \"6 5 1 4 4\\n1 2 5\\n2 3 5\\n2 4 10\\n2 3 1\\n2 4 -1\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 4\\n2 1 7\\n1 2 8\\n1 4 0\\n0 0 0 0 0\", \"6 5 1 4 4\\n1 2 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0\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 3\\n1 0 5\\n1 0 5\\n2 1 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"6 5 1 1 4\\n1 2 1\\n2 0 5\\n2 3 5\\n1 3 6\\n1 4 8\\n0 0 0 0 0\", \"7 5 1 3 4\\n1 2 10\\n3 6 0\\n2 4 5\\n1 3 9\\n1 4 8\\n0 0 0 0 0\", \"7 5 1 3 4\\n1 2 5\\n6 5 9\\n2 4 5\\n1 3 18\\n1 4 8\\n0 0 0 0 0\", \"6 5 1 2 4\\n1 2 5\\n4 3 5\\n2 3 0\\n1 3 8\\n1 4 14\\n0 0 0 0 0\", \"4 5 1 4 4\\n1 2 1\\n2 3 3\\n2 1 7\\n1 0 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 3\\n1 0 5\\n1 0 0\\n2 1 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\", \"6 5 1 1 4\\n1 2 1\\n1 0 5\\n2 3 5\\n1 3 6\\n1 4 8\\n0 0 0 0 0\", \"7 5 1 3 4\\n1 2 10\\n3 6 0\\n2 4 5\\n1 3 2\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 4 4\\n1 2 5\\n2 3 5\\n2 4 5\\n2 3 1\\n2 4 0\\n0 0 0 0 0\", \"4 5 1 4 4\\n1 2 1\\n2 3 3\\n2 1 10\\n1 0 8\\n1 4 8\\n0 0 0 0 0\", \"4 5 1 3 4\\n1 2 5\\n2 3 5\\n2 4 5\\n1 3 8\\n1 4 8\\n0 0 0 0 0\"], \"outputs\": [\"16\\n\", \"11\\n\", \"13\\n\", \"18\\n\", \"17\\n\", \"22\\n\", \"20\\n\", \"9\\n\", \"19\\n\", \"8\\n\", \"26\\n\", \"7\\n\", \"15\\n\", \"10\\n\", 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|
In 21XX, humanity finally began a plan to relocate to Mars. Selected as the first group of immigrants to Mars, you are assigned to the Administrative Center of Mars to deal with various problems that occur on Mars. The biggest problem at the moment of the Central Bureau is securing an independent supply and demand cycle. Since it takes several months for relief supplies from the moon to arrive, basically the demand within Mars needs to be resolved within Mars. In addition, it is necessary to save resources as much as possible until the circulation system is established.
The Central Bureau of Administration has begun mining ice in the polar regions. The ultimate goal is to melt it with sunlight and supply it as water to individual bases. As a first step, we decided to lay water pipes from the base with the water source to the two main bases. In addition, at present, only some bases and roads connecting them have been cultivated, and laying water pipes in undeveloped areas requires a great deal of cost and fuel, so water pipes should be installed along the roads. I decided to lay it. Moreover, due to technical constraints, their water pipes always allow water to flow in only one direction.
Your job is to create a program that minimizes the cost of laying water pipes under these conditions.
Input
The input consists of multiple datasets.
The first row of the dataset consists of five integers. These are, in order, the number of bases on Mars n (3 <= n <= 100), the number of roads connecting the bases m (2 <= m <= 1000), the number of the base that serves as the water source, and the number of the water pipes. Represents the numbers g1 and g2 of the two main bases that serve as destinations. The base number is represented by an integer from 1 to n. s, g1 and g2 are different from each other.
The following m lines are given information on the roads on which water pipes can be laid. Each line represents road information between two bases and consists of three integers b1, b2, c (1 <= c <= 1000). Here, b1 and b2 represent the numbers of the bases at the beginning and end of the road, which are different from each other. c is the cost of laying a water pipe from base b1 to base b2.
For all datasets, it can be assumed that there is always a route for water from the source to the destination. Also, since there is at most one road between two bases, cost information is given at most once in each direction.
The end of the input is represented by a line containing five zeros separated by a space character.
Output
For each dataset, output the minimum cost of laying the water pipe on one line.
Sample Input
4 5 1 3 4
1 2 5
2 3 5
2 4 5
1 3 8
1 4 8
0 0 0 0 0
Output for the Sample Input
15
Example
Input
4 5 1 3 4
1 2 5
2 3 5
2 4 5
1 3 8
1 4 8
0 0 0 0 0
Output
15
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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\"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7601\\n[^[^ab][^cd]]\\n4562\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3622\\n[^[^ab][^cd]]\\n2398\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n343\\n[^[^ab][^cd]]\\n1396\\nb\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n116\\n[^[^ab][^cd]]\\n3411\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1973\\na\\n2640\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n30432\\n[^[^ab][^cd]]\\n1295\\na\\n5955\\n[^dd]\\n1131\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*bd]a]]\\n30432\\n[^[^ab][^cd]]\\n1295\\na\\n4682\\n[^cd]\\n1131\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2528\\nc\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n1991\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n2119\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n1886\\n[^[^ab][^cd]]\\n2119\\na\\n9876\\n[^dd]\\n9268\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n3703\\na\\n9876\\n[^dc]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2347\\na\\n8261\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2600\\na\\n9876\\n[^db]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n343\\n[^[^ab][^cd]]\\n2570\\nb\\n6192\\n[^dd]\\n9090\\n.\", \"[+c[*a[^cd]]]\\n0404\\n[*b[*[*cd]a]]\\n7601\\n[^[^ab][^cd]]\\n2029\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1973\\na\\n9876\\n[^cd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2054\\na\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n30432\\n[^[^ab][^cd]]\\n1295\\na\\n6295\\n[^dd]\\n1131\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7601\\n[^[^ab][^cd]]\\n8424\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3622\\n[^[^ab][^cd]]\\n2398\\na\\n1403\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7591\\n[^[^ab][^cd]]\\n1479\\na\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n11859\\n[^[^ab][^cd]]\\n1361\\nb\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n2501\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n4689\\nb\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2600\\na\\n9876\\n[^db]\\n2809\\n.\", \"[+c[*a[^bd]]]\\n700\\n[*b[*[*cd]a]]\\n116\\n[^[^ab][^cd]]\\n2026\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1973\\na\\n4873\\n[^cd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2054\\na\\n5687\\n[^dd]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n11859\\n[^[^ab][^cd]]\\n1361\\nb\\n5192\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2600\\na\\n2555\\n[^db]\\n2809\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n8997\\n[^[^ab][^cd]]\\n2489\\na\\n9876\\n[^dd]\\n9456\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2054\\na\\n3150\\n[^dd]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n2501\\na\\n6204\\n[^dd]\\n8372\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2054\\nb\\n3150\\n[^dd]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n2456\\n[^[^ab][^cd]]\\n2501\\na\\n6204\\n[^dd]\\n8372\\n.\", \"[+c[*a[^cd]]]\\n0404\\n[*b[*[*cd]a]]\\n2456\\n[^[^ab][^cd]]\\n2501\\na\\n6204\\n[^dd]\\n8372\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2529\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3622\\n[^[^ab][^cd]]\\n1295\\na\\n4317\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1141\\na\\n9876\\n[^dc]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2131\\nb\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1645\\nb\\n8482\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n343\\n[^[^ab][^cd]]\\n1396\\nb\\n1132\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n1115\\nb\\n9876\\n[^dd]\\n2643\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n324\\n[^[^ab][^bd]]\\n2570\\nb\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n8583\\n[^[^ab][^cd]]\\n3703\\na\\n9876\\n[^dc]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^dd]]\\n2600\\na\\n9876\\n[^db]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n519\\n[^[^ab][^cd]]\\n2570\\na\\n3236\\n[^dd]\\n6945\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3622\\n[^[^ab][^cd]]\\n4574\\na\\n1403\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1519\\na\\n9876\\n[^db]\\n2809\\n.\", \"[+c[*a[^bd]]]\\n700\\n[*b[*[*cd]a]]\\n116\\n[^[^ab][^cd]]\\n2026\\na\\n2887\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n2731\\n[^[^ab][^cd]]\\n3767\\na\\n1403\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n11859\\n[^[^ab][^cd]]\\n1361\\nb\\n4214\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n14187\\n[^[^ab][^cd]]\\n2600\\na\\n2555\\n[^db]\\n2809\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n2501\\na\\n5173\\n[^dd]\\n8372\\n.\", \"[+c[*a[^cd]]]\\n0404\\n[*b[*[*cd]a]]\\n2456\\n[^[^ab][^cd]]\\n2501\\na\\n1863\\n[^dd]\\n8372\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n12488\\n[^[^ab][^cd]]\\n1141\\na\\n9876\\n[^dc]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n1673\\n[^[^ab][^cd]]\\n2358\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^dd]]\\n2600\\nb\\n9876\\n[^db]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n8997\\n[^[^ab][^cd]]\\n1458\\nb\\n9876\\n[^dd]\\n4467\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2886\\nb\\n9876\\n[^dc]\\n4997\\n.\", \"[+c[*a[^bd]]]\\n700\\n[*b[*[*cd]a]]\\n116\\n[^[^ab][^cd]]\\n3952\\na\\n2887\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9325\\n[^[^ab][^cd]]\\n2489\\nb\\n9876\\n[^dc]\\n9456\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1973\\na\\n7164\\n[^dc]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n8207\\n[^[^ab][^cd]]\\n2131\\na\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n30432\\n[^[^ab][^cd]]\\n1408\\na\\n5101\\n[^dd]\\n1131\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n476\\n[^[^ab][^cd]]\\n1183\\nb\\n1132\\n[^dd]\\n9090\\n.\", \"[+c[*a[^bd]]]\\n0404\\n[*b[*[*cc]a]]\\n1673\\n[^[^ab][^cd]]\\n2358\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7793\\n[^[^ab][^dd]]\\n2600\\nb\\n9876\\n[^db]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n15341\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n1131\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^cb][^ad]]\\n2570\\nb\\n9876\\n[^dd]\\n9090\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n1295\\nb\\n9876\\n[^dd]\\n4997\\n.\", \"[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n9090\\n.\"], \"outputs\": [\"0 10\\n7 1\\n0 712\\n9 1000\\n0 10000\\n\", \"0 450\\n7 1\\n0 712\\n9 1000\\n0 10000\\n\", \"4 220\\n7 1\\n15 544\\n9 1000\\n0 10000\\n\", \"0 10\\n7 1\\n0 712\\n1 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n0 712\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n15 544\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n0 712\\n9 1000\\n9 400\\n\", \"0 450\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n2 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n2 704\\n9 1000\\n0 10000\\n\", \"0 10\\n2 225\\n15 544\\n9 1000\\n0 10000\\n\", \"0 10\\n7 1\\n4 704\\n9 1000\\n9 400\\n\", \"0 10\\n0 8895\\n2 704\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n11 544\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n0 712\\n2 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n7 704\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n0 712\\n7 1000\\n0 10000\\n\", \"0 510\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n4 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n12 544\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n11 544\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n4 1000\\n2 800\\n\", \"0 10\\n0 8895\\n6 704\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n15 544\\n7 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n5 704\\n9 1000\\n0 10000\\n\", \"0 10\\n2 225\\n0 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n13 544\\n8 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n7 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n12 544\\n2 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n5 1000\\n0 10000\\n\", \"0 10\\n0 7630\\n15 544\\n4 1000\\n2 800\\n\", \"0 10\\n0 8895\\n13 544\\n7 1000\\n0 10000\\n\", \"0 450\\n1 593\\n0 712\\n9 1000\\n0 10000\\n\", \"0 450\\n1 593\\n11 544\\n9 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n11 544\\n9 1000\\n0 10000\\n\", \"0 10\\n7 1\\n7 704\\n9 1000\\n9 400\\n\", \"0 10\\n7 1\\n2 704\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n4 704\\n9 1000\\n0 1000\\n\", \"0 10\\n0 8895\\n0 712\\n1 1000\\n0 10000\\n\", \"0 510\\n0 8895\\n9 544\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n12 544\\n9 1000\\n9 400\\n\", \"0 10\\n0 8895\\n3 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n6 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n10 544\\n9 1000\\n0 10000\\n\", \"0 10\\n2 225\\n0 712\\n1 1000\\n0 10000\\n\", \"0 10\\n1 593\\n11 544\\n9 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n5 704\\n8 1000\\n0 10000\\n\", \"0 450\\n1 593\\n6 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n3 704\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n4 704\\n9 1000\\n1 1000\\n\", \"0 450\\n0 8895\\n6 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n12 544\\n4 1000\\n9 400\\n\", \"0 10\\n0 8895\\n3 704\\n5 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n5 704\\n1 1000\\n0 10000\\n\", \"0 10\\n7 1\\n4 704\\n2 1000\\n1 1000\\n\", \"0 10\\n0 8895\\n7 704\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n3 704\\n3 1000\\n0 10000\\n\", \"0 450\\n1 593\\n6 704\\n6 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n3 704\\n1 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n6 704\\n6 1000\\n0 10000\\n\", \"0 510\\n0 8895\\n6 704\\n6 1000\\n0 10000\\n\", \"0 10\\n7 1\\n12 544\\n9 1000\\n0 10000\\n\", \"0 10\\n2 225\\n15 544\\n4 1000\\n0 10000\\n\", \"0 10\\n7 1\\n5 704\\n9 1000\\n9 400\\n\", \"0 10\\n0 8895\\n1 712\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n6 704\\n4 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n13 544\\n1 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n4 704\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n2 800\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n7 704\\n9 1000\\n9 400\\n\", \"0 10\\n7 1\\n4 800\\n9 1000\\n0 1000\\n\", \"0 10\\n0 8895\\n0 712\\n3 1000\\n0 10000\\n\", \"0 10\\n2 225\\n2 704\\n1 1000\\n0 10000\\n\", \"0 10\\n7 1\\n12 544\\n9 1000\\n1 1000\\n\", \"0 450\\n0 8895\\n6 704\\n2 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n5 704\\n1 1000\\n0 10000\\n\", \"0 450\\n0 8895\\n5 704\\n2 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n4 704\\n2 1000\\n1 1000\\n\", \"0 450\\n1 593\\n6 704\\n5 1000\\n0 10000\\n\", \"0 510\\n0 8895\\n6 704\\n1 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n5 704\\n9 1000\\n9 400\\n\", \"0 450\\n0 8895\\n12 544\\n9 1000\\n0 10000\\n\", \"0 10\\n7 1\\n4 800\\n8 1000\\n0 1000\\n\", \"0 10\\n0 8895\\n8 544\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n4 704\\n8 1000\\n14 400\\n\", \"0 450\\n0 8895\\n13 544\\n2 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n7 704\\n8 1000\\n3 800\\n\", \"0 10\\n0 8895\\n12 544\\n7 1000\\n9 400\\n\", \"0 10\\n0 8895\\n1 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n13 544\\n5 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n11 544\\n1 1000\\n0 10000\\n\", \"0 450\\n0 7630\\n12 544\\n9 1000\\n0 10000\\n\", \"0 10\\n1 593\\n4 800\\n8 1000\\n0 1000\\n\", \"0 10\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n9 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n0 712\\n8 1000\\n0 10000\\n\", \"0 10\\n0 8895\\n15 544\\n8 1000\\n0 10000\\n\", \"0 10\\n7 1\\n15 544\\n9 1000\\n0 10000\"]}", "source": "taco"}
|
Proof of knowledge
The entrance door of the apartment you live in has a password-type lock. This password consists of exactly four digits, ranging from 0 to 9, and you always use the password P given to you by the apartment manager to unlock this door.
One day, you wondered if all the residents of the apartment were using the same password P as you, and decided to ask a friend who lives in the same apartment. You and your friends can tell each other that they are using the same password by sharing their password with each other. However, this method is not preferable considering the possibility that passwords are individually assigned to each inhabitant. You should only know your password, not others.
To prevent this from happening, you and your friend decided to enter their password into the hash function and communicate the resulting hash value to each other. The hash function formula S used here is the lowercase alphabet'a','b','c','d' and the symbols'[',']','+','*','^' It consists of and is represented by <Hash> defined by the following BNF.
> <Hash> :: = <Letter> |'['<Op> <Hash> <Hash>']' <Op> :: ='+' |'*' |'^' <Letter> :: =' a'|'b' |'c' |'d'
Here,'a',' b',' c', and'd' represent the first, second, third, and fourth digits of the 4-digit password, respectively. '+','*','^' Are operators and have the following meanings.
*'+': OR the following two <Hash> in binary.
*'*': Takes the logical product of the following two <Hash> in binary.
*'^': Take the exclusive OR when the following two <Hash> are expressed in binary.
Here, the truth tables of OR, AND, and Exclusive OR are as follows.
A | B | [+ AB]
--- | --- | ---
0 | 0 | 0
1 | 0 | 1
0 | 1 | 1
1 | 1 | 1
A | B | [* AB]
--- | --- | ---
0 | 0 | 0
1 | 0 | 0
0 | 1 | 0
1 | 1 | 1
A | B | [^ AB]
--- | --- | ---
0 | 0 | 0
1 | 0 | 1
0 | 1 | 1
1 | 1 | 0
As an example, if you enter the password 0404 in the hash function [+ c [+ a [^ bd]]], you will get 0 as the hash value. There are 0000, 0101, 0202, 0303, 0505, 0606, 0707, 0808, 0909 as passwords that can obtain the same hash value.
Output the result of entering your password P into the hash function S. Also, to prevent the use of a hash function that can uniquely identify the password from the hash value, output the number of passwords that have the same hash value as your password.
Input
The input consists of up to 50 datasets. Each dataset is represented in the following format.
> SP
The first line of each dataset is the hash function formula S. The second line of each dataset is the password P, which consists of four digits in the range 0-9. It can be assumed that the length of the hash function S is 80 or less.
The end of the input is represented by a line containing only one character,'.'.
Output
For each dataset, output the hash value obtained by entering P in S and the number of passwords that can obtain the same hash value as P, separated by blanks.
Sample Input
[+ c [+ a [^ bd]]]]
0404
[* b [* [* cd] a]]
7777
[^ [^ ab] [^ cd]]
1295
a
9876
[^ dd]
9090
..
Output for the Sample Input
0 10
7 1
15 544
9 1000
0 10000
Example
Input
[+c[+a[^bd]]]
0404
[*b[*[*cd]a]]
7777
[^[^ab][^cd]]
1295
a
9876
[^dd]
9090
.
Output
0 10
7 1
15 544
9 1000
0 10000
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 1\\n1 1 2 2\\n2 2 3 3\\n3 3 4 4\\n\", \"4 1\\n1 1 2 2\\n1 9 2 10\\n9 9 10 10\\n9 1 10 2\\n\", \"3 0\\n1 1 2 2\\n1 1 1000000000 1000000000\\n1 3 8 12\\n\", \"11 8\\n9 1 11 5\\n2 2 8 12\\n3 8 23 10\\n2 1 10 5\\n7 1 19 5\\n1 8 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"20 5\\n1 12 21 22\\n9 10 15 20\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 28\\n9 1 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n1 1 100 100\\n\", \"1 0\\n1 1 2 2\\n\", \"1 0\\n1 1 4 4\\n\", \"2 1\\n1 1 1000000000 1000000000\\n100 200 200 300\\n\", \"2 1\\n1 1 1000000000 2\\n1 1 2 1000000000\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 1 1000000000 999999999\\n\", \"1 0\\n1 1 1000000000 1000000000\\n\", \"1 0\\n100 300 400 1000\\n\", \"1 0\\n2 2 3 3\\n\", \"2 1\\n1 1 1000000000 1000000000\\n100 200 200 300\\n\", \"1 0\\n1 1 100 100\\n\", \"2 1\\n1 1 1000000000 2\\n1 1 2 1000000000\\n\", \"1 0\\n1 1 1000000000 1000000000\\n\", \"1 0\\n1 1 2 2\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 1 1000000000 999999999\\n\", \"1 0\\n100 300 400 1000\\n\", \"11 8\\n9 1 11 5\\n2 2 8 12\\n3 8 23 10\\n2 1 10 5\\n7 1 19 5\\n1 8 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"20 5\\n1 12 21 22\\n9 10 15 20\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 28\\n9 1 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n1 1 4 4\\n\", \"1 0\\n2 2 3 3\\n\", \"1 0\\n1 0 100 100\\n\", \"11 8\\n9 1 11 5\\n2 2 8 12\\n3 8 23 10\\n2 1 10 5\\n6 1 19 5\\n1 8 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"11 8\\n9 1 11 5\\n2 2 8 12\\n3 8 23 10\\n2 1 10 5\\n6 1 19 5\\n1 2 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 49\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"2 1\\n1 2 1000000000 2\\n1 1 2 1000000000\\n\", \"1 0\\n1 1 4 2\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 1 0000000000 999999999\\n\", \"1 0\\n100 300 400 1010\\n\", \"20 5\\n1 12 21 22\\n9 10 15 20\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 28\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n2 0 3 3\\n\", \"1 0\\n1 0 100 000\\n\", \"2 1\\n1 2 1000000000 2\\n1 1 0 1000000000\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 1 0000010000 999999999\\n\", \"1 0\\n100 300 342 1010\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 28\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n2 0 5 3\\n\", \"1 0\\n2 0 100 000\\n\", \"2 1\\n1 4 1000000000 2\\n1 1 0 1000000000\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 0 0000010000 999999999\\n\", \"11 8\\n9 1 11 5\\n2 1 8 12\\n3 8 23 10\\n2 1 10 5\\n6 1 19 5\\n1 2 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"1 0\\n2 -1 5 3\\n\", \"1 0\\n4 0 100 000\\n\", \"2 1\\n1 4 1000000000 2\\n2 1 0 1000000000\\n\", \"2 1\\n1 1 999999999 1010000000\\n1 0 0000010000 999999999\\n\", \"11 8\\n9 1 11 5\\n2 1 8 12\\n4 8 23 10\\n2 1 10 5\\n6 1 19 5\\n1 2 3 10\\n1 5 3 9\\n1 2 3 4\\n1 2 3 4\\n4 2 12 16\\n8 5 12 9\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 49\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n15 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n0 -1 5 3\\n\", \"2 1\\n1 4 1000000000 2\\n4 1 0 1000000000\\n\", \"2 1\\n1 1 999999999 1010001000\\n1 0 0000010000 999999999\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 41\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n15 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n1 -1 5 3\\n\", \"2 1\\n1 4 1000000000 2\\n4 2 0 1000000000\\n\", \"2 1\\n1 1 999999999 1010001000\\n1 0 0000010010 999999999\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 41\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n15 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 9 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n1 -1 5 2\\n\", \"2 1\\n1 4 1000000000 2\\n4 1 0 1100000000\\n\", \"2 1\\n1 1 999999999 1010001000\\n1 0 0000010110 999999999\\n\", \"20 5\\n1 12 21 22\\n9 10 15 18\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 20 24\\n3 3 19 27\\n3 4 23 41\\n9 0 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n15 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 9 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n1 -2 5 2\\n\", \"2 1\\n1 4 1000000000 2\\n4 0 0 1000000000\\n\", \"1 0\\n1 -4 5 2\\n\", \"2 1\\n2 4 1000000000 2\\n4 0 0 1000000000\\n\", \"2 1\\n2 5 1000000000 2\\n4 0 0 1000000000\\n\", \"2 1\\n2 8 1000000000 2\\n4 0 0 1000000000\\n\", \"2 1\\n2 8 1000000000 2\\n4 0 0 1000001000\\n\", \"2 1\\n2 7 1000000000 2\\n4 0 0 1000001000\\n\", \"2 1\\n1 1 1000000000 0000000000\\n100 200 200 300\\n\", \"2 1\\n1 1 1000000000 2\\n1 1 2 1100000000\\n\", \"1 0\\n0 1 2 2\\n\", \"2 1\\n1 1 999999999 1000000000\\n1 1 1000000010 999999999\\n\", \"20 5\\n1 12 21 22\\n9 10 15 20\\n10 12 12 20\\n1 1 25 29\\n5 10 21 22\\n4 9 16 25\\n12 10 14 24\\n3 3 19 27\\n3 4 23 28\\n12 1 11 31\\n9 14 17 18\\n8 12 14 20\\n8 11 18 19\\n12 3 14 29\\n7 8 13 22\\n6 4 16 30\\n11 3 13 27\\n9 16 15 18\\n6 13 14 21\\n9 12 15 22\\n\", \"1 0\\n2 2 3 1\\n\", \"4 1\\n1 1 2 2\\n1 9 2 10\\n9 9 10 10\\n9 1 10 2\\n\", \"3 1\\n1 1 2 2\\n2 2 3 3\\n3 3 4 4\\n\", \"3 0\\n1 1 2 2\\n1 1 1000000000 1000000000\\n1 3 8 12\\n\"], \"outputs\": [\"1\\n\", \"64\\n\", \"249999999000000001\\n\", \"4\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"3\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"64\\n\", \"1\\n\", \"249999999000000001\\n\"]}", "source": "taco"}
|
Edo has got a collection of n refrigerator magnets!
He decided to buy a refrigerator and hang the magnets on the door. The shop can make the refrigerator with any size of the door that meets the following restrictions: the refrigerator door must be rectangle, and both the length and the width of the door must be positive integers.
Edo figured out how he wants to place the magnets on the refrigerator. He introduced a system of coordinates on the plane, where each magnet is represented as a rectangle with sides parallel to the coordinate axes.
Now he wants to remove no more than k magnets (he may choose to keep all of them) and attach all remaining magnets to the refrigerator door, and the area of the door should be as small as possible. A magnet is considered to be attached to the refrigerator door if its center lies on the door or on its boundary. The relative positions of all the remaining magnets must correspond to the plan.
Let us explain the last two sentences. Let's suppose we want to hang two magnets on the refrigerator. If the magnet in the plan has coordinates of the lower left corner (x_1, y_1) and the upper right corner (x_2, y_2), then its center is located at ($\frac{x_{1} + x_{2}}{2}$, $\frac{y_{1} + y_{2}}{2}$) (may not be integers). By saying the relative position should correspond to the plan we mean that the only available operation is translation, i.e. the vector connecting the centers of two magnets in the original plan, must be equal to the vector connecting the centers of these two magnets on the refrigerator.
The sides of the refrigerator door must also be parallel to coordinate axes.
-----Input-----
The first line contains two integers n and k (1 ≤ n ≤ 100 000, 0 ≤ k ≤ min(10, n - 1)) — the number of magnets that Edo has and the maximum number of magnets Edo may not place on the refrigerator.
Next n lines describe the initial plan of placing magnets. Each line contains four integers x_1, y_1, x_2, y_2 (1 ≤ x_1 < x_2 ≤ 10^9, 1 ≤ y_1 < y_2 ≤ 10^9) — the coordinates of the lower left and upper right corners of the current magnet. The magnets can partially overlap or even fully coincide.
-----Output-----
Print a single integer — the minimum area of the door of refrigerator, which can be used to place at least n - k magnets, preserving the relative positions.
-----Examples-----
Input
3 1
1 1 2 2
2 2 3 3
3 3 4 4
Output
1
Input
4 1
1 1 2 2
1 9 2 10
9 9 10 10
9 1 10 2
Output
64
Input
3 0
1 1 2 2
1 1 1000000000 1000000000
1 3 8 12
Output
249999999000000001
-----Note-----
In the first test sample it is optimal to remove either the first or the third magnet. If we remove the first magnet, the centers of two others will lie at points (2.5, 2.5) and (3.5, 3.5). Thus, it is enough to buy a fridge with door width 1 and door height 1, the area of the door also equals one, correspondingly.
In the second test sample it doesn't matter which magnet to remove, the answer will not change — we need a fridge with door width 8 and door height 8.
In the third sample you cannot remove anything as k = 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.
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