meetforever/GRPO_CL huggingface dataset:
user: You have integer $n$. Calculate how many ways are there to fully cover belt-like area of $4n-2$ triangles with diamond shapes. 

Diamond shape consists of two triangles. You can move, rotate or flip the shape, but you cannot scale it. 

$2$ coverings are different if some $2$ triangles are covered by the same diamond shape in one of them and by different diamond shapes in the other one.

Please look at pictures below for better understanding.

 $\theta$ On the left you can see the diamond shape you will use, and on the right you can see the area you want to fill.

[Image] These are the figures of the area you want to fill for $n = 1, 2, 3, 4$. 

You have to answer $t$ independent test cases.


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 10^{4}$) — the number of test cases.

Each of the next $t$ lines contains a single integer $n$ ($1 \le n \le 10^{9}$).


-----Output-----

For each test case, print the number of ways to fully cover belt-like area of $4n-2$ triangles using diamond shape. It can be shown that under given constraints this number of ways doesn't exceed $10^{18}$.


-----Example-----
Input
2
2
1

Output
2
1



-----Note-----

In the first test case, there are the following $2$ ways to fill the area:

 [Image] 

In the second test case, there is a unique way to fill the area:

 [Image]
user: Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.

Example:


Input:
[
  ["1","0","1","0","0"],
  ["1","0","1","1","1"],
  ["1","1","1","1","1"],
  ["1","0","0","1","0"]
]
Output: 6

Answer: {"fn_name": "maximalRectangle", "inputs": [[[["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]], [[["0","0"]]]], "outputs": [6,0]}
user: The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.

Example 1:


Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1


Example 2:


Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

Answer: {"fn_name": "grayCode", "inputs": [[2], [1]], "outputs": [[0,1,3,2],[0,1]]}
user: Given a positive integer n, generate a square matrix filled with elements from 1 to n2 in spiral order.

Example:


Input: 3
Output:
[
 [ 1, 2, 3 ],
 [ 8, 9, 4 ],
 [ 7, 6, 5 ]
]

Answer: {"fn_name": "generateMatrix", "inputs": [[3], [1]], "outputs": [[[1,2,3],[8,9,4],[7,6,5]], [[1]]]}
user: A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Now consider if some obstacles are added to the grids. How many unique paths would there be?



An obstacle and empty space is marked as 1 and 0 respectively in the grid.

Note: m and n will be at most 100.

Example 1:


Input:
[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]
Output: 2
Explanation:
There is one obstacle in the middle of the 3x3 grid above.
There are two ways to reach the bottom-right corner:
1. Right -> Right -> Down -> Down
2. Down -> Down -> Right -> Right

Answer: {"fn_name": "uniquePathsWithObstacles", "inputs": [[[[0,0,0],[0,1,0],[0,0,0]]], [[[0,1],[0,0]]]], "outputs": [2, 1]}
user: There are a total of n courses you have to take, labeled from 0 to n-1.

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]

Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?

Example 1:


Input: 2, [[1,0]] 
Output: true
Explanation: There are a total of 2 courses to take. 
             To take course 1 you should have finished course 0. So it is possible.

Example 2:


Input: 2, [[1,0],[0,1]]
Output: false
Explanation: There are a total of 2 courses to take. 
             To take course 1 you should have finished course 0, and to take course 0 you should
             also have finished course 1. So it is impossible.


Note:


       The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
       You may assume that there are no duplicate edges in the input prerequisites.

Answer: {"fn_name": "canFinish", "inputs": [[2, [[1,0]]], [2, [[1,0],[0,1]]]], "outputs": [true, false]}
user: Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:


Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

Answer: {"fn_name": "minPathSum", "inputs": [[[[1,3,1],[1,5,1],[4,2,1]]], [[[1,2,3],[4,5,6]]]], "outputs": [7, 12]}
user: table.dungeon, .dungeon th, .dungeon td {
  border:3px solid black;
}

 .dungeon th, .dungeon td {
    text-align: center;
    height: 70px;
    width: 70px;
}

The demons had captured the princess (P) and imprisoned her in the bottom-right corner of a dungeon. The dungeon consists of M x N rooms laid out in a 2D grid. Our valiant knight (K) was initially positioned in the top-left room and must fight his way through the dungeon to rescue the princess.

The knight has an initial health point represented by a positive integer. If at any point his health point drops to 0 or below, he dies immediately.

Some of the rooms are guarded by demons, so the knight loses health (negative integers) upon entering these rooms; other rooms are either empty (0's) or contain magic orbs that increase the knight's health (positive integers).

In order to reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.

 

Write a function to determine the knight's minimum initial health so that he is able to rescue the princess.

For example, given the dungeon below, the initial health of the knight must be at least 7 if he follows the optimal path RIGHT-> RIGHT -> DOWN -> DOWN.


       
               
                       -2 (K)
                       -3
                       3
               
               
                       -5
                       -10
                       1
               
               
                       10
                       30
                       -5 (P)
               
       


 

Note:


       The knight's health has no upper bound.
       Any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.

Answer: {"fn_name": "calculateMinimumHP", "inputs": [[[[-2,-3,3],[-5,-10,1],[10,30,-5]]], [[[0]]]], "outputs": [7, 1]}
user: Given a set of distinct integers, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

Example:


Input: nums = [1,2,3]
Output:
[
  [3],
  [1],
  [2],
  [1,2,3],
  [1,3],
  [2,3],
  [1,2],
  []
]

Answer: {"fn_name": "subsets", "inputs": [[[1,2,3]], [[0]]], "outputs": [[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]], [[],[0]]]}
user: Given a matrix of m x n elements (m rows, n columns), return all elements of the matrix in spiral order.

Example 1:


Input:
[
 [ 1, 2, 3 ],
 [ 4, 5, 6 ],
 [ 7, 8, 9 ]
]
Output: [1,2,3,6,9,8,7,4,5]


Example 2:

Input:
[
  [1, 2, 3, 4],
  [5, 6, 7, 8],
  [9,10,11,12]
]
Output: [1,2,3,4,8,12,11,10,9,5,6,7]

Answer: {"fn_name": "spiralOrder", "inputs": [[[[1,2,3],[4,5,6],[7,8,9]]], [[[1,2,3,4],[5,6,7,8],[9,10,11,12]]]], "outputs": [[1,2,3,6,9,8,7,4,5], [1,2,3,4,8,12,11,10,9,5,6,7]]}
user: A city's skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Now suppose you are given the locations and height of all the buildings as shown on a cityscape photo (Figure A), write a program to output the skyline formed by these buildings collectively (Figure B).
       

The geometric information of each building is represented by a triplet of integers [Li, Ri, Hi], where Li and Ri are the x coordinates of the left and right edge of the ith building, respectively, and Hi is its height. It is guaranteed that 0 ≤ Li, Ri ≤ INT_MAX, 0 < Hi ≤ INT_MAX, and Ri - Li > 0. You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0.

For instance, the dimensions of all buildings in Figure A are recorded as: [ [2 9 10], [3 7 15], [5 12 12], [15 20 10], [19 24 8] ] .

The output is a list of "key points" (red dots in Figure B) in the format of [ [x1,y1], [x2, y2], [x3, y3], ... ] that uniquely defines a skyline. A key point is the left endpoint of a horizontal line segment. Note that the last key point, where the rightmost building ends, is merely used to mark the termination of the skyline, and always has zero height. Also, the ground in between any two adjacent buildings should be considered part of the skyline contour.

For instance, the skyline in Figure B should be represented as:[ [2 10], [3 15], [7 12], [12 0], [15 10], [20 8], [24, 0] ].

Notes:


       The number of buildings in any input list is guaranteed to be in the range [0, 10000].
       The input list is already sorted in ascending order by the left x position Li.
       The output list must be sorted by the x position.
       There must be no consecutive horizontal lines of equal height in the output skyline. For instance, [...[2 3], [4 5], [7 5], [11 5], [12 7]...] is not acceptable; the three lines of height 5 should be merged into one in the final output as such: [...[2 3], [4 5], [12 7], ...]

Answer: {"fn_name": "getSkyline", "inputs": [[[[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]], [[[0,2,3],[2,5,3]]]], "outputs": [[[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]], [[0,3],[5,0]]]}
user: Given a collection of numbers that might contain duplicates, return all possible unique permutations.

Example:


Input: [1,1,2]
Output:
[
  [1,1,2],
  [1,2,1],
  [2,1,1]
]

Answer: {"fn_name": "permuteUnique", "inputs": [[[1,1,2]], [[1,2,3]]], "outputs": [[[1,1,2], [1,2,1], [2,1,1]], [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]]}
user: Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle


[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]


The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

Answer: {"fn_name": "minimumTotal", "inputs": [[[[2],[3,4],[6,5,7],[4,1,8,3]]], [[[-10]]]], "outputs": [11, -10]}
user: Given a collection of integers that might contain duplicates, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

Example:


Input: [1,2,2]
Output:
[
  [2],
  [1],
  [1,2,2],
  [2,2],
  [1,2],
  []
]

Answer: {"fn_name": "subsetsWithDup", "inputs": [[[1,2,2]], [[0]]], "outputs": [[[],[1],[1,2],[1,2,2],[2],[2,2]], [[],[0]]]}
user: There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.
Snuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.
The lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.
In each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.
Snuke wants to maximize the number of squares lighted by the lamp.
You are given H strings S_i (1 \leq i \leq H), each of length W. If the j-th character (1 \leq j \leq W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is ., there is no obstacle on that square.
Find the maximum possible number of squares lighted by the lamp.

-----Constraints-----
 - 1 \leq H \leq 2,000
 - 1 \leq W \leq 2,000
 - S_i is a string of length W consisting of # and ..
 - . occurs at least once in one of the strings S_i (1 \leq i \leq H).

-----Input-----
Input is given from Standard Input in the following format:
H W
S_1
:
S_H

-----Output-----
Print the maximum possible number of squares lighted by the lamp.

-----Sample Input-----
4 6
#..#..
.....#
....#.
#.#...

-----Sample Output-----
8

If Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.
user: We have N colored balls arranged in a row from left to right; the color of the i-th ball from the left is c_i.
You are given Q queries. The i-th query is as follows: how many different colors do the l_i-th through r_i-th balls from the left have?

-----Constraints-----
 - 1\leq N,Q \leq 5 \times 10^5
 - 1\leq c_i \leq N
 - 1\leq l_i \leq r_i \leq N
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N Q
c_1 c_2 \cdots c_N
l_1 r_1
l_2 r_2
:
l_Q r_Q

-----Output-----
Print Q lines. The i-th line should contain the response to the i-th query.

-----Sample Input-----
4 3
1 2 1 3
1 3
2 4
3 3

-----Sample Output-----
2
3
1

 - The 1-st, 2-nd, and 3-rd balls from the left have the colors 1, 2, and 1 - two different colors.
 - The 2-st, 3-rd, and 4-th balls from the left have the colors 2, 1, and 3 - three different colors.
 - The 3-rd ball from the left has the color 1 - just one color.
user: We have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.
We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.
The i-th and j-th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0.
In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq N \leq 2 \times 10^5
 - -10^{18} \leq A_i, B_i \leq 10^{18}

-----Input-----
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N

-----Output-----
Print the count modulo 1000000007.

-----Sample Input-----
3
1 2
-1 1
2 -1

-----Sample Output-----
5

There are five ways to choose the set of sardines, as follows:
 - The 1-st
 - The 1-st and 2-nd
 - The 2-nd
 - The 2-nd and 3-rd
 - The 3-rd
user: We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}.
Process the following q queries in order:
 - The i-th query contains three integers n_i, x_i, and m_i.
Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j =  \begin{cases}    x_i & ( j = 0 ) \\    a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 )  \end{cases}\end{eqnarray}
Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i).
Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0).

-----Constraints-----
 - All values in input are integers.
 - 1 \leq k, q \leq 5000
 - 0 \leq d_i \leq 10^9
 - 2 \leq n_i \leq 10^9
 - 0 \leq x_i \leq 10^9
 - 2 \leq m_i \leq 10^9

-----Input-----
Input is given from Standard Input in the following format:
k q
d_0 d_1 ... d_{k - 1}
n_1 x_1 m_1
n_2 x_2 m_2
:
n_q x_q m_q

-----Output-----
Print q lines.
The i-th line should contain the response to the i-th query.

-----Sample Input-----
3 1
3 1 4
5 3 2

-----Sample Output-----
1

For the first query, the sequence {a_j} will be 3,6,7,11,14.
 - (a_0~\textrm{mod}~2) > (a_1~\textrm{mod}~2)
 - (a_1~\textrm{mod}~2) < (a_2~\textrm{mod}~2)
 - (a_2~\textrm{mod}~2) = (a_3~\textrm{mod}~2)
 - (a_3~\textrm{mod}~2) > (a_4~\textrm{mod}~2)
Thus, the response to this query should be 1.
user: We have a permutation P = P_1, P_2, \ldots, P_N of 1, 2, \ldots, N.
You have to do the following N - 1 operations on P, each exactly once, in some order:
 - Swap P_1 and P_2.
 - Swap P_2 and P_3.
\vdots
 - Swap P_{N-1} and P_N.
Your task is to sort P in ascending order by configuring the order of operations.
If it is impossible, print -1 instead.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq N \leq 2 \times 10^5
 - P is a permutation of 1, 2, \ldots, N.

-----Input-----
Input is given from Standard Input in the following format:
N
P_1 P_2 \ldots P_N

-----Output-----
If it is impossible to sort P in ascending order by configuring the order of operations, print -1.
Otherwise, print N-1 lines to represent a sequence of operations that sorts P in ascending order.
The i-th line (1 \leq i \leq N - 1) should contain j, where the i-th operation swaps P_j and P_{j + 1}.
If there are multiple such sequences of operations, any of them will be accepted.

-----Sample Input-----
5
2 4 1 5 3

-----Sample Output-----
4
2
3
1

The following sequence of operations sort P in ascending order:
 - First, swap P_4 and P_5, turning P into 2, 4, 1, 3, 5.
 - Then, swap P_2 and P_3, turning P into 2, 1, 4, 3, 5.
 - Then, swap P_3 and P_4, turning P into 2, 1, 3, 4, 5.
 - Finally, swap P_1 and P_2, turning P into 1, 2, 3, 4, 5.
user: AtCoDeer the deer and his friend TopCoDeer is playing a game.
The game consists of N turns.
In each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:
(※) After each turn, (the number of times the player has played Paper)≦(the number of times the player has played Rock).
Each player's score is calculated by (the number of turns where the player wins) - (the number of turns where the player loses), where the outcome of each turn is determined by the rules of Rock-paper-scissors.
(For those who are not familiar with Rock-paper-scissors: If one player plays Rock and the other plays Paper, the latter player will win and the former player will lose. If both players play the same gesture, the round is a tie and neither player will win nor lose.)
With his supernatural power, AtCoDeer was able to foresee the gesture that TopCoDeer will play in each of the N turns, before the game starts.
Plan AtCoDeer's gesture in each turn to maximize AtCoDeer's score.
The gesture that TopCoDeer will play in each turn is given by a string s. If the i-th (1≦i≦N) character in s is g, TopCoDeer will play Rock in the i-th turn. Similarly, if the i-th (1≦i≦N) character of s in p, TopCoDeer will play Paper in the i-th turn.

-----Constraints-----
 - 1≦N≦10^5
 - N=|s|
 - Each character in s is g or p.
 - The gestures represented by s satisfy the condition (※).

-----Input-----
The input is given from Standard Input in the following format:
s

-----Output-----
Print the AtCoDeer's maximum possible score.

-----Sample Input-----
gpg

-----Sample Output-----
0

Playing the same gesture as the opponent in each turn results in the score of 0, which is the maximum possible score.
user: There is a cave.
The cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.
It is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.
Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.
 - If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.
Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq N \leq 10^5
 - 1 \leq M \leq 2 \times 10^5
 - 1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)
 - A_i \neq B_i\ (1 \leq i \leq M)
 - One can travel between any two rooms by traversing passages.

-----Input-----
Input is given from Standard Input in the following format:
N M
A_1 B_1
:
A_M B_M

-----Output-----
If there is no way to place signposts satisfying the objective, print No.
Otherwise, print N lines. The first line should contain Yes, and the i-th line (2 \leq i \leq N) should contain the integer representing the room indicated by the signpost in Room i.

-----Sample Input-----
4 4
1 2
2 3
3 4
4 2

-----Sample Output-----
Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:
 - Starting in Room 2, you will reach Room 1 after traversing one passage: (2) \to 1. This is the minimum number of passages possible.
 - Starting in Room 3, you will reach Room 1 after traversing two passages: (3) \to 2 \to 1. This is the minimum number of passages possible.
 - Starting in Room 4, you will reach Room 1 after traversing two passages: (4) \to 2 \to 1. This is the minimum number of passages possible.
Thus, the objective is satisfied.
user: We have an H \times W grid whose squares are painted black or white. The square at the i-th row from the top and the j-th column from the left is denoted as (i, j).
Snuke would like to play the following game on this grid. At the beginning of the game, there is a character called Kenus at square (1, 1). The player repeatedly moves Kenus up, down, left or right by one square. The game is completed when Kenus reaches square (H, W) passing only white squares.
Before Snuke starts the game, he can change the color of some of the white squares to black. However, he cannot change the color of square (1, 1) and (H, W). Also, changes of color must all be carried out before the beginning of the game.
When the game is completed, Snuke's score will be the number of times he changed the color of a square before the beginning of the game. Find the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed, that is, Kenus can never reach square (H, W) regardless of how Snuke changes the color of the squares.  
The color of the squares are given to you as characters s_{i, j}. If square (i, j) is initially painted by white, s_{i, j} is .; if square (i, j) is initially painted by black, s_{i, j} is #.