meetforever/GRPO_CL huggingface dataset:
user: -----Problem Statement-----
You all must have played the game candy crush. So here is a bomb which works much the fruit bomb in candy crush. A designer, Anton, designed a very powerful bomb. The bomb, when placed on a location $(x, y)$ in a $R \times C$ grid, wipes out the row $x$ and column $y$ completely.
You are given a $R\times C$ grid with $N$ targets. You have only one bomb. Your aim is to maximize the damage and hence destroy most number of targets. Given the location of targets on the grid, find out the number of targets that can destroyed.
The grid system uses index starting with $0$.

-----Input-----
- First line contains three space separated integers, $R$, $C$ and $N$. Then, $N$ lines follow.
- Each line contains space separated integers $r$ and $c$ mentioning the location of the target.

-----Output-----
A single integer giving the number of targets that can be destroyed.

-----Constraints-----
- $1 \leq R, C \leq 3 \times 10^5$
- $1 \leq N \leq min(R \times C,  3 \times 10^5)$
- $0 \leq r < R$
- $0 \leq c < C$
- Any input pair $(r, c)$ is not repeated.

-----Subtasks-----
The total marks will be divided into:
- 20% : $R, C \leq 10^3$
- 80% : Original Constraints

-----Sample Input-----
2 3 3
1 1
0 0
0 2

-----Sample Output-----
3

-----EXPLANATION-----
It is possible to destroy all the targets if we place the bomb at $(0, 1)$. Hence, total number of targets destroyed is $3$, which is our answer.
user: Chef is now a corporate person. He has to attend office regularly. But chef does not want to go to office, rather he wants to stay home and discover different recipes and cook them. 
In the office where chef works, has two guards who count how many times a person enters into the office building. Though the duty of a guard is 24 hour in a day, but sometimes they fall asleep during their duty and could not track the entry of a person in the office building. But one better thing is that they never fall asleep at the same time. At least one of them remains awake and counts who enters into the office.
Now boss of Chef wants to calculate how many times Chef has entered into the building. He asked to the guard and they give him two integers A and B, count of first guard and second guard respectively.
Help the boss to count the minimum and maximum number of times Chef could have entered into the office building.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of the T test cases follows. 
Each test case consists of a line containing two space separated integers A and B.

-----Output-----
For each test case, output a single line containing two space separated integers, the minimum and maximum number of times Chef could have entered into the office building.

-----Constraints-----
- 1 ≤ T ≤ 100
- 0 ≤ A, B ≤ 1000000

-----Example-----
Input:
1
19 17

Output:
19 36
user: Indian National Olympiad in Informatics 2012
You are given a table with 2 rows and N columns. Each cell has an integer in it. The score of such a table is defined as follows: for each column, consider the sum of the two numbers in the column; the maximum of the N numbers so obtained is the score. For example, for the table
7162
1234

the score is max(7 + 1, 1 + 2, 6 + 3, 2 + 4) = 9.

The first row of the table is fixed, and given as input. N possible ways to fill the second row are considered:
1,2,...,N
2,3,...,N,1
3,4,...,N,1,2
···
N, 1, ... , ,N − 1

For instance, for the example above, we would consider each of the following as possibilities for the second row.
1234
2341
3412
4123

Your task is to find the score for each of the above choices of the second row. In the example above, you would evaluate the following four tables,
7162 7162 7162 7162
1234 2341 3412 4123

and compute scores 9, 10, 10 and 11, respectively.

-----Input format -----
The first line of the input has a single integer, N. The second line of the input has N integers, representing the first row, from left to right.

-----Output format -----
The output should consist of a single line with N integers. For 1 ² k ² N, the kth number in the output should be the score when the second row of the table is taken to be k,k+1,...,N,1,...,k−1.

-----Test Data -----
The testdata is grouped into two subtasks with the following constraints on the inputs.
• Subtask 1 [30 points] : 1 ≤ N ≤ 3000.
• Subtask 2 [70 points] : 1 ≤ N ≤ 200000.
In both the subtasks, all the integers in the first row of the table are between 1 and 100000, inclusive.

-----Example -----
Here is the sample input and output corresponding to the example above.

-----Sample input -----
4
7 1 6 2

-----Sample output-----
9 10 10 11

Note: Your program should not print anything other than what is specified in the output format. Please remove all diagnostic print statements before making your final submission. A program with extraneous output will be treated as incorrect!
user: Chef likes problems on geometry a lot. Please help him to solve one such problem.
Find all possible triangles with integer sides which has the radius of inscribed circle (also known as incircle) equal to R.
Two triangles are said to be different if they have at least one different side lengths. Formally, let there be two triangles T1, T2. Let a, b, c denote the sides of triangle T1, such that a ≤ b ≤ c. Similarly, Let d, e, f denote the sides of triangle T2, such that d ≤ e ≤ f. Then T1 will said to be different from T2 if either a ≠ d, or b ≠ e or c ≠ f.

-----Input-----
There is a single test case per test file.
The only line of input contains an integer R.

-----Output-----
Output in first line single number - number of triangles satisfying statement.
Order the sides of triangles in non-decreasing order. Output all triangles in non-decreasing order, i.e. order first by smallest sides, otherwise by second smallest sides, if first and second sides equal, then by third.

-----Constraints-----
- 1 ≤ R ≤ 100 

-----Subtasks-----
- Subtask #1: (20 points)  1 ≤ R ≤ 3
- Subtask #2: (30 points)  1 ≤ R ≤ 20
- Subtask #3: (50 points)  Original constraints

-----Example-----
Input:2

Output:5
5 12 13
6 8 10
6 25 29
7 15 20
9 10 17
user: Lucy had recently learned the game, called Natural Numbers.
The rules of the game are really simple. There are N players. At the same time, every player says one natural number. Let's call the number said by the i-th player Ai. The person with the smallest unique number (that is, the smallest number that was not said by anybody else) wins. Sometimes, there is a case when there are no unique numbers at all. Then the game is obviously a draw, so nobody wins it.
Sometimes, it's hard to determine the winner, especially, when the number of players is enormous. So in this problem, your assignment will be: given the names of the players and the numbers every of them have said. Please, tell the name of the winner, or determine that nobody wins.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.

The first line of every test case consists of a single integer N - the number of players. Then, N lines will follow. Each of these N lines will consist of the player's name and the number Ai said by her, separated by a single space.

-----Output-----
For each test case, output a single line containing an answer to the corresponding test case - the name of the winner, or a string "Nobody wins.", if nobody wins the game.

-----Example-----
Input:
2
5
Kouta 1
Yuka 1
Mayu 3
Lucy 2
Nana 5
2
Lucy 2
Nana 2

Output:
Lucy
Nobody wins.

-----Scoring-----
Subtask 1 (17 points): T = 10000, 1 <= N <= 10, 1 <= Ai <= 10 

Subtask 2 (19 points): T = 10000, 1 <= N <= 10, 1 <= Ai <= 2*109

Subtask 3 (30 points): T = 100, 1 <= N <= 1000, 1<= Ai <= 2*109

Subtask 4 (34 points): T = 10, 1 <= N <= 10000, 1 <= Ai <= 2*109

You can safely assume that in all the test cases the length of any name will not exceed five letters. All the players'  names  are unique.
user: Write a program that reads numbers until -1 is not given.
The program finds how many of the given numbers are more than 30, $N$.
It also finds the average weighted sum of even numbers, $A$.
The weight of the $i$th number is defined as the position of the number (1 based indexing) times the number. To find the average weighted sum, you need to add all these weights for the even numbers, then divide the sum by the sum of the positions of the numbers.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains some numbers, terminated by -1

-----Output:-----
For each testcase, output in a single line the count of numbers that are greater than 30, $N$, and the average weighted sum of the even numbers, $A$, separated by a space. Make sure to set the precision of the average weighted sum to 2 places after the decimal point.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq N \leq 1000$

-----Sample Input:-----
1
33 100 77 42 12 -1

-----Sample Output:-----
4 38.91

-----EXPLANATION:-----
In the series of numbers 33 100 77 42 12 -1, the count of numbers greater than 30 is 4
The average weighted sum of the even numbers is given by:
((2 * 100) + (4 * 42) + (5 * 12)) / (2 + 4 + 5)
user: Mance Rayder, the King-Beyond-the-Wall, has always wanted to lead the largest army the North has ever seen against the NIght’s Watch. For this humungous feat he has banded the waring tribes, the Giants, Thenns and Wildings, together by going to great extents. But the King is facing with an issue he always saw it coming.
The huge army is divided into smaller divisions and each division can be of the type $G, T$ or $W$ standing for Giants, Thenns and Wildings respectively. Mance doesn’t want two divisions of the same type standing together as he fears it might lead to a mutiny or an unorganised charge or retreat. 
For a given numbers of $G, T$ and $W$, find whether an army can be organised in accordance to the rules set by Mance. Not to forget that Mance has to include all the divisions in his battle formation in order to stand a chance against the Wall’s defences.

-----Input:-----
- First line will contain $N$, the number of test cases.
- Each of the next $N$ lines will contain three integers $G$, $T$ and $W$ - the number of Giant, Thenn and Wildling divisions respectively.

-----Output:-----
For each testcase, output in a single line $Yes$ if a battle formation is possible or $No$ otherwise.

-----Constraints-----
- $1 \leq N \leq 100$
- $1 \leq G,T,W \leq 10^9$

-----Sample Input:-----
1
1 2 1

-----Sample Output:-----
Yes

-----Explanation:-----
The first case can be formed as : $ TGWT $. Hence the answer is $ Yes $.
user: Master Oogway has forseen that a panda named Po will be the dragon warrior, and the master of Chi. But he did not tell anyone about the spell that would make him the master of Chi, and has left Po confused. Now Po has to defeat Kai, who is the super villian, the strongest of them all. Po needs to master Chi, and he finds a spell which unlocks his powerful Chi. But the spell is rather strange. It asks Po to calculate the factorial of a number! Po is very good at mathematics, and thinks that this is very easy. So he leaves the spell, thinking it's a hoax. But little does he know that this can give him the ultimate power of Chi. Help Po by solving the spell and proving that it's not a hoax.

-----Input-----
First line of input contains an integer T denoting the number of test cases.
The next T lines contain an integer N.

-----Output-----
For each test case, print a single line containing the solution to the spell which is equal to factorial of N, i.e. N!. Since the output could be large, output it modulo 1589540031(Grand Master Oogway's current age).

-----Constraints-----
- 1 ≤ T ≤ 100000
- 1 ≤ N ≤ 100000

-----Example-----
Input:
4
1
2
3
4

Output:
1
2
6
24
user: Chef is in need of money, so he decided to play a game with Ramsay. In this game, there are $N$ rows of coins (numbered $1$ through $N$). For each valid $i$, the $i$-th row contains $C_i$ coins with values $A_{i, 1}, A_{i, 2}, \ldots, A_{i, C_i}$.
Chef and Ramsay alternate turns; Chef plays first. In each turns, the current player can choose one row that still contains coins and take one of the coins remaining in this row. Chef may only take the the first (leftmost) remaining coin in the chosen row, while Ramsay may only take the last (rightmost) remaining coin in the chosen row. The game ends when there are no coins left.
Each player wants to maximise the sum of values of the coins he took. Assuming that both Chef and Ramsay play optimally, what is the maximum amount of money (sum of values of coins) Chef can earn through this game?

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains an integer $C_i$, followed by a space and $C_i$ space-separated integers $A_{i, 1}, A_{i, 2}, \ldots, A_{i, C_i}$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum amount of money Chef can earn.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^4$
- $1 \le C_i \le 10$ for each valid $i$
- $1 \le A_{i, j} \le 10^5$ for each valid $i$ and $j$

-----Subtasks-----
Subtask #1 (20 points): $N = 1$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
2
4 5 2 3 4
2 1 6

-----Example Output-----
8

-----Explanation-----
Example case 1: One optimal sequence of moves is: Chef takes the coin with value $5$, Ramsay takes $4$, Chef takes $2$, Ramsay takes $3$, Chef takes $1$ and Ramsay takes $6$. At the end, Chef has $5+2+1 = 8$ units of money.
user: Consider a currency system in which there are notes of six denominations, namely, Rs. 1, Rs. 2, Rs. 5, Rs. 10, Rs. 50, Rs. 100.
If the sum of Rs. N is input, write a program to computer smallest number of notes that will combine to give Rs. N.

-----Input-----

The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer N. 

-----Output-----
For each test case, display the smallest number of notes that will combine to give N, in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ N ≤ 1000000

-----Example-----
Input
3 
1200
500
242

Output
12
5
7
user: After fixing the mercury leak, Kim has arrived in the planning room, where he finds a square map of a field, with $N$ rows and $N$ columns. Each cell in the field is either empty, or has a lookout tower on it. Using his notes, he immediately realises that this field is where the JSA will build their new base!
Kim knows that Soum is a fan of symmetric base design, and will only approve of a base to be built if it is square. Furthermore, Soum also requires that all the rows in the base, and all the columns in the base have exactly one tower square in them. 
This means that a base plan is valid if and only if:
- It is square in shape
- Every row in the base has exactly one lookout tower in it.
- Every column in the base has exactly one lookout tower in it.
Kim notices that all the rows and all the columns in the field have exactly one tower square in them, but he knows that some of them could have been built to throw him off! Can you help Kim find how many valid base plans are possible in this field? Two base plans are considered different if one contains a cell in the grid that the other does not.
Please refer to the samples for more details.

-----Input:-----
- The first line of input contains $T$, the number of testcases.
- The first line of each testcase contains a single integer, $N$, representing the side length of the field.
- The next $N$ lines of each testcase contain a string of length $N$, consisting of only 0 and 1. If position $j$ in string $i$ is 0, it means that this the field has no tower at $[i][j]$, and if it is 1, then this cell does have a tower at $[i][j]$.
It is guaranteed that every row in the input will have exactly one tower, and every column in the input will also have exactly one tower.

-----Output:-----
For each testcase, output a single integer $K$, representing the number of different base plans possible.

-----Subtasks-----
- For all subtasks, $N \leq 2500$ and $T \leq 10$. 
- In addition, the sum of $N$ in any testfile is at most $2500$.
Subtask 1 [28 points] : All the towers will be on the diagonal from the top-left to the bottom-right positions. Formally, all positions where $i = j$ have a tower. And no other position has a tower
Subtask 2 [39 points] : $N \leq 600$
Subtask 3 [33 points] : $N \leq 2500$

-----Sample Input:-----
2
2
10
01
4
1000
0010
0100
0001

-----Sample Output:-----
3
8

-----Explanation:-----

In the first testcase, there are three valid base plans: The entire 2x2 square, the 1x1 square which contains only the cell (1, 1) and the 1x1 square which contains only the cell (2, 2).

In the second testcase, 

There are eight valid base plans:
- The 4x4 square with top left corner at (1, 1)
- The 3x3 square with top left corner at (1, 1)
- The 3x3 square with top left corner at (2, 2)
- The 3x3 square with top left corner at (1, 1)
- The 2x2 square with top left corner at (2, 2)
- The 1x1 square which contains only the cell (1, 1)
- The 1x1 square which contains only the cell (2, 3)
- The 1x1 square which contains only the cell (3, 2)
- The 1x1 square which contains only the cell (4, 4)
user: Nobody outside the cooking community knows that Chef is a big fan of Chefgram™ — a social network where chefs and cooks upload their secret kitchen photos.
Recently Chef clicked a beautiful photo, which is represented using 10 pixels in a single row. Respecting Chefgram™'s boolean roots, every pixel is either white or black.

Chefgram™ has N filters. Every filter is a string containing 10 symbols. Every symbol is either '+' or '-'.

- A '+' at the ith position in a filter means that if Chef applies this filter to his photo, the ith pixel will be inverted: it becomes black if it was originally white, and vice versa. 
- A '-' at the ith position in a filter string means that if Chef applies this filter to his photo, the ith pixel will remain unchanged.

Chef can apply as many filters as he wants from a list. He can pick any subset of filters and consequently apply them to a photo.

For example:

- Imagine that Chef has a photo "bbwwbbwwbb" (where 'b' stands for black and 'w' stands for white).
- He applies filters "++--++--++", "-+-+-+-+-+".
- Applying the first filter will transform his picture to "wwwwwwwwww". 
- Applying the second filter on the transformed picture will give Chef the picture "wbwbwbwbwb".

Even if Chefgram™ has two or more identical filters, they are still considered different!

Chef is extremely interested in knowing how many different subsets of all the Chefgram™ filters can he apply to transform his photo into 10 black pixels?

-----Input-----
- The first line of input contains a single integer T — the number of test cases.
- First line of each test case contains a string S. Each symbol is either 'b' or 'w'. This is Chef's photo.
- Second line of each test case contains a single integer N — the number of Chefgram™ filters.
- Each of the next N lines contains a single string Fi, each symbol of which is either '+' or '-'. This string is the ith Chefgram™ filter.

-----Output-----
- For each test case, output a single line containing a single integer — answer to Chef's question modulo 109+7.

-----Constraints-----
- 1 ≤ T ≤ 5
- |S| = 10
- 1 ≤ N ≤ 10^5
- |Fi| = 10

-----Subtasks-----
- Subtask 1: T ≤ 5; N ≤ 20; Points: 20
- Subtask 2: T ≤ 5; N ≤ 10^3; Points: 30
- Subtask 3: T ≤ 5; N ≤ 10^5; Points: 50

-----Example-----
Input:
3
wwwwwwwwww
3
+-+-+-+-+-
----------
+---------
wbwbwbwbwb
3
+-+-+-+-+-
+-+-------
----+-+-+-
bbbbbbbbbb
2
----------
----------

Output:
0
2
4

-----Explanation-----
Example case 1. There is no filter or combination of filters transforming the picture to whole black. 
Example case 2. Chef can either apply the first filter (and invert all whites) or apply the second and third filters in any order.
Example case 3. Picture is already fully black, and we have two different identity filters. Chef can either apply the empty subset of filters, the first filter only, the second filter only, or both.
user: During quarantine chef’s friend invented a game. In this game there are two players, player 1 and Player 2. In center of garden there is one finish circle and both players are at different distances respectively $X$ and $Y$ from finish circle.
Between finish circle and Player 1 there are $X$ number of circles and between finish circle and Player 2 there are $Y$ number of circles. Both player wants to reach finish circle with minimum number of jumps. Player can jump one circle to another circle.
Both players can skip $2^0-1$ or $2^1- 1$ or …. or $2^N-1$ circles per jump. A player cannot skip same number of circles in a match more than once. If both players uses optimal way to reach finish circle what will be the difference of minimum jumps needed to reach finish circle by both players. 
If both players reach finish circle with same number of jumps answer will be $0$ $0$.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The 
description of $T$ test cases follows.
- The first line of each test case contains 2 space separated integers $X$ and $Y$.

-----Output:-----
For each test case, print a single line containing 2 space-separated integers which player win and what is the difference between number of minimum jump required by both players to reach finish circle.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq X,Y \leq 2*10^7$

-----Sample Input:-----
2
4 5
3 5

-----Sample Output:-----
0 0
1 1

-----Explanation:-----
Test Case 1:

Test Case 2:
user: Chef is playing a game with his brother Chefu. He asked Chefu to choose a positive integer $N$, multiply it by a given integer $A$, then choose a divisor of $N$ (possibly $N$ itself) and add it to the product. Let's denote the resulting integer by $M$; more formally, $M = A \cdot N + d$, where $d$ is some divisor of $N$.
Chefu told Chef the value of $M$ and now, Chef should guess $N$. Help him find all values of $N$ which Chefu could have chosen.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $A$ and $M$.

-----Output-----
For each test case, print two lines. The first line should contain a single integer $C$ denoting the number of possible values of $N$. The second line should contain $C$ space-separated integers denoting all possible values of $N$ in increasing order.
It is guaranteed that the sum of $C$ over all test cases does not exceed $10^7$.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le M \le 10^{10}$
- $1 \le A < M$

-----Subtasks-----
Subtask #1 (50 points):
- $M \le 10^6$
Subtask #2 (50 points): original constraints

-----Example Input-----
3
3 35
5 50
4 65

-----Example Output-----
1
10
0

3
13 15 16