meetforever/GRPO_CL huggingface dataset:
user: To protect people from evil, 
a long and tall wall was constructed a few years ago. 
But just a wall is not safe, there should also be soldiers on it, 
always keeping vigil. 
The wall is very long and connects the left and the right towers. 
There are exactly N spots (numbered 1 to N) on the wall for soldiers. 
The Kth spot is K miles far from the left tower and (N+1-K) miles from the right tower.

Given a permutation of spots P of {1, 2, ..., N}, soldiers occupy the N spots in that order. 
The P[i]th spot is occupied before the P[i+1]th spot. 
When a soldier occupies a spot, he is connected to his nearest soldier already placed to his left. 
If there is no soldier to his left, he is connected to the left tower. The same is the case with right side. 
A connection between two spots requires a wire of length equal to the distance between the two.

The realm has already purchased a wire of M miles long from Nokia, 
possibly the wire will be cut into smaller length wires. 
As we can observe, the total length of the used wire depends on the permutation of the spots P. Help the realm in minimizing the length of the unused wire. If there is not enough wire, output -1.

-----Input-----
First line contains an integer T (number of test cases, 1 ≤ T ≤ 10 ). Each of the next T lines contains two integers N M, as explained in the problem statement (1 ≤ N ≤ 30 , 1 ≤ M ≤ 1000).

-----Output-----
For each test case, output the minimum length of the unused wire, or -1 if the the wire is not sufficient.

-----Example-----
Input:
4
3 8
3 9
2 4
5 25

Output:
0
0
-1
5

Explanation:

In the 1st case, for example, the permutation P = {2, 1, 3} will use the exact 8 miles wires in total.

In the 2nd case, for example, the permutation P = {1, 3, 2} will use the exact 9 miles wires in total.

To understand the first two cases, you can see the following figures:



In the 3rd case, the minimum length of wire required is 5, for any of the permutations {1,2} or {2,1}, so length 4 is not sufficient.

In the 4th case, for the permutation {1, 2, 3, 4, 5} we need the maximum length of the wire = 20. So minimum possible unused wire length = 25 - 20 = 5.
user: Given a square matrix of size N×N, calculate the absolute difference between the sums of its diagonals. 

-----Input-----
The first line contains a single integer N. The next N lines denote the matrix's rows, with each line containing N space-separated integers describing the columns.

-----Output-----
Print the absolute difference between the two sums of the matrix's diagonals as a single integer.

-----Constraints-----
1<=N<=10

-----Example-----
Input:
3
11 2 4
4 5 6
10 8 -12

Output:
15

-----Explanation-----
The primary diagonal is: 
11
5
-12
Sum across the primary diagonal: 11 + 5 - 12 = 4
The secondary diagonal is:
4
5
10
Sum across the secondary diagonal: 4 + 5 + 10 = 19 
Difference: |4 - 19| = 15
user: You are given a matrix of integers $A$ with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Each element of this matrix is either $0$ or $1$.
A move consists of the following steps:
- Choose two different rows $r_1$ and $r_2$ or two different columns $c_1$ and $c_2$.
- Apply the bitwise OR operation with the second row/column on the first row/column. Formally, if you chose two rows, this means you should change $A_{r_1, k}$ to $A_{r_1, k} \lor A_{r_2, k}$ for each $1 \le k \le M$; if you chose two columns, then you should change $A_{k, c_1}$ to $A_{k, c_1} \lor A_{k, c_2}$ for each $1 \le k \le N$.
For each element of the matrix, compute the minimum number of moves required to make it equal to $1$ or determine that it is impossible. Note that these answers are independent, i.e. we are starting with the initial matrix for each of them.

-----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 two space-separated integers $N$ and $M$.
- $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$-th of these lines contains $M$ integers $A_{i, 1}, A_{i, 2}, \dots, A_{i, M}$ NOT separated by spaces.

-----Output-----
For each test case, print $N$ lines. For each valid $i$, the $i$-th of these lines should contain $M$ space-separated integers; for each valid $j$, the $j$-th of these integers should be the minimum number of moves required to make $A_{i, j}$ equal to $1$, or $-1$ if it is impossible.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, M \le 1,000$
- $A_{i, j} \in \{0, 1\}$ for each valid $i, j$
- the sum of $N \cdot M$ for all test cases does not exceed $1,000,000$

-----Example Input-----
1
3 3
010
000
001

-----Example Output-----
1 0 1
2 1 1
1 1 0
user: Every Friday Chef and his N - 1 friends go for a party. At these parties, they play board games. This Friday, they are playing a game named "Boats! Boats! Boats!". In this game players have to transport cookies between Venice and Constantinople. Each player has a personal storage. The players are numbered from 1 to N, Chef is numbered 1. Rules for determining a winner are very difficult, therefore Chef asks you to write a program, which will determine who is a winner. 

There are 6 types of cookies. For each cookie in the storage player gets 1 point. Also player gets additional points if he packs his cookies in some boxes as follows: 

- A box containing 4 different types of cookies fetches 1 additional point.
- A box containing 5 different types of cookies fetches 2 additional points.
- A box containing 6 different types of cookies fetches 4 additional points.

Obviously a cookie can be put into a single box.

For each player, you know the number of cookies in his storage (denoted by c[i]), also the types of cookies in the storage given denoted by type[i][j].

Your task is to determine the winner of this game. Output "tie" if there are two or more players with same maximum score, "chef" if only Chef has a maximum score, winner's index in all other cases.

-----Input-----

The first line of input contains a single integer T denoting the number of test cases. This will be followed by T test cases.
The first line of each test case contains an integer N denoting the number of players.
The second line of each test case contains an integer c[i] denoting the number of cookies in the i-th storage, followed by c[i] space-separated integers type[i][j] which denote the type if j-th cookie in the storage i-th.

-----Output-----
For each test case, output a single line containing the answer as specified in the statement.

-----Constraints and Subtasks-----Subtask #1 : (20 points)  

- 1 ≤ T ≤ 10 
- 1 ≤  N  ≤ 100  
- 1 ≤  c[i]  ≤  100  
- 1 ≤  type[i][j]  ≤  3   
Subtask #2 : (80 points)  

- 1 ≤ T ≤ 10 
- 1 ≤  N  ≤ 100  
- 1 ≤  c[i]  ≤  100  
- 1 ≤  type[i][j]  ≤  6  

-----Example-----
Input:
3
2
6 1 2 3 4 5 6
9 3 3 3 4 4 4 5 5 5
2
5 2 3 4 5 6
7 1 1 2 2 3 3 4
3
4 1 1 2 3
4 1 2 2 3
4 1 2 3 3
Output:
chef
2
tie

-----Explanation-----
Example case 1.
Chef has total 6 cookie, so he gets 6 points for that. Also, he can put all his cookies (as they are all distinct) in a bag of size 6. It will fetch him additional 4 points. So, Chef's total points will be 10.
The second player has 9 cookies, he gets 9 points for that. Other than this, he can't create a bag with either 4, 5 or 6 distinct cookies. So, his final score is 9.
10 > 9 - Chef wins.
Example case 2.
Chef has 5 + 2 (a bag with 5 different cookies) = 7.
The second player has 7 + 1(a bag with 4 different cookies) = 8.
7 < 8 - the second player wins.
Example case 3.
Every player has 4 cookies and can't create any bag of sweets. So, it's a tie.
user: -----Indian National Olympiad in Informatics 2014-----
Nikhil’s slogan has won the contest conducted by Drongo Airlines and he is entitled to a free ticket between any two destinations served by the airline. All cities served by Drongo Airlines can be reached from each other by some sequence of connecting flights. Nikhil is allowed to take as many connecting flights as needed, but he must take the cheapest route between his chosen destinations.
Each direct flight between two cities has a fixed price. All pairs of cities connected by direct flights have flights in both directions and the price is the same in either direction. The price for a sequence of connecting flights is the sum of the prices of the direct flights along the route.
Nikhil has information about the cost of each direct flight. He would like to maximize the value of his prize, so he would like to choose a pair of cities on the network for which the cost of the cheapest route is as high as possible.
For instance, suppose the network consists of four cities {1, 2, 3, 4}, connected as shown on the right.
In this case, Nikhil should choose to travel between 1 and 4, where the cheapest route has cost 19. You can check that for all other pairs of cities, the cheapest route has a smaller cost. For instance, notice that though the direct flight from 1 to 3 costs 24, there is a cheaper route of cost 12 from 1 to 2 to 3.

-----Input Format:-----
- Line 1 : Two space-separated integers, C and F . C is the number of cities on the network, numbered 1, 2, . . . , C. F is the number of pairs of cities connected by a direct flight
- Lines 2 to F + 1 : Each line describes one direct flight between a pair of cities and consists of three integers, x, y and p, where x and y are the two cities connected by this flight and p is the price of this
For all direct flights, $x \neq y$, and no pair of cities is connected by more than one direct flight. If there is a direct flight from x to y with price p, there is also a flight from y to x with price p and exactly one of these two will be listed.

-----Output Format-----
- The output consists of a single integer, the maximum cost among the cheapest routes between all pairs of cities across the airline’s network.

-----Test Data-----
The testdata is grouped into three subtasks. In all subtasks, 2 ≤ C ≤ 230 and 1 ≤ F ≤ 23665. In addition, each subtask has the following constraints on the inputs.
- Subtask 1 (20 marks) : F = C − 1 (that is, the airline network is a tree) and p = 1 for each direct flight.
- Subtask 2 (30 marks) : There is no constraint on the shape of the network, but for each direct flight, p = 1.
- Subtask 3 (50 marks) : There is no constraint on the shape of the network, but for each direct flight, 0 ≤ p ≤ $10^5$.

-----Sample Input-----
4 5
1 2 10
1 3 24
2 3 2
2 4 15
3 4 7

-----Sample Output-----
19

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: Alice and Bob are walking on an infinite straight street. Initially, both are at the position $X=0$ and they start walking in the direction of increasing $X$. After $N$ seconds, they stop. Let's denote Alice's speed and Bob's speed during the $i$-th of these seconds by $A_i$ and $B_i$ respectively.
Sometimes, Alice and Bob walk together, i.e. with the same speed side by side. Let's define the weird distance as the total distance they walk this way. Find this weird distance.

-----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 $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains $N$ space-separated integers $B_1, B_2, \ldots, B_N$.

-----Output-----
For each test case, print a single line containing one integer ― the total weird distance. It can be proved that this distance is an integer.

-----Constraints-----
- $1 \le T \le 20$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^5$ for each valid $i$
- $1 \le B_i \le 10^5$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (30 points): $1 \le N \le 1,000$
Subtask #2 (70 points): original constraints

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

-----Example Output-----
5
0
6

-----Explanation-----
Example case 1:
- Alice and Bob walk side by side during the first second, from $X=0$ to $X=1$.
- Then, Alice starts walking faster than Bob, so they do not walk side by side during second $2$. At the end of second $2$, Alice is at $X=4$, while Bob is at $X=3$.
- During the next second, they again do not walk side by side, but Bob walks faster, so they both end up at $X=7$.
- During the last second, they both walk side by side and the distance they walk is $4$.
- Alice and Bob walk side by side during the $1$-st and $4$-th second and the total weird distance they travel is $1+4=5$.
Example case 2:
- First, Alice walks with speed $2$ and Bob walks with speed $3$, so they do not walk side by side. Alice ends up at $X=2$, while Bob ends up at $X=3$ at the end of the $1$-st second.
- Then, Alice walks with speed $3$ and Bob walks with speed $2$, so they do not walk side by side either.
- Although Alice and Bob both end up at $X=5$ at the end of the $2$-nd second, the weird distance is $0$.
Example case 3: We can see that Alice and Bob always walk together, so the weird distance is $3+3=6$.
user: Given a string consisting of only lowercase English alphabets, your task is to find the smallest palindromic substring.
In case there are multiple palindromic substrings of the same length present, print the lexicographically smallest substring. 
Formally, a substring is a contiguous sequence of characters within a string. So in a string "abcdef", "abc" is a substring whereas "adf" is not a substring.
A palindrome is a word, phrase, or sequence that reads the same backwards as forwards, e.g. madam or mom.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains of two lines of input, two integers.
- First, we have a single integer $N$ which signifies the length of the substring.
- Next, we have a string of length $N$ that only has lowercase English alphabets.

-----Output:-----
For each testcase, output in a single line the shortest palindromic substring.

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq N \leq 10^5$

-----Sample Input:-----
2
2
zy
1
cd

-----Sample Output:-----
y
c

-----EXPLANATION:-----
There are only two possibilities. "z" and "y". Since both of them have the same length. We print the lexicographically smaller substring which is y.
user: Chef has $N$ markers. There is a cap on each marker. For each valid $i$, the $i$-th marker has colour $a_i$. Initially, for each valid $i$, the colour of the cap on the $i$-th marker is also $a_i$.
Chef wants to rearrange the caps in such a way that no marker has the same colour as its cap. (Obviously, each marker must have exactly one cap.) Can he do that? If he can, find one such way to rearrange the caps. If there are multiple solutions, you may find any one.

-----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 $N$.
- The second line contains $N$ space-separated integers $a_1, a_2, \ldots, a_N$.

-----Output-----
- For each test case:
- If Chef cannot successfully rearrange the caps, print a single line containing the string "No" (without quotes).
- Otherwise, print two lines. The first line should contain the string "Yes" (without quotes). The second line should contain $N$ space-separated integers describing a valid rearrangement of caps. For each valid $i$, the $i$-th of these integers should denote the final colour of the cap on the $i$-th marker.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le a_i \le 10^9$ for each valid $i$

-----Example Input-----
2
9
1 1 1 2 2 2 3 3 3
2
1 1

-----Example Output-----
Yes
2 2 2 3 3 3 1 1 1
No
user: Harish has decided to go to Arya's hotel this morning. We all know he is crazy for masala dosas. And as usual he is always hungry. He decided to order all the masala dosas at once. But then he realised that he did not have enough money to buy all of them. So he decided to share the amount with his friend Ozil. But both of them are fans of even numbers. Both of them says they want to eat even number of dosas. Ozil is ready to put the share if and only if , he is sure that he can get even number of dosas. So given N number of dosas can you please help Harish to decide, if he will be able to get all the dosas at once from the hotel.

-----Input-----
The first line of input contains an integer T which denotes the number of test files. Next T lines contains an integer N where N is the total number of dosas.

-----Output-----
Print "YES" if both can get even number of dosas. If it is not possible print "NO".

-----Constraints-----
- 1 ≤ T ≤ 10^6
- 1 ≤ N ≤ 10^18

-----Subtasks-----
Subtask #1 : (20 points)
- 1 ≤ T ≤ 10
- 1 ≤ N≤ 100

Subtask 2 : (80 points) 

- 1 ≤ T ≤ 10^6
- 1 ≤ N≤ 10^18

-----Example-----
Input:
2 
16 
27
Output:
YES
NO
user: Gargi is thinking of a solution to a problem. Meanwhile, her friend asks her to solve another problem. Since Gargi is busy in her own problem, she seeks your help to solve the new problem.

You are given a string S containing characters a-z (lower case letters) only. You need to change the string to a new string consisting of only one letter from a-z.

For a given character S[i] in the string, if you change it to a character having lower ASCII value than the character S[i], you gain points equal to the difference in ASCII value of the old character and the new character. Similarly, for a given character S[j] in the string, if you change it to a character having higher ASCII value than the character S[j], you lose points equal to the difference in ASCII value of the old character and the new character.

However, Gargi does not like gaining or losing points. She has asked you to change the string in such a way that the total losing or gaining of points at the end of the string conversion is minimum.

Give Gargi the absolute value of the points you have at the end of the string conversion.

-----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 each of the T test case contains a string S containing only lower case characters (a-z)

-----Output-----
For each test case, output a single line containing the answer.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ |S| ≤ 100000

-----Example-----
Input:
1
abba

Output:
2

-----Explanation-----
Example case 1. The new string can be aaaa where you have +2 points at the end of string conversion or it can be bbbb where you have -2 points at the end of string conversion. Hence the output is 2.
user: Rodriguez is a happy and content farmer. He has got a square field of side length $x$. Miguel, his son has himself grown into a man and his father wants to gift him something out of which he can make a living. So he gift's his son a square piece of land cut out from a corner of his field of side length $ y (y < x) $ leaving him with a L-shaped land.
But in Spanish tradition, it is considered inauspicious to own something which is prime in number. This worries Rodriguez as he doesn't want his left out area to be a prime number leading to bad luck. Find whether the spilt will be in terms with the tradition leaving Rodriguez happy.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains two integers $x, y$. 

-----Output:-----
Print YES if Rodriguez will be happy. Otherwise print NO.

-----Constraints-----
- $1 \leq T \leq 5$
- $1 \leq y < x \leq 100000000000$

-----Sample Input:-----
2
7 5
6 5

-----Sample Output:-----
YES
NO

-----EXPLANATION:-----
In case 1 :
Left out area is 24, which is not prime.
In case 2:
Left out area is 11, which is prime.
user: Calculate the power of an army of numbers from 1 to $N$, both included.

-----Input:-----
- First line will contain a single integer $N$.

-----Output:-----
For each testcase, output in a single line containing the answer.

-----Constraints-----
- $1 \leq N \leq 5000$

-----Sample Input:-----
24

-----Sample Output:-----
5
user: Mr. X stays in a mansion whose door opens in the North. He travels every morning to meet his friend Ms. Y walking a predefined path.

To cut the distance short, one day he decides to construct a skywalk from his place to his friend’s place. Help him to find the shortest distance between the two residences.


-----Input-----

The first line contains a single positive integer T <= 100, the number of test cases. T test cases follow. The only line of each test case contains a string which is the path from X to Y. The integer value represents the distance. The character R or L represents a Right or a Left respectively.

-----Output-----

For each test case, output a single line containing the minimum distance and the direction(N,S,W,E,NE,NW,SE,SW) of Y’s residence with respect to X’s residence. The output distance should have only 1 decimal place with no approximation. Print “0.0” if X’s and Y’s residence coincide.

-----Example-----
Input:
1
2 L 2 R 2 L 1

Output:
5.0NW

Explanation
Mr. X travels 2units and then takes a Left, and then he travels 2units and takes a Right, then after travelling 2units he takes a Left and finally travels 1unit to reach Y’s residence.
(Unlike Input, Output does not have spaces between the distance and direction)
user: There is a field with plants — a grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$); out of its $NM$ cells, $K$ cells contain plants, while the rest contain weeds. Two cells are adjacent if they have a common side.
You want to build fences in the field in such a way that the following conditions hold for each cell that contains a plant:
- it is possible to move from this cell to each adjacent cell containing a plant without crossing any fences
- it is impossible to move from this cell to any cell containing weeds or to leave the grid without crossing any fences
The fences can only be built between cells or on the boundary of the grid, i.e. on the sides of cells. The total length of the built fences is the number of pairs of side-adjacent cells such that there is a fence built on their common side plus the number of sides of cells on the boundary of the grid which have fences built on them. Find the minimum required total length of fences that need to be built.

-----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 three space-separated integers $N$, $M$ and $K$.
- $K$ lines follow. Each of these lines contains two space-separated integers $r$ and $c$ denoting that the cell in row $r$ and column $c$ contains a plant.

-----Output-----
For each test case, print a single line containing one integer — the minimum required length of fences.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N, M \le 10^9$
- $1 \le K \le 10^5$
- $1 \le r \le N$
- $1 \le c \le M$
- the cells containing plants are pairwise distinct

-----Subtasks-----
Subtask #1 (30 points): $1 \le N, M \le 1,000$
Subtask #2 (70 points): original constraints

-----Example Input-----
2
4 4 9
1 4
2 1 
2 2
2 3
3 1
3 3
4 1
4 2
4 3
4 4 1
1 1

-----Example Output-----
20
4

-----Explanation-----
Example case 1: The field looks like this ('x' denotes a cell containing a plant, '.' denotes a cell containing weeds):
...x
xxx.
x.x.
xxx.

An optimal solution is to build fences around the topmost plant (with length $4$), around the remaining eight plants (with length $12$) and around the hole between them (with length $4$). The total length is $4+12+4 = 20$.
user: Given a positive integer K > 2, with prime
factorization:

K = p1^a1 * p2^a2 ... * pn^an

Compute the following:

S = a1*p1 + a2*p2 ... + an*pn.

-----Input-----
A list of <100 integers, one on each line,
all less than $2*10^{18}$.

-----Output-----
For each integer compute the super factor
sum and output it on a single line.

-----Example-----
Input:
6
7
Output:
5
7