meetforever/GRPO_CL huggingface dataset:
user: Chef is very fond of horses. He enjoys watching them race. As expected, he has a stable full of horses. He, along with his friends, goes to his stable during the weekends to watch a few of these horses race. Chef wants his friends to enjoy the race and so he wants the race to be close. This can happen only if the horses are comparable on their skill i.e. the difference in their skills is less.
There are N horses in the stable. The skill of the horse i is represented by an integer S[i]. The Chef needs to pick 2 horses for the race such that the difference in their skills is minimum. This way, he would be able to host a very interesting race. Your task is to help him do this and report the minimum difference that is possible between 2 horses in the race.

-----Input:-----
First line of the input file contains a single integer T, the number of test cases.

Every test case starts with a line containing the integer N.

The next line contains N space separated integers where the i-th integer is S[i].

-----Output:-----
For each test case, output a single line containing the minimum difference that is possible.

-----Constraints:-----
1 ≤ T ≤ 10
2 ≤ N ≤ 5000
1 ≤ S[i] ≤ 1000000000

-----Example:-----Input:
1
5
4 9 1 32 13

Output:
3

Explanation: The minimum difference can be achieved if we pick horses with skills 1 and 4 for the race.
user: Special Numbers 
Mani has encountered a problem on Special numbers in Bytecode. A number S is called a special number if its digits are in an arithmetic progression modulo 10. He has an array consisting of all numbers from 1 to N and needs your help to find the number of special numbers in the array. He has promised you a significant share of the prize money if he wins the contest :p 
Note:
123,99,802 are special numbers.
146 is not a special number 

-----Input-----

Input consists of 1 integer - the value of N

-----Output-----
Print one integer in the first line - the solution to this problem

-----Constraints-----
- 1 ≤ Number of digits in N ≤ 105

Example

Input

123

Output

102
user: Omy and Ish were learning the pattern printing. In order to learn they give themselves a task. In this task they are given a string and they have to form a pyramid with the pattern as follows:
RowNumber are one based indexed.
- 
If (RowNumber % 3 == 0) then string is written in left to right while in other cases it is written in right to left order.
- 
if the string end it will be started again and end of the pyramid need not to be the end of string.
For eg: string is “$CODING$” and height of pyramid is “$5$”
C
D O
I N G
I D O C
D O C G N

Omi will be asked $Q$ queries and he has to tell the frequency of a character  C in that particular row $R$ of pyramid.

-----Input:-----
- First line will contain $N$, height of pyramid.
- Next line contain a string consists only of Uppercase English Alphabets, length not exceed $10^6$
- Third line contain a single integer $Q$, the number of queries to be asked.
- Each query contain two space separated integers, $R$ and $C$, where $R$ is the row number and $C$ is the character.

-----Output:-----
- For each query, output in a single line the frequency of the alphabet in the given row.

-----Constraints:-----
- $1$ $\leq$ $N$ $\leq$ $10$^$18$
- $1$ $\leq$ $Q$ $\leq$ $50000$
- $1 \leq R \leq N$
- $A \leq C \leq Z$

-----Sample Input:-----
5
CODING
2
1 C
2 D

-----Sample Output:-----
1
1
user: Given an array $A$ of size $N$ , count number of pairs of index $i,j$ such that $A_i$ is even, $A_j$ is odd and $i < j$

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases.   
- The first line of each test case contains integer $N$.    
- The second line of each test case contains $N$ space separated integers $A_i$. 

-----Output-----
For each test case, print a single line containing an integer denoting number of pairs.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le N \le 10^5$ 
- $1 \le A_i \le 10^9$
- Sum of $N$ over all test cases doesn't exceed $10^6 $ 

-----Subtasks-----
Subtask #1 (30 points):
- $2 \le N \le 100$ 
Subtask #2 (70 points): original constraints

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

-----Example Output-----
2
3

-----Explanation-----
Example case 1:$(A_2,A_3)$ and $(A_2,A_4)$ . 
Example case 2:$(A_2,A_3)$ , $(A_2,A_5)$ and $(A_4,A_5)$  .
user: This problem is about sequences of positive integers $a_1,a_2,...,a_N$. A subsequence of a sequence is anything obtained by dropping some of the elements. For example, $3,7,11,3$ is a subsequence of $6,3,11,5,7,4,3,11,5,3$ , but $3,3,7$ is not a subsequence of $6,3,11,5,7,4,3,11,5,3$ .
A fully dividing sequence is a sequence $a_1,a_2,...,a_N$ where $a_i$ divides $a_j$ whenever $i < j$. For example, $3,15,60,720$ is a fully dividing sequence.
Given a sequence of integers your aim is to find the length of the longest fully dividing subsequence of this sequence.
Consider the sequence $2,3,7,8,14,39,145,76,320$
It has a fully dividing sequence of length $3$, namely $2,8,320$, but none of length $4$ or greater.
Consider the sequence $2,11,16,12,36,60,71,17,29,144,288,129,432,993$.
It has two fully dividing subsequences of length $5$,
- $2,11,16,12,36,60,71,17,29,144,288,129,432,993$ and
- $2,11,16,12,36,60,71,17,29,144,288,129,432,993$
and none of length $6$ or greater.

-----Input:-----
The first line of input contains a single positive integer $N$ indicating the length of the input sequence. Lines $2,...,N+1$ contain one integer each. The integer on line $i+1$ is $a_i$.

-----Output:-----
Your output should consist of a single integer indicating the length of the longest fully dividing subsequence of the input sequence.

-----Constraints:-----
- $1 \leq N \leq 10000$
- $1 \leq a_i \leq 1000000000$

-----Sample input 1:-----
9
2 
3 
7 
8 
14 
39 
145 
76 
320

-----Sample output 1:-----
3

-----Sample input 2:-----
14
2
11 
16 
12 
36 
60 
71 
17 
29 
144 
288 
129 
432 
993

-----Sample output 2:-----
5
user: Problem Statement:Captain America and Iron Man are at WAR and the rage inside Iron Man is rising.

But Iron Man faces a problem to identify the location of Captain America.

There are N buildings situtaed adjacently to each other and Captain America can be at any building.

Iron Man has to arrange the Buildings from 1 to N is such a way that Value(i.e abs(Building Number -Position of Building))=K for every building.

Can You help Iron Man to Find The Arrangement of the Buildings?

P.S- If no arrangement exist, then print         
“CAPTAIN AMERICA EVADES”.

Input Format:
The first line of input contains a single integer,T, denoting the number of test cases.

Each of the T  subsequent lines contains 2 space-separated integers describing the respective N and K values for a test case.

Output Format:
On a new line for each test case, 

Print the lexicographically smallest arrangement; 

If no absolute arrangement exists, print “CAPTAIN AMERICA EVADES”.

Constraints:
SubTask#1
1<=T<=10

1<=N<=10^5

0<=K<=N

SubTask#2
Original Constraints..

SubTask#3
Original Constraints..

Sample Input:
3

2 1

3 0

3 2

Sample Output:

2 1

1 2 3

CAPTAIN AMERICA EVADES

Explanation:
Case 1:

N=2 and K=1

Therefore the arrangement is [2,1].

Case 2:

N=3 and K=0

Therefore arrangement is [1,2,3].
user: Back in 2015, Usain Bolt announced that he'll be retiring after the 2017 World Championship. Though his final season did not end gloriously, we all know that he is a true legend and we witnessed his peak during 2008 - 2013. 
Post retirement, Usain Bolt is still leading an adventurous life. He's exploring the unexplored parts of the globe. But sometimes he gets bored, and reads questions asked about him on Quora. One such question he read was, "Who would win a race between Usain Bolt and a tiger if the race is on a straight line track and the tiger is $distancetoBolt$ meters behind Bolt? The finishing point is $finish$ meters away from Bolt's starting position. The tiger starts with an initial speed of $0$ $meter/second$, and will accelerate itself with $tigerAccelaration$ $m/s^2$. Bolt can run with a constant speed of $boltSpeed$ $m/s$ from start to finish. Given these values, find out who will win the race - Bolt or the tiger? "
Note that Bolt will win the race if and only if he touches the finishing line before the tiger touches it. If both of them finish together, the tiger is announced as the winner since Bolt was given an initial advantage. See the figure below for more clarity.

Since Bolt was busy practicing in the tracks during his Physics school classes, he is asking for your help to solve the question. Can you please help him?
He just remembers two formulae from the class, and thinks that they will be useful to you:
$Displacement (S) $ = $ut$ +$ (1/2)at^2$ where $u$ is the initial velocity , #$ $is the acceleration and $t$ is the time taken.
$Velocity$ = $Displacement /Time$

-----Input:-----
- The first line will contain $T$, the number of testcases. Then the description of each test case follow. 
- Each test case contains 4 integers $finish, distancetoBolt, tigerAccelaration, boltSpeed$. 

-----Output:-----
For each testcase, output in a single line, the word "Bolt" or "Tiger" without quotes, depending on whether Bolt wins or the tiger wins.

-----Constraints-----
- $1 \leq T \leq 100000$
- $1 \leq finish\leq 10^5$
- $1 \leq distancetoBolt\leq 10^5$
- $1 \leq tigerAccelaration\leq 10^5$
- $1 \leq boltSpeed\leq 10^5$

-----Sample Input:-----
2
10 100 10 10
100 10 5 10

-----Sample Output:-----
Bolt
Tiger
user: You are given a sequence of non-negative integers $A_1, A_2, \ldots, A_N$. At most once, you may choose a non-negative integer $X$ and for each valid $i$, change $A_i$ to $A_i \oplus X$ ($\oplus$ denotes bitwise XOR).
Find the minimum possible value of the sum of all elements of the resulting sequence.

-----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 the input 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, print a single line containing one integer ― the minimum possible sum.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $1 \le N \le 10^3$
- $1 \le A_i \le 10^3$ for each valid $i$
Subtask #2 (50 points): original constraints

-----Example Input-----
3
5
2 3 4 5 6
4
7 7 7 7
3
1 1 3

-----Example Output-----
14
0
2

-----Explanation-----
Example case 1: If we choose $X = 6$, the sequence becomes $(4, 5, 2, 3, 0)$.
Example case 2: We can choose $X = 7$ to make all elements of the resulting sequence equal to $0$.
Example case 3: We can choose $X = 1$. The sequence becomes $(0, 0, 2)$, with sum $2$.
user: Chef and Paja are bored, so they are playing an infinite game of ping pong. The rules of the game are as follows:
- The players play an infinite number of games. At the end of each game, the player who won it scores a point.
- In each game, one of the players serves. Chef serves in the first game.
- After every $K$ points are scored (regardless of which players scored them), i.e. whenever $K$ games have been played since the last time the serving player changed, the player that serves in the subsequent games changes: if Chef served in the game that just finished, then Paja will serve in the next game and all subsequent games until the serving player changes again; if Paja served, then Chef will serve.
The players got a little too caught up in the game and they forgot who is supposed to serve in the next game. Will you help them determine that? So far, Chef has scored $X$ points and Paja has scored $Y$ points.

-----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 three space-separated integers $X$, $Y$ and $K$.

-----Output-----
For each test case, print a single line containing the string "Chef" if Chef is supposed to serve next or "Paja" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 50$
- $0 \le X, Y \le 10^9$
- $1 \le K \le 10^9$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
3
1 3 3
5 7 2
38657 76322 564

-----Example Output-----
Paja
Chef
Paja

-----Explanation-----
Example case 1: Chef served for the first three games, after that Paja started serving. He only served in one game, so he is supposed to serve next.
user: Theatre Square in the capital city of Berland has a rectangular shape with the size n × m meters. On the occasion of the city's anniversary, a decision was taken to pave the Square with square granite flagstones. Each flagstone is of the size a × a.
What is the least number of flagstones needed to pave the Square? It's allowed to cover the surface larger than the Theatre Square, but the Square has to be covered. It's not allowed to break the flagstones. The sides of flagstones should be parallel to the sides of the Square.
Input
The input contains three positive integer numbers in the first line: n,  m and a (1 ≤  n, m, a ≤ 10^9).
Output
Print the needed number of flagstones in new line.
Examples
input
6 6 4
output
4
user: The Chef once decided to prepare some nice dishes on his birthday. There are N items kept on his shelf linearly from position 1 to N. Taste of the i-th item is denoted by a integer Ai.

He wants to make Q dishes. A dish will be made using some ingredients in the continuous range AL, AL + 1, , , AR (1-base indexing). Quality of the dish will be determined by the ingredient with minimum taste.

Chef wants help of his assistant Rupsa to find out sum and product of qualities of the dishes. As product of the qualities of the dishes could be very large, print it modulo 109 + 7. Also, you are given an integer K and you are assured that for each dish, the size of continuous range of the ingredients (i.e. R - L + 1) will always lie between K and 2 * K, both inclusive.

Method of generation of Array A 

You are given non-negative integer parameters a, b, c, d, e, f, r, s, t, m, A[1]

for x = 2 to N:
	if(t^x mod s  <= r)        // Here t^x signifies "t to the power of x"
		A[x] = (a*A[x-1]^2 + b*A[x-1] + c) mod m
	else
		A[x] = (d*A[x-1]^2 + e*A[x-1] + f) mod m

Method of generation of range of ingredients for Q dishes 

You are given non-negative integer parameters L1, La, Lc, Lm, D1, Da, Dc, Dm

for i = 1 to Q:
	L1 = (La * L1 + Lc) mod Lm;
	D1 = (Da * D1 + Dc) mod Dm; 
	L = L1 + 1;
	R = min(L + K - 1 + D1, N);

-----Input-----
- The first line contains three integers N, K and Q.
- The second line contains the integers a, b, c, d, e, f, r, s, t, m, and A[1].
- Then third line contains the integers L1, La, Lc, Lm, D1, Da, Dc, and Dm

-----Output-----
Output two space separated integers:

- The sum of qualities of the dishes.
- The product of qualities of the dishes modulo 109+7.

-----Constraints-----
- 1 ≤ N, Q ≤ 107
- 1 ≤ K ≤ N
- 0 ≤ a, b, c, d, e, f, r, s, t, m, A[1] ≤ 109+7
- 1 ≤ Lm ≤ N - K + 1
- 1 ≤ Dm ≤ K + 1
- 1 ≤ La, Lc ≤ Lm
- 1 ≤ Da, Dc ≤ Dm
- 1 ≤ L1 ≤ N
- 1 ≤ D1 ≤ K

-----Sub tasks-----
- Subtask #1: 1 ≤ N, Q ≤ 1000 (10 points)
- Subtask #2: 1 ≤ Q ≤ 104 (20 points)
- Subtask #3: original constraints (70 points)

-----Example-----
Input:
4 2 1
1 1 1 1 1 1 1 1 1 100 1 
1 1 1 3 1 1 1 2

Output:
13 13

-----Explanation-----
- The array A comes out to be {1, 3, 13, 83} and the first dish has L = 3 and R = 4. The minimum in this range is 13, thus the sum and product both are 13 and hence the answer.

-----Note-----
Multiplier for C# and Java have been reduced to 1.5 instead of 2.
user: January and February are usually very cold in ChefLand. The temperature may reach -20 and even -30 degrees Celsius. Because of that, many people seal up windows in their houses.
Sergey also lives in ChefLand. He wants to seal the window in his house. The window has the shape of a   simple convex polygon with N vertices.
For the sealing, there are M kinds of sticky stripes, which are sold in the shops. The stripe of the ith type has the length of Li millimeters and the cost of Ci rubles.
The sealing process consists in picking the stripe and sticking it on the border of the window. The stripe can't be cut (it is made of very lasting material) and can only be put straight, without foldings. It is not necessary to put the strip strictly on the window border, it can possibly extend outside the border side of window too (by any possible amount). The window is considered sealed up if every point on its' border is covered with at least one stripe.
Now Sergey is curious about the stripes he needs to buy. He wonders about the cheapest cost, at which he can seal his window. Please help him.

-----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 test case contains a single integer N denoting the number of number of vertices in the polygon denoting Sergey's window.
Each of the following N lines contains a pair of space-separated integer numbers Xi Yi, denoting the coordinates of the ith points.
The following line contains a single integer M denoting the number of types of sticky stripe which is sold in the shop.
Each of the following M lines contains a pair of space-separated integers Li Ci denoting the length and the cost of the sticky stripe of the ith type respectively.

-----Output-----
For each test case, output a single line containing the minimum cost of sealing up the window.

-----Constraints-----
- 1 ≤ T ≤ 10
- The coordinates of the window are given either in clockwise or in a counter-clockwise order.
- No three or more vertices lie on the same line (i.e. are collinear).
- 0 ≤ Xi, Yi ≤ 106
- 1 ≤ Li, Ci ≤ 106

-----Subtasks-----
- Subtask #1 (17 points): 3 ≤ N ≤ 10,  M = 1
- Subtask #2 (24 points): 3 ≤ N ≤ 42, M ≤ 2
- Subtask #3 (59 points): 3 ≤ N ≤ 2000, 1 ≤ M ≤ 10

-----Example-----
Input:1
4
0 0
1000 0
1000 2000
0 2000
2
1000 10
2000 15

Output:50

-----Explanation-----
Example case 1. In this case, Sergey's window is a rectangle with the side lengths of 1000 and 2000. There are two types of the sticky stripes in the shop - the one of the length 1000 with the cost of 10 rubles and with the length of 2000 and the cost of 15 rubles. The optimal solution would be to buy 2 stripes of the first type 2 stripes of the second type. The cost will be 2 × 15 + 2 × 10 = 50 rubles.
user: Supermarket Dilemma
Chef is going to local supermarket but there appears a problem with chef as he is confused about which Supermarket he can choose to go as he is not able to decide whether he can park his car in that particular supermarket’s parking lot or not! There are N parking slots in each supermarket which are marked from 1,2,3,4…N.
Chef will go to that supermarket in which he gets to know that there is exactly 1 empty parking slot having number K that exactly divides the total number of slots (N) available in that supermarket.
The 1st and Nth parking slots are always occupied by the staff of every supermarket. Rest parking slots are empty as Chef is arriving early morning to the supermarket.
Now Chef needs your help in determining whether he can park his car in a supermarket or not!
Input
The first line contains the single integer N showing how many supermarkets are there for the chef to choose.
The next N lines contain a number ‘ai’ which represents the total parking slots available in ith supermarket.
Output
You need to output "YES" (without the quotes), if a supermarket can be reached by Chef, and "NO" (without the quotes), if it can't.
Constraints
1<=N<=10^5
1<=ai<=10^12
Sample Input :
2
4
5
Sample Output :
YES
NO
user: You are given an integer sequence $A_1, A_2, \ldots, A_N$ and an integer $X$. Consider a $N \times N$ matrix $B$, where $B_{i,j} = A_i + A_j$ for each valid $i$ and $j$.
You need to find the number of square submatrices of $B$ such that the sum of their elements is $X$. Formally, find the number of quartets $(x_1, y_1, x_2, y_2)$ such that $1 \le x_1 \le x_2 \le N$, $1 \le y_1 \le y_2 \le N$, $x_2-x_1 = y_2-y_1$ and $\sum_{i=x_1}^{x_2}\sum_{j=y_1}^{y_2} B_{i,j} = X$.

-----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 $X$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the number of square submatrices with sum $X$.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le X \le 10^6$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points): the sum of $N$ over all test cases does not exceed $1,000$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
5 36
1 2 3 1 12
4 54
3 3 3 3

-----Example Output-----
6
4
user: Mr. Krabs loves money. He enters a bank and sees that there are n rooms arranged in a row. The only rooms with doors are the two rooms on either corner. Initially, all the rooms are locked (including the corner ones). To enter a room, it must be unlocked with a key.
Mr. Krabs is able to steal k keys from the sleeping night guard. Each key can be used to unlock only one room. To reach one of the inner rooms, he has to unlock an adjacent room first.
Eg: If there are 5 rooms labelled: 1 2 3 4 5
Only Rooms 1 and 5 can be accessed initially. To unlock room 2, either room 1 or room 3 must be unlocked. Similarly to unlock Room 4, he must unlock room 5 or room 3 first.
Each room has some money in it. The money present in room i is given by A[i]. Using the k keys, calculate what is the maximum possible amount of money obtainable.

-----Input:-----
- First line will contain n,  number of rooms.
- Second line will contain space separated integers, denoting A[i], money present in each room.
- Third line will contain an integer, k, the number of keys available.

-----Output:-----
Maximum money obtained.

-----Constraints-----
- 1 <= Number of Rooms <= 10^5
- 1 <= A[i] <= 10^4
- 1 <= k <= Number of Rooms

-----Subtasks-----
- 40 points : 1 <= Number of Rooms <= 100
- 60 points : Number of Rooms > 100

-----Sample Input:-----
7
1 2 3 4 5 6 1
3

-----Sample Output:-----
12

-----Explanation:-----
For the first step, Mr. Krabs can only unlock the room at the left corner or the right corner. If he unlocks the room in the right corner, he obtains 1 dollar. He can then go on to unlock the second last room and gain 6 dollars, for a total of 7 dollars. Finally he can unlock the third last room and get 5 dollars, for a total of 12 dollars. 
This is the maximum amount of money he can get with only 3 keys.