meetforever/GRPO_CL huggingface dataset:
user: Dhote and Shweta went on a tour by plane for the first time.Dhote was surprised by the conveyor belt  at the airport.As Shweta was getting bored Dhote had an idea of playing a game with her.He asked Shweta to count the number of bags whose individual weight is greater than or equal to the half of the total number of bags on the conveyor belt.Shweta got stuck in the puzzle! Help Shweta. 

-----Input:-----
- First line will contain T$T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, one  integers N$N$.
- next line conatins N$N$ integers that represents weight of bag 

-----Output:-----
For each testcase, print required answer in new line .

-----Constraints-----
- 1≤T≤1000$1 \leq T \leq 1000$
- 1≤N≤105$1 \leq N \leq 10^5$
- 1≤weightofbag≤105$ 1\leq  weight of bag   \leq 10^5$ 

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

-----Sample Output:-----
3
user: Dio Brando has set  a goal for himself of becoming the richest and the most powerful being on earth.To achieve his goals he will do anything using either manipulation,seduction or plain violence.
Only one guy stands between his goal of conquering earth ,named Jotaro Kujo aka JoJo .Now Dio has a stand (visual manifestation of life energy  i.e, special power )  “Za Warudo” ,which can stop time itself but needs to chant few words to activate the time stopping ability of the stand.There is a code hidden inside the words and if you can decipher the code then Dio loses his power.
In order to stop Dio ,Jotaro asks your help to decipher the code since he can’t do so while fighting Dio at the same time.
You will be given a string as input and you have to find the shortest substring which contains all the characters of itself and then make a number based on the alphabetical ordering of the characters.
For example : “bbbacdaddb”
shortest substring will be “bacd” and based on the alphabetical ordering
the answer is 2134

-----NOTE:-----
A substring is a contiguous subsegment of a string. For example, "acab" is a substring of "abacaba" (it starts in position 3 and ends in position 6), but "aa" or "d" aren't substrings of this string. So the substring of the string s from position l to position r is

S[l;r]=SlSl+1…Sr.

-----Input :-----
The first line contains $T$,number of test cases.
The second line contains a string $S$.

-----Output:-----
For each test cases ,output the number you can get from the shortest string 

-----Constraints:-----
$1 \leq t \leq 100$
$1 \leq |S| \leq 10^6$

-----Test Cases:-----

-----Sample Input:-----
6

abcdfgh

urdrdrav

jojojojoj

bbbbaaa

cddfsccs

tttttttttttt   

-----Sample Output:-----
1234678

2118418418122

1015

21

46193

20

-----Explanation:-----
Test case 1: abcdfgh is the shortest substring containing all char of itself and the number is 1234678
user: The chef is placing the laddus on the large square plat. The plat has the side of length N. Each laddu takes unit sq.unit area. Cheffina comes and asks the chef one puzzle to the chef as, how many squares can be formed in this pattern with all sides of new square are parallel to the original edges of the plate.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, one integer $N$. 

-----Output:-----
For each test case, output in a single line answer as maximum squares on plate satisfying the condition.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^5$

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

-----Sample Output:-----
1
5

-----EXPLANATION:-----
For 1) Only 1 Square
For 2) 4 squares with area 1 sq.unit
1 square with area 4 sq.unit
user: Chef is making polygon cakes in his kitchen today! 
Since the judge panel is very strict, Chef's cakes must be beautiful and have sharp and precise $internal$ angles in arithmetic progression. 
Given the number of sides, $N$, of the cake Chef is baking today and also the measure of its first angle(smallest angle), $A$, find the measure of the $K^{th}$ angle.

-----Input:-----
- The first line contains a single integer $T$, the number of test cases. 
- The next $T$ lines contain three space separated integers $N$, $A$ and $K$, the number of sides of polygon, the first angle and the $K^{th}$ angle respectively. 

-----Output:-----
For each test case, print two space separated integers $X$ and $Y$, such that the $K^{th}$ angle can be written in the form of $X/Y$ and $gcd(X, Y) = 1$

-----Constraints-----
- $1 \leq T \leq 50$
- $3 \leq N \leq 1000$
- $1 \leq A \leq 1000000000$
- $1 \leq K \leq N$
- It is guaranteed the answer is always valid.

-----Sample Input:-----
1
3 30 2

-----Sample Output:-----
60 1
user: Indian National Olympiad in Informatics 2016
	Boing Inc, has N employees, numbered 1 ... N. Every employee other than Mr. Hojo (the head of the company) has a manager (P[i] denotes the manager of employee i). Thus an employee may manage any number of other employees but he reports only to one manager, so that the organization forms a tree with Mr. Hojo at the root. We say that employee B is a subordinate of employee A if B appears in the subtree rooted at A.

	Mr. Hojo, has hired Nikhil to analyze data about the employees to suggest how to identify faults in Boing Inc. Nikhil, who is just a clueless consultant, has decided to examine wealth disparity in the company. He has with him the net wealth of every employee (denoted A[i] for employee i). Note that this can be negative if the employee is in debt. He has already decided that he will present evidence that wealth falls rapidly as one goes down the organizational tree. He plans to identify a pair of employees i and j, j a subordinate of i, such A[i] - A[j] is maximum. Your task is to help him do this.

	Suppose, Boing Inc has 4 employees and the parent (P[i]) and wealth information (A[i]) for each employee are as follows:

i		1	2	3	4
A[i]		5	10	6	12
P[i]		2	-1	4	2

P[2] = -1 indicates that employee 2 has no manager, so employee 2 is Mr. Hojo.

In this case, the possible choices to consider are (2,1) with a difference in wealth of 5, (2,3) with 4, (2,4) with -2 and (4,3) with 6. So the answer is 6.


-----Input format-----
	There will be one line which contains (2*N + 1) space-separate integers. The first integer is N, giving the number of employees in the company. The next N integers A[1], .., A[N] give the wealth of the N employees. The last N integers are P[1], P[2], .., P[N], where P[i] identifies the manager of employee i. If Mr. Hojo is employee i then, P[i] = -1, indicating that he has no manager.


-----Output format-----
	One integer, which is the needed answer.


-----Test data-----
-108 ≤ A[i] ≤ 108, for all i.
Subtask 1 (30 Marks) 1 ≤ N ≤ 500.
Subtask 2 (70 Marks) 1 ≤ N ≤ 105.


-----Sample Input-----
4 5 10 6 12 2 -1 4 2

-----Sample Output-----
6
user: A tennis tournament is about to take place with $N$ players participating in it.
Every player plays with every other player exactly once and there are no ties. That is, every match has a winner and a loser. 
With Naman's birthday approaching, he wants to make sure that each player wins the same number of matches so that nobody gets disheartened.  
Your task is to determine if such a scenario can take place and if yes find one such scenario.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single integer $N$ denoting number of players.

-----Output:-----
- If it's impossible for everyone to win the same number of matches, print "NO" (without quotes).
- Otherwise print "YES" (without quotes) and then print $N$ lines , each line should consist of a string containing only 0s and 1s and should be of size $N$. 
- If the jth character in the ith line is 1 then it means in the match between $i$ and $j$ , $i$ wins. 
- You will get a WA if the output does not correspond to a valid tournament, or if the constraints are not satisfied.
- You will get also WA verdict if any 2 lines have contradicting results or if a player beats himself.

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq N \leq 100$

-----Subtasks-----
- 10 points : $2 \leq N \leq 6$
- 90 points :  Original Constraints. 

-----Sample Input:-----
2
3
2

-----Sample Output:-----
YES
010
001
100
NO

-----Explanation:-----
One such scenario for $N$ = $3$ is when player $1$ beats player $2$, player $2$ to beats player $3$ and player $3$ beats player $1$. Here all players win exactly $1$ match.
user: You like tracking airplane flights a lot. Specifically, you maintain history of an airplane’s flight at several instants and record them in your notebook. Today, you have recorded N such records h1, h2, ..., hN, denoting the heights of some airplane at several instants. These records mean that airplane was first flying on height h1, then started changing its height to h2, then from h2 to h3 and so on. The airplanes are usually on cruise control while descending or ascending, so 
you can assume that plane will smoothly increase/decrease its height from hi to hi + 1 with a constant speed. You can see that during this period, the airplane will cover all possible heights in the range [min(hi, hi+1), max(hi, hi+1)] (both inclusive). It is easy to see that the plane will be at all possible heights in the range exactly a single instant of time during this ascend/descend.

You are interested in finding the maximum integer K such that the plane was at some height exactly K times during the flight.

-----Input-----
There is a single test case.
First line of the input contains an integer N denoting the number of records of heights of the plane.
Second line contains N space separated integers denoting h1, h2, ..., hN.

-----Output-----
Output a single maximum integer K in one line, such that the plane was at some height exactly K times during the flight.

-----Constraints-----
- hi ≠ hi+1

-----Subtasks-----
Subtask #1: (30 points)
- 1 ≤ N ≤ 1000
- 1 ≤ hi ≤ 1000

Subtask #2: (70 points)
- 1 ≤ N ≤ 105
- 1 ≤ hi ≤ 109

-----Example-----
Input:
5
1 2 3 2 3

Output:
3

-----Explanation-----

The flight can be draw as:

3  /\/
2 /
1

There are infinitely many heights at which the plane was 3 times during the flight, for example 2.5, 2.1. Notice that the plane was only 2 times at height 2. Moreover, there are no height at which the plane was more than 3 times, so the answer is 3.
user: You must have tried to solve the Rubik’s cube. You might even have succeeded at it. Rubik’s cube is a 3x3x3 cube which has 6 different color for each face.The Rubik’s cube is made from 26 smaller pieces which are called cubies. There are 6 cubies at the centre of each face and these comprise of a single color. There are 8 cubies at the 8 corners which comprise of exactly 3 colors. The 12 reamaining cubies comprise of exactly 2 colors.

Apple has come up with a variation of the Rubik’s Cube, it’s the Rubik’s cuboid which has different colors on its 6 faces. The Rubik’s Cuboid comes in various sizes represented by M x N x O (M,N,O are natural numbers). Apple is giving away 100 Rubik’s cuboid for free to people who can answer a simple questions. Apple wants to know, in a Rubik’s cuboid with arbitrary dimensions, how many cubies would be there, which comprise of exactly 2 color.

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

Each test case comprises of 3 natural numbers, M,N & O, which denote the dimensions of the Rubiks Cuboid.

-----Output-----
For each test case you are required to output the number of  cubies which comprise of 2 squares, each of which is of a different color.

-----Constraints-----
- 1 ≤ T ≤ <1000
- 1 ≤ M ≤ <100000
- 1 ≤ N ≤ <100000
- 1 ≤ O ≤ <100000

-----Example-----
Input:
1
3
3
3

Output:

12
user: The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$

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

-----Sample Output:-----
12
21
123
231
312
1234
2341
3412
4123

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: You are given $N$ gears numbered $1$ through $N$. For each valid $i$, gear $i$ has $A_i$ teeth. In the beginning, no gear is connected to any other. Your task is to process $M$ queries and simulate the gears' mechanism. There are three types of queries:
- Type 1: Change the number of teeth of gear $X$ to $C$.
- Type 2: Connect two gears $X$ and $Y$.
- Type 3: Find the speed of rotation of gear $Y$ if gear $X$ rotates with speed $V$.
It is known that if gear $i$ is directly connected to gear $j$ and gear $i$ rotates with speed $V$, then gear $j$ will rotate with speed $-V A_i / A_j$, where the sign of rotation speed denotes the direction of rotation (so minus here denotes rotation in the opposite direction). You may also notice that gears can be blocked in some cases. This happens when some gear would have to rotate in different directions. If a gear is connected to any blocked gear, it is also blocked. For example, if three gears are connected to each other, this configuration can not rotate at all, and if we connect a fourth gear to these three, it will also be blocked and not rotate.

-----Input-----
- The first line of the input contains two space-separated integers $N$ and $M$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.
- The following $M$ lines describe queries. Each of these lines begins with an integer $T$ denoting the type of the current query.
- If $T = 1$, it is followed by a space and two space-separated integers $X$ and $C$.
- If $T = 2$, it is followed by a space and two space-separated integers $X$ and $Y$.
- If $T = 3$, it is followed by a space and three space-separated integers $X$, $Y$ and $V$.

-----Output-----
For each query of type 3, print a single line containing two integers separated by a slash '/' — the numerator and denominator of the rotation speed of the given gear expressed as an irreducible fraction (even if this speed is an integer), or $0$ if the gear does not rotate at all.

-----Constraints-----
- $1 \le N \le 10^5$
- $1 \le M \le 2\cdot 10^5$
- $6 \le A_i \le 10^6$ for each valid $i$
- $1 \le X, Y \le N$
- $1 \le C, V \le 10^6$

-----Subtasks-----
Subtask #1 (30 points):
- $N \le 2,000$
- $M \le 5,000$
Subtask #2 (70 points): original constraints

-----Example Input-----
4 10
6 8 10 13
3 1 2 2
2 1 2
3 1 2 3
2 2 3
1 1 7
3 1 3 10
2 3 1
3 1 3 2
2 1 4
3 1 4 6

-----Example Output-----
0
-9/4
7/1
0
0

-----Explanation-----
For the first query of type 3, there are no connections between gears, so the answer is $0$.
For the second query of type 3, we can calculate the rotation speed using the formula $-3\cdot\frac{6}{8} = \frac{-9}{4}$.
For the third query of type 3, we can use the formula twice, so the speed of the second gear is $-10\cdot\frac{7}{8} = -\frac{35}{4}$, and the speed of the third gear is $-(-\frac{35}{4})\frac{8}{10} = \frac{7}{1}$.
For the last query of type 3, all gears are blocked.
user: Given an alphanumeric string made up of digits and lower case Latin characters only, find the sum of all the digit characters in the string.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. Then T test cases follow.
- Each test case is described with a single line containing a string S, the alphanumeric string.

-----Output-----
- For each test case, output a single line containing the sum of all the digit characters in that string.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ |S| ≤ 1000, where |S| is the length of the string S.

-----Example-----
Input:
1
ab1231da

Output:
7

-----Explanation-----
The digits in this string are 1, 2, 3 and 1. Hence, the sum of all of them is 7.
user: You are given an integer sequence $A_1, A_2, \ldots, A_N$. For any pair of integers $(l, r)$ such that $1 \le l \le r \le N$, let's define $\mathrm{OR}(l, r)$ as $A_l \lor A_{l+1} \lor \ldots \lor A_r$. Here, $\lor$ is the bitwise OR operator.
In total, there are $\frac{N(N+1)}{2}$ possible pairs $(l, r)$, i.e. $\frac{N(N+1)}{2}$ possible values of $\mathrm{OR}(l, r)$. Determine if all these values are pairwise distinct.

-----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, print a single line containing the string "YES" if all values of $\mathrm{OR}(l, r)$ are pairwise distinct or "NO" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 300$
- $1 \le N \le 10^5$
- $0 \le A_i \le 10^{18}$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $3 \cdot 10^5$

-----Example Input-----
4
3
1 2 7
2
1 2
3
6 5 8
5
12 32 45 23 47

-----Example Output-----
NO
YES
YES
NO

-----Explanation-----
Example case 1: The values of $\mathrm{OR}(l, r)$ are $1, 2, 7, 3, 7, 7$ (corresponding to the contiguous subsequences $[1], [2], [7], [1,2], [2,7], [1,2,7]$ respectively). We can see that these values are not pairwise distinct.
Example case 2: The values of $\mathrm{OR}(l, r)$ are $1, 2, 3$ (corresponding to the contiguous subsequences $[1], [2], [1, 2]$ respectively) and they are pairwise distinct.
user: In this problem the input will consist of a number of lines of English text consisting of the letters of the English alphabet, the punctuation marks ' (apostrophe), . (full stop), , (comma), ; (semicolon), :(colon) and white space characters (blank, newline).
Your task is print the words in the text in lexicographic order (that is, dictionary order). Each word should appear exactly once in your list. You can ignore the case (for instance, "The" and "the" are to be treated as the same word). There should be no uppercase letters in the output.
For example, consider the following candidate for the input text: 
This is a sample piece of text to illustrate this 
problem.

The corresponding output would read as:
a
illustrate
is
of
piece
problem
sample
text
this
to

-----Input format-----
- The first line of input contains a single integer $N$, indicating the number of lines in the input.
- This is followed by $N$ lines of input text.

-----Output format-----
- The first line of output contains a single integer $M$ indicating the number of distinct words in the given text. 
- The next $M$ lines list out these words in lexicographic order.

-----Constraints-----
- $1 \leq N \leq 10000$
- There are at most 80 characters in each line.
- There are at the most 1000 distinct words in the given text.

-----Sample Input-----
2
This is a sample piece of text to illustrate this 
problem. 

-----Sample Output-----
10
a
illustrate
is
of
piece
problem
sample
text
this
to
user: Kajaria has an empty bag and 2 types of tiles - 
tiles of type $1$ have the number $X$ written and those of type $2$ have the number $Y$ written on them. He has an infinite supply of both type of tiles.
In one move, Kajaria adds exactly $1$ tile to the bag. He adds a tile of type $1$ with probability $p$ and a tile of type $2$ with probability $(1 - p)$.
If $2$ tiles in the bag have the same number written on them (say $Z$), they are merged into a single tile of twice that number ($2Z$).
Find the expected number of moves to reach the first tile with number $S$ written on it.
Notes on merging: 
- Consider that the bag contains tiles $(5, 10, 20, 40)$ and if the new tile added is $5$, then it would merge with the existing $5$ and the bag would now contain $(10, 10, 20, 40)$. The tiles $10$ (already present) and $10$ (newly formed) would then merge in the same move to form $(20, 20, 40)$, and that will form $(40, 40)$, which will form $(80)$.
Kajaria guarantees that:
- $X$ and $Y$ are not divisible by each other.
- A tile with number $S$ can be formed.

-----Input-----
- First line contains a single integer $T$ - the total no. of testcases
- Each testcase is described by $2$ lines:
- $X, Y, S$ - $3$ space-separated natural numbers
- $u, v$ - $2$ space-separated natural numbers describing the probability $p$
The value of $p$ is provided as a fraction in its lowest form $u/v$ ($u$ and $v$ are co-prime)

-----Output-----
- For each testcase, if the expected number of moves can be expressed as a fraction $p/q$ in its lowest form, print $(p * q^{-1})$ modulo $10^9 + 7$, where $q^{-1}$ denotes the modular inverse of $q$ wrt $10^9 + 7$.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $2 \leq X, Y \leq 5 * 10^{17}$
- $1 \leq S \leq 10^{18}$
- $1 \leq u < v \leq 10^{9}$

-----Sample Input-----
1
5 3 96
1 3

-----Sample Output-----
48
user: There are n cards of different colours placed in a line, each of them can be either red, green or blue cards. Count the minimum number of cards to withdraw from the line so that no two adjacent cards have the same colour.

-----Input-----
- The first line of each input contains an integer n— the total number of cards.
- The next line of the input contains a string s, which represents the colours of the cards. We'll consider the cards in a line numbered from 1 to n from left to right. Then the $i^t$$^h$ alphabet equals "G", if the $i^t$$^h$ card is green, "R" if the card is red,  and "B", if it's blue.

-----Output-----
- Print a single integer — the answer to the problem.

-----Constraints-----
- $1 \leq n \leq 50$

-----Sample Input 1:-----
5
RGGBG

-----Sample Input 2:-----
5
RRRRR

-----Sample Input 3:-----
2
BB

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

-----Sample Output 2:-----
4

-----Sample Output 3:-----
1
user: Devu loves to play with his dear mouse Jerry.  One day they play a game on 2 dimensional grid of dimensions n * n (n ≥ 2). Jerry is currently at coordinates (sx, sy) and wants to move to location (ex, ey) where cheese is placed by Devu. Also Devu is very cunning and has placed a bomb at location (bx, by). All these three locations are distinct. 

In a single move, Jerry can go either up, down, left or right in the grid such that it never goes out of the grid. Also, it has to avoid the bomb. Find out minimum number of moves Jerry needs. It is guaranteed that it is always possible to do so.

-----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 seven space separated integers n, sx, sy , ex, ey, bx, by. 

-----Output-----
- For each test case, output a single line containing an integer corresponding to minimum number of moves Jerry needs.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 2 ≤ n ≤ 20
-  1 ≤ sx, sy , ex, ey, bx, by ≤ n 
- No two or more poitns in the three points are same.

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

Output:
2
4

-----Explanation-----
Example case 1. ...
Jerry will move directly (1, 1) to (2, 1) and then to (2, 2) in total 2 moves.

Example case 2. ...