meetforever/GRPO_CL huggingface dataset:
user: Devu and Churu love to play games a lot. Today, they have an array A consisting of N positive integers. First they listed all N × (N+1) / 2 non-empty continuous subarrays of the array A on a piece of paper and then replaced all the subarrays on the paper with the maximum element present in the respective subarray.
Devu and Churu decided to play a game with numbers on the paper. They both have decided to make moves turn by turn. In one turn, the player picks some number from the list and discards that number. The one who is not able to make a valid move will be the loser. To make the game more interesting, they decided to put some constraints on their moves.
A constraint on a game can be any of following three types :
-  > K : They are allowed to choose numbers having values strictly greater than K only.
-  < K : They are allowed to choose numbers having values strictly less than K only.
-  = K : They are allowed to choose numbers having values equal to K only.

Given M constraints and who goes first, you have to tell the outcome of each game. Print 'D' if Devu wins otherwise print 'C' without quotes.
Note that M games are independent, that is, they'll rewrite numbers by using array A after each game. (This is the task for the loser of the previous game!)

-----Input -----
First line of input contains two space separated integers N and M denoting the size of array A and number of game played by them. Next line of input contains N space-separated integers denoting elements of array A. Each of the next M lines of input contains three space-separated parameters describing a game. First two parameter are a character C ∈ {<, >, =} and an integer K denoting the constraint for that game. The last parameter is a character X ∈ {D, C} denoting the player who will start the game. 

----- Output -----
Output consists of a single line containing a string of length M made up from characters D and C only, where ith character in the string denotes the outcome of the ith game.

----- Constraints: -----
- 1 ≤ N, M ≤ 106
- 1 ≤ Ai, K ≤ 109 
- X ∈ {D, C}
- C ∈ {<, >, =}

-----Subtasks: -----
- Subtask 1 : 1 ≤ N, M ≤ 104 : ( 20 pts )
- Subtask 2 : 1 ≤ N, M ≤ 105 : ( 30 pts )
- Subtask 3 : 1 ≤ N, M ≤ 106 : ( 50 pts )

-----Example:-----
Input:
3 5
1 2 3
> 1 D
< 2 C
= 3 D
> 4 C
< 5 D

Output:
DCDDC

-----Explanation: -----
Subarray List :
- [1]

- [2]

- [3]

- [1,2]

- [2,3]

- [1,2,3]

Numbers on the paper after replacement :

- [1]

- [2]

- [3]

- [2]

- [3]

- [3]

Game 1 : There are only 5 numbers > 1 in the list.
Game 2 : There is only 1 number < 2 in the list.
Game 3 : There are only 3 numbers = 3 in the list.
Game 4 : There are no numbers > 4 in the list. So the first player cannot make his move.
Game 5 : There are 6 numbers < 5 in the list.
user: -----
RANJANA QUIZ
-----

Prof. Ranjana decided to conduct a quiz in her class. She divided all the students of her
class into groups of three. Consider that no student was left out after the division. She gave
different sets of questions to every group. A set is said to be unique if there is no other team that
received the same number of maths, science and english questions. In every set, maximum
questions for each group were related to maths, then science, and the least number of
questions were related to English. Total number of questions given to each team can be
different. 

	
	

After the test, the CR of the class asked every team to report the number of questions
they got on each subject. The CR wants to know the number of unique sets of questions that
were given to the teams, the problem is that all the students have just submitted the number of
questions of each subject but in no particular order. Help the CR to find the number of unique
sets

		
		

-----Input Format-----

Line 1 contains the number of teams ‘n’. In the next n lines, each line contains three space separated integers,i.e, the number of questions of each subject(in no particular order).
employee

-----Output-----

Print the number of unique sets

		
		

-----Example Text Case-----
Input:

5
6 5 4
2 3 7
4 6 5
7 2 3
5 3 1
	
Output:
1
user: You are given a weighted undirected graph consisting of n$n$ nodes and m$m$ edges. The nodes are numbered from 1$1$ to n$n$. The graph does not contain any multiple edges or self loops.
A walk W$W$ on the graph is a sequence of vertices (with repetitions of vertices and edges allowed) such that every adjacent pair of vertices in the sequence is an edge of the graph. We define the cost of a walk W$W$, Cost(W)$Cost(W)$, as the maximum over the weights of the edges along the walk. 
You will be given q$q$ queries. In each query, you will be given an integer X$X$.

You have to count the number of different walks W$W$ of length 4$4$ such that Cost(W)$Cost(W)$ = X$X$.

Two walks are considered different if they do not represent the same edge sequence.

-----Input:-----
- First line contains 2 integers : the number of nodes n$n$ and number of edges m$m$.
- Next m$m$ lines each describe u$u$, v$v$ and w$w$, describing an edge between u$u$ and v$v$ with weight w$w$.
- Next line contains q$q$, the number of queries.
- Next q$q$ lines each describe an integer X$X$ - the cost of the walk in the query.

-----Output:-----
For each query, output in a single line the number of different possible walks.

-----Constraints-----
- 1≤n≤100$1 \leq n \leq 100$
- 1≤m≤n(n−1)2$1 \leq m \leq \frac{n (n-1)}{2}$
- 1≤u,v≤n$1 \leq u, v \leq n$
- 1≤w≤100$1 \leq w \leq 100$
- 1≤q≤100$1 \leq q \leq 100$
- 1≤X≤100$1 \leq X \leq 100$

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

-----Sample Output:-----
2
10
36

-----EXPLANATION:-----
For X=2$X = 2$, all possible 10$10$ walks are listed below :
- 1 -> 2 -> 1 -> 2 -> 3
- 1 -> 2 -> 3 -> 2 -> 1
- 1 -> 2 -> 3 -> 2 -> 3
- 2 -> 1 -> 2 -> 3 -> 2
- 2 -> 3 -> 2 -> 1 -> 2
- 2 -> 3 -> 2 -> 3 -> 2
- 3 -> 2 -> 1 -> 2 -> 1
- 3 -> 2 -> 1 -> 2 -> 3
- 3 -> 2 -> 3 -> 2 -> 1
- 3 -> 2 -> 3 -> 2 -> 3
user: You are given an equilateral triangle ΔABC with the side BC being the base. Each side of the triangle is of length L. There are L-1 additional points on each of the sides dividing the sides into equal parts of unit lengths. Points on the sides of the triangle are called major points. Joining these points with lines parallel to the sides of ΔABC will produce some more equilateral triangles. The intersection points of these parallel lines are called minor points. 

Look at the picture below. It contains 

- Major points: A, B, C, P1, P2, Q1, Q3, R1, R4, S1, S2, S3 (note that we consider A, B, C as major points as well)
- Minor points: Q2, R2, R3
- Equilateral triangles ΔP1Q1Q2, ΔQ2S1S3, etc

We consider an equilateral triangle to be valid if

- Each of its vertices is either a major or a minor point, and
- The distance from its base (the base of a triangle is the side parallel to BC) to BC is less than the distance from the other vertex of the triangle (i.e. opposite vertex that doesn't lie on the base of triangle) to BC.

In the figure above, ΔQ2P1P2 is not a valid triangle but ΔQ2R2R3 is a valid triangle.

You will be given L, the length of the original triangle ΔABC. You need to find out the number of valid equilateral triangles with side length exactly K.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of each testcase follows.
- Each test case has one line containing two space-separated integers: L and K.

-----Output-----
For each testcase, print "Case i: ", and then the answer, where i is the testcase number, 1-indexed.

-----Constraints-----
- 1 ≤ T ≤ 500
-  1 ≤ L, K ≤ 5000

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

Output:
Case 1: 3
Case 2: 1

-----Explanation-----

The figure presented in the problem description is a triangle with side length 4.
In testcase 1, the valid triangles are ΔAR1R4, ΔP1BS3, ΔP2S1C

In testcase 2, the only valid triangle is ΔABC
user: A despotic king decided that his kingdom needed to be rid of corruption and disparity. He called his prime minister and ordered that all corrupt citizens be put to death. Moreover, he wanted this done quickly.
The wily prime minister realised that investigating every citizen to decide who was corrupt and who was not was rather difficult. So he decided on the following plan: He ordered all the citizens to appear in the court one by one and declare their wealth.
The king does not sit in the court all the time (he has other important business to attend to - for instance, meet dignitaries from neighbouring kingdoms, spend time with his family …) Whenever the king walks into the court, the prime minister pulls out the richest man who has appeared before the court so far and is still alive and beheads him for being corrupt. Since the rich are more likely to be corrupt, he hopes to get rid of most of the corrupt and the king is happy as he sees his policy being implemented enthusiastically.
Suppose the wealth of the citizens trooping into the court is
1376518911241376518911241\; 3\; 7\; 6\; 5\; 18\;  9\; 11\;  2\; 4
and the king walked in three times: the first time after the first four persons have seen the minister, the second time after the first five persons have seen the minister and, finally after the first nine persons have seen the minister.
At the king's first visit the richest person to have met the minister has wealth $7$ and he would be beheaded. At the second visit, the wealth of the richest person who has met the minister and is still alive has wealth $6$ and so he would be beheaded. At the third visit the richest person to have met the minister who is still alive has wealth $18$ and so he would be beheaded.
You may assume that the input is such that whenever the king walks in, it is always possible to behead someone.
Your aim is to write a program that will enable the prime minister to identify the richest man to have met the minister and who is still alive quickly. You may assume that no two citizens have the same wealth.

-----Input:-----
The first line of the input consists of two numbers $N$ and $M$, where $N$ is the number of citizens in the kingdom and M is the number of visits to the court by the king.
The next $N+M$ lines describe the order in which the $N$ citizens' appearances are interleaved with the $M$ visits by the king. A citizen's visit is denoted by a positive integer, signifying his wealth. You may assume that no two citizens have the same wealth. A visit by the king is denoted by $-1$.

-----Output:-----
Your output should consist of $M$ lines, where the $i^{th}$ line contains the wealth of the citizen who is beheaded at the $i^{th}$ visit of the king.

-----Constraints:-----
- $1 \leq M \leq 10000$.
- $1 \leq N \leq 100000$.
- You may assume that in $50 \%$ of the inputs $1 \leq M \leq 1000$ and $1 \leq N \leq 8000$.

-----Sample Input-----
10 3
1 
3 
7 
6 
-1 
5 
-1 
18 
9 
11
2
-1
4

-----Sample Output-----
7
6
18
user: Chef has many friends, but his best friend is Hemant. They both love to watch anime.
In fact, their weekends are meant for that only. Also, Hemant is highly into games, of which Chef is unaware. Hemant once gave a game to Chef and asked him to determine the winner of the game. Since the Chef is busy, and you are also his friend, he asked you to help him.
The Game is played between two players, $A$ and $B$. There are $N$ marbles. $A$ and $B$ plays alternately, and $A$ goes first. Each player can choose $1$ marble or $even$ number of marbles in his turn. The player who is not able to choose any marbles loses the game.

-----Input:-----
- The first line consists of a single integer $T$ denoting the number of test cases.
- The Second line contains an integers $N$, denoting the number of marbles.

-----Output:-----
For each test case, print the name of the player who loses the game.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^9$

-----Sample Input:-----
3
1 
3
7 

-----Sample Output:-----
B
A
B
user: The chef is trying to solve some series problems, Chef wants your help to code it. Chef has one number N. Help the chef to find N'th number in the series.
0, 1, 5, 14, 30, 55 …..

-----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 as the pattern.

-----Constraints-----
- $1 \leq T \leq 10^4$
- $1 \leq N \leq 10^4$

-----Sample Input:-----
3
1
7
8

-----Sample Output:-----
0
91
140
user: Snackdown 2019 is coming! There are two rounds (round A and round B) after the qualification round. From both of them, teams can qualify to the pre-elimination round. According to the rules, in each of these two rounds, teams are sorted in descending order by their score and each team with a score greater or equal to the score of the team at the $K=1500$-th place advances to the pre-elimination round (this means it is possible to have more than $K$ qualified teams from each round in the case of one or more ties after the $K$-th place).
Today, the organizers ask you to count the number of teams which would qualify for the pre-elimination round from round A for a given value of $K$ (possibly different from $1500$). They provided the scores of all teams to you; you should ensure that all teams scoring at least as many points as the $K$-th team qualify.

-----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 $K$.
- The second line contains $N$ space-separated integers $S_1, S_2, \dots, S_N$.

-----Output-----
For each test case, print a single line containing one integer — the number of qualified teams.

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

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

-----Example Output-----
2
4
user: The government of Siruseri has just commissioned one of the longest and most modern railway routes in the world. This route runs the entire length of Siruseri and passes through many of the big cities and a large number of small towns and villages in Siruseri.
The railway stations along this route have all been constructed keeping in mind the comfort of the travellers. Every station has big parking lots, comfortable waiting rooms and plenty of space for eateries. The railway authorities would like to contract out the catering services of these eateries.
The Siruseri Economic Survey has done a through feasibility study of the different stations and documented the expected profits (or losses) for the eateries in all the railway stations on this route. The authorities would like to ensure that every station is catered to. To prevent caterers from bidding only for profitable stations, the authorities have decided to give out catering contracts for contiguous segments of stations.
The minister in charge realises that one of the bidders is his bitter adversary and he has decided to hand out as useless a segment as possible to him. On the other hand, he does not want to be seen to be blatantly unfair by handing out a large loss-making section to the adversary. Instead he wants to find the largest segment whose sum is closest to $0$, so that his adversary spends all his time running a large number of canteens and makes either a small loss or a small profit or, even better, nothing at all!
In other words, if the profits/losses at the stations are $p_1, p_2, ..., p_N$ the minister would like to handover a sequence $i, i+1, ..., j$ such that the absolute value of $p_i + p_{i+1} + ... + p_j$ is minimized. If there is more than one sequence with this minimum absolute value then he would like to hand over the longest one.
For example, suppose there are $8$ stations along the line and their profitability is as follows:
$ $
Station              1    2    3    4    5    6    7    8 
Expected Profits   -20   90  -30  -20   80  -70  -60  125 

$ $
If the adversary is awarded the section $1$ through $4$, he will make a net profit of $20$. On the other hand if he is given stations $6, 7$ and $8$, he will make loss of $5$ rupees. This is the best possible value.

-----Input:-----
The first line of the input contains a single integer $N$ indicating the number of stations. The next $N$ lines (lines $2, 3, ..., N+1$) describe the profitability of the $N$ stations. Line $i+1$ contains a single integer denoting the expected profit at station $i$.

-----Output:-----
The first line contains a single integer indicating the minimum possible profit/loss among all segments. The second line contains two integers indicating the starting and ending point of the longest sequence with this minimum profit/loss. If there is more than one answer, it suffices to print one.

-----Constraints:-----
- $1 \leq N \leq 100000$.
- $-10^9 \leq p_i \leq 10^9$

-----Subtasks-----
- Subtask 1 - 40% - $1 \leq N \leq 4000$
- Subtask 2 - 60% - Original constraints

-----Sample Input-----
8
-20
90
-30
-20
80
-70
-60
125

-----Sample Output-----
-5
6 8
user: Gru wants to distribute $N$ bananas to $K$ minions on his birthday.
Gru does not like to just give everyone the same number of bananas, so instead, he wants to distribute bananas in such a way that each minion gets a $distinct$ amount of bananas. That is, no two minions should get the same number of bananas.
Gru also loves $gcd$. The higher the $gcd$, the happier Gru and the minions get. So help Gru in distributing the bananas in such a way that each Minion gets a distinct amount of bananas and gcd of this distribution is highest possible. Output this maximum gcd. If such a distribution is not possible output $-1$.
Note: You have to distribute $all$ $N$ bananas. 

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase consists of a single line of input, which has two integers: $N, K$. 

-----Output:-----
For each testcase, output in a single line the maximum gcd or -1.

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

-----Sample Input:-----
1
6 3

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

-----EXPLANATION:-----
The only possible distribution is $[1, 2, 3]$. So the answer is 1.
user: Teacher brought a fruit basket for three students. The basket contains only Apples, Mangoes and Oranges. Student A knows a value $a$, the total number of Apples and Mangoes in the Basket, B knows a value $b$, the total number of Mangoes and Oranges in the basket and Student C knows a value $c$, the total number of Oranges and Apples in the Basket. Since the teacher brought it he knows a value $d$ , the total number of fruits in the basket. You have to determine the exact number of Apples , Mangoes and Oranges in the basket separately.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, four integers $a,b,c,d$. 

-----Output:-----
For each testcase, output in a single line the number of Apples , Mangoes and Oranges in this order.

-----Constraints-----
- $1 \leq T \leq 100$
- $0 \leq a \leq 1000$
- $0 \leq b \leq 1000$
- $0 \leq c \leq 1000$
- $0 \leq d \leq 1000$ 
-The Solution always exisits

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

7 9 8 12

3 8 7 9

-----Sample Output:-----
3 4 5

1 2 6
user: There are $N$ cars (numbered $1$ through $N$) on a circular track with length $N$. For each $i$ ($2 \le i \le N$), the $i$-th of them is at a distance $i-1$ clockwise from car $1$, i.e. car $1$ needs to travel a distance $i-1$ clockwise to reach car $i$. Also, for each valid $i$, the $i$-th car has $f_i$ litres of gasoline in it initially.
You are driving car $1$ in the clockwise direction. To move one unit of distance in this direction, you need to spend $1$ litre of gasoline. When you pass another car (even if you'd run out of gasoline exactly at that point), you steal all its gasoline. Once you do not have any gasoline left, you stop.
What is the total clockwise distance travelled by your car? 

-----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 $f_1, f_2, \ldots, f_N$.

-----Output-----
For each test case, print a single line containing one integer ― the total clockwise distance travelled.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 100$
- $0 \le f_i \le 100$ for each valid $i$

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

-----Example Input-----
3
5
3 0 0 0 0
5
1 1 1 1 1
5
5 4 3 2 1

-----Example Output-----
3
5
15
user: Firdavs is living on planet F. There are $N$ cities (numbered $1$ through $N$) on this planet; let's denote the value of city $i$ by $v_i$. Firdavs can travel directly from each city to any other city. When he travels directly from city $x$ to city $y$, he needs to pay $f(x, y) = |v_y-v_x|+y-x$ coins (this number can be negative, in which case he receives $-f(x, y)$ coins).
Let's define a simple path from city $x$ to city $y$ with length $k \ge 1$ as a sequence of cities $a_1, a_2, \ldots, a_k$ such that all cities in this sequence are different, $a_1 = x$ and $a_k = y$. The cost of such a path is $\sum_{i=1}^{k-1} f(a_i, a_{i+1})$.
You need to answer some queries for Firdavs. In each query, you are given two cities $x$ and $y$, and you need to find the minimum cost of a simple path from city $x$ to city $y$. Then, you need to find the length of the longest simple path from $x$ to $y$ with this cost.

-----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 $Q$.
- The second line contains $N$ space-separated integers $v_1, v_2, \ldots, v_N$.
- The following $Q$ lines describe queries. Each of these lines contains two space-separated integers $x$ and $y$.

-----Output-----
For each query, print a single line containing two space-separated integers ― the minimum cost and the maximum length.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, Q \le 2 \cdot 10^5$
- $0 \le v_i \le 10^9$ for each valid $i$
- $1 \le x, y \le N$
- the sum of $N$ in all test cases does not exceed $5 \cdot 10^5$
- the sum of $Q$ in all test cases does not exceed $5 \cdot 10^5$

-----Subtasks-----
Subtask #1 (30 points):
- $1 \le N, Q \le 1,000$
- $v_1 < v_2 < \ldots < v_N$
- the sum of $N$ in all test cases does not exceed $5,000$
- the sum of $Q$ in all test cases does not exceed $5,000$
Subtask #2 (70 points): original constraints

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

-----Example Output-----
4 3
3 2
-1 2

-----Explanation-----
Example case 1: For the first query, there are two paths with cost $4$ from city $2$ to city $3$:
- $2 \rightarrow 1 \rightarrow 3$: cost $(|4-2|+1-2)+(|5-4|+3-1) = 4$, length $3$
- $2 \rightarrow 3$: cost $|5-2|+3-2 = 4$, length $2$
All other paths have greater costs, so the minimum cost is $4$. Among these two paths, we want the one with greater length, which is $3$.
user: Chef loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Chef has a positive integer N. He can apply any of the following operations as many times as he want in any order:

-  Add 1 to the number N.

-  Take some digit of N and replace it by any non-zero digit.

-  Add any non-zero leading digit to N.

Find the minimum number of operations that is needed for changing N to the lucky number.

-----Input-----
The first line contains a single positive integer T, the number of test cases. T test cases follow. The only line of each test case contains a positive integer N without leading zeros. 

-----Output-----
For each T test cases print one integer, the minimum number of operations that is needed for changing N to the lucky number.

-----Constraints-----

1 ≤ T ≤ 10

1 ≤ N < 10100000

-----Example-----
Input:
3
25
46
99

Output:
2
1
2