meetforever/GRPO_CL huggingface dataset:
user: The Fibonacci sequence $F_0, F_1, \ldots$ is a special infinite sequence of non-negative integers, where $F_0 = 0$, $F_1 = 1$ and for each integer $n \ge 2$, $F_n = F_{n-1} + F_{n-2}$.
Consider the sequence $D$ of the last decimal digits of the first $N$ Fibonacci numbers, i.e. $D = (F_0 \% 10, F_1 \% 10, \ldots, F_{N-1} \% 10)$. Now, you should perform the following process:
- Let $D = (D_1, D_2, \ldots, D_l)$.
- If $l = 1$, the process ends.
- Create a new sequence $E = (D_2, D_4, \ldots, D_{2 \lfloor l/2 \rfloor})$. In other words, $E$ is the sequence created by removing all odd-indexed elements from $D$.
- Change $D$ to $E$.
When this process terminates, the sequence $D$ contains only one number. You have to find this number.

-----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 a single integer $N$.

-----Output-----
For each test case, print a single line containing one integer ― the last remaining number.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le N \le 10^{18}$

-----Subtasks-----
Subtask #1 (20 points):
- $1 \le T \le 10^5$
- $1 \le N \le 10^7$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
9

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

-----Explanation-----
Example case 1: The first $N$ Fibonacci numbers are $(0, 1, 1, 2, 3, 5, 8, 13, 21)$. The sequence $D$ is $(0, 1, 1, 2, 3, 5, 8, 3, 1) \rightarrow (1, 2, 5, 3) \rightarrow (2, 3) \rightarrow (3)$.
user: The bustling town of Siruseri has just one sports stadium. There are a number of schools, colleges, sports associations, etc. that use this stadium as the venue for their sports events.
Anyone interested in using the stadium has to apply to the Manager of the stadium indicating both the starting date (a positive integer $S$) and the length of the sporting event in days (a positive integer $D$) they plan to organise. Since these requests could overlap it may not be possible to satisfy everyone. Also, there should be at least one gap day between any two approved events, so that the stadium can be cleaned.
It is the job of the Manager to decide who gets to use the stadium and who does not. The Manager, being a genial man, would like to keep as many organisations happy as possible and hence would like to allocate the stadium so that maximum number of events are held.
Suppose, for example, the Manager receives the following 4 requests:
$ $
Event No.   Starting Date        Length 

1                   2                    5
2                   9                    7
3                  15                    6
4                   9                    3

$ $ 
He would allot the stadium to events $1$, $4$ and $3$. Event $1$ begins on day $2$ and ends on day $6$, event $4$ begins on day $9$ and ends on day $11$ and event $3$ begins on day $15$ and ends on day $20$. You can verify that it is not possible to schedule all the $4$ events (since events $2$ and $3$ overlap and only one of them can get to use the stadium).
Your task is to help the manager find the best possible allotment (i.e., the maximum number of events that can use the stadium).

-----Input:-----
The first line of the input will contain a single integer $N$ indicating the number of events for which the Manager has received a request. Lines $2,3,...,N+1$ describe the requirements of the $N$ events. Line $i+1$ contains two integer $S_i$ and $D_i$ indicating the starting date and the duration of event $i$.

-----Output:-----
Your output must consist of a single line containing a single integer $M$, indicating the maximum possible number of events that can use the stadium.

-----Constraints:-----
- $1 \leq N \leq 100000$.
- $1 \leq S_i \leq 1000000$.
- $1 \leq D_i \leq 1000$.
- $50 \%$ of test cases will also satisfy $1 \leq N \leq 10000$.

-----Sample input:-----
4
2 5
9 7
15 6
9 3

-----Sample output:-----
3
user: Chef Loves to listen to remix songs, but currently he had already finished the entire playlist of remix songs.
As Chef is smart, so he thought let's make my own remix songs of the original songs.
Chef is not having much knowledge of making remix songs, so he came up with the simple technique in which he will pick the word which contains the smallest number of characters from the lyrics of the song, and then he will append that word to the start and end of the lyrics, also Chef will insert this word between every two words of the lyrics.
Note: While inserting a new word Chef will also insert extra white-spaces, so that every word in the final remixed lyrics is separated by space.
It is Recommended to use fast Input/Ouput techniques.

-----Input:-----
- The input contains the text $S$, which denotes the lyrics of the song.

-----Output:-----
- Print the Remixed, lyrics as done by Chef.

-----Constraints:-----
- $1 \leq Length of text $S$ \leq 10^7$

-----Sample Input:-----
Mai Hu Jiyaan

-----Sample Output:-----
Hu Mai Hu Hu Hu Jiyaan Hu
user: ----- Statement -----

You need to find a string which has exactly K positions in it such that the character at that position comes alphabetically later than the character immediately after it. If there are many such strings, print the one which has the shortest length. If there is still a tie, print the string which comes the lexicographically earliest (would occur earlier in a dictionary).

-----Input-----
The first line contains the number of test cases T. Each test case contains an integer K (≤ 100).

-----Output-----
Output T lines, one for each test case, containing the required string.  Use only lower-case letters a-z.

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

-----Sample Output-----
ba
cba
user: You are given a grid with $R$ rows (numbered $1$ through $R$) and $C$ columns (numbered $1$ through $C$). A cell in row $r$ and column $c$ is denoted by $(r, c)$. Two cells in the grid are adjacent if they have a common side. For each valid $i$ and $j$, there is a value $a_{i, j}$ written in cell $a_{i, j}$.
A cell in the grid is stable if the number of cells in the grid which are adjacent to this cell is strictly greater than the value written in this cell. The whole grid is stable if all cells in the grid are stable.
Can you determine whether the grid is stable?

-----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 $R$ and $C$.
- $R$ lines follow. For each $i$ ($1 \le i \le R$), the $i$-th of these lines contains $C$ space-separated integers $a_{i, 1}, a_{i, 2}, \ldots, a_{i, C}$.

-----Output-----
For each test case, print a single line containing the string "Stable" if the grid is stable or "Unstable" if it is unstable (without quotes).

-----Constraints-----
- $1 \le T \le 3,000$
- $3 \le R, C \le 10$
- $0 \le a_{i, j} \le 4$ for each valid $i, j$

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

-----Example Output-----
Stable
Unstable

-----Explanation-----
Example case 1: Each cell of the grid is stable, so the grid is stable.
Example case 2: The cell in row $3$ and column $3$ is unstable since the number of cells adjacent to this cell is $3$.
user: There is a rectangular grid of cells consisting of n rows and m columns.
You will place a robot on one of the grid cells and provide it with a command string s, consisting of characters ‘L’, ‘R’, ‘U’, ‘D’.
After being placed, the robot will follow the instructions of the command string, where 'L' corresponds moving to the left, 'R' towards the right, 'U' for moving up, and 'D' means down.

You have already selected the command string s, and are wondering if it is possible to place the robot in one of the grid cells initially and have it always stay entirely within the grid upon execution of the command string s.
Output “safe” if there is a starting cell for which the robot doesn’t fall off the grid on following command s, otherwise, output "unsafe".

-----Input-----

The first line of input will contain an integer T, the number of test cases.

Each test case will be on two lines. 

The first line will have two space separated integers n,m. 

The second line will have the command string s.

-----Output-----

For each test case, output "safe" (without quotes) or "unsafe" (without quotes) in a new line.

-----Constraints-----
-  1 ≤ T ≤ 1,000
-  1 ≤ n,m ≤ 10
-  1 ≤ |s| ≤ 10

-----Example-----
Input:
5
1 1
R
2 3
LLRU
3 2
LLRU
4 3
ULURUDRDLD
3 6
RURUR

Output:
unsafe
safe
unsafe
safe
safe

-----Explanation-----

For the first case, there is only one grid square, so we must place our robot there. When the robot follows the command, it'll fall off, so it is unsafe.

For the second case, we can place the robot on the bottom right grid square. Here is an image denoting the moves that the robot will make.
user: Consider the infinite x$x$ axis. There are N$N$ impacts on this X-axis at integral points (X1$X_1$,X2$X_2$,....XN$X_N$)  (all distinct) . An impact at a point X$X$i propagates such that at a point X$X$0, the effect of the impact is K|Xi−X0|$K^{|X_i - X_0|}$. Given the point X0$X_0$, N$N$ and K$K$. Assume the total impact on X0$X_0$ is M$M$, find if it is possible to do so.Note: You are not required to find the set X

Formally print "yes" if this is possible and "no" if not possible.

-----Input:-----
- First line will contain T$T$, number of testcases. Then the testcases follow. 
-  Each testcase contains of a single line of input, four integers N$N$,K$K$,M$M$,X$X$0 

-----Output:-----
-  The output of each test case is either "yes" or "no"

-----Constraints -----
-  1≤T≤1000$1\leq T \leq 1000$
-  1≤N≤100$1\leq N \leq 100$
-  1≤K≤1000$1\leq K \leq 1000$
-  1≤M≤1018$1\leq M \leq 10^{18}$
-  −109≤X0≤109$-10^9 \leq X_0 \leq 10^9$ 

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

4 3 10 10

2 3 10 10

-----Sample Output:-----
	no

yes
user: You are given a sequence $A_1, A_2, \ldots, A_N$. You have to split the array into maximum number of non-empty subarrays such that the gcd of elements of each subarray is equal to 1.

-----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 one integer ― the maximum number of subarrays formed, or $-1$ if the array cannot be split while satisfying the above condition.

-----Constraints-----
- $1 \le T \le 3$
- $1 \le N \le 5 \cdot 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$

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

-----Sample Output:-----
1
2
user: Abhi Ram analyses london stock exchange and invests in a software company C-.gate . He wants to sell his shares after 5 weeks.

Given the investment  m, increase or decrease of share prices of 5 weeks(+/- pi) , help him to calculate his net profit or loss percentage(n%) of his investment to establish his own company KMC.

-----Input:-----

- The first line contains an integer T which denotes the number of test cases.
- Each test case comprises of two lines: the first line contains the integer m which denotes the amount invested.

The second line consists of five space separated integers(p1, p2, p3, p4, p5) each preceeded by + (increase) or - (decrease) which give the percentage of change in share prices over 5 weeks.
.

-----Output:-----
The output contains a single number n which gives the percentage of profit or loss preceeded by + (profit) or - (loss).

-----Constraints:-----
- 1 ≤ T ≤ 100
- 1 ≤ m ≤ 105
- -100 ≤ pi ≤ 100

-----Example:-----
Input:
2
10000
+5 -3 -2 +10 +15
6256250
-24 +22 +4 -16 +20

Output:
+26.2634
-2.79977
user: Chef published a blog post, and is now receiving many queries about it. On day $i$, he receives $Q_i$ queries. But Chef can answer at most $k$ queries in a single day. 
Chef always answers the maximum number of questions that he can on any given day (note however that this cannot be more than $k$). The remaining questions (if any) will be carried over to the next day.
Fortunately, after $n$ days, the queries have stopped. Chef would like to know the first day during which he has some free time, i.e. the first day when he answered less than $k$ questions. 

-----Input:-----
- First line will contain $T$, the number of testcases. Then the testcases follow.
- The first line of each testcase contains two space separated integers $n$ and $k$.
- The second line of each testcase contains $n$ space separated integers, namely $Q_1, Q_2, ... Q_n$.

-----Output:-----
For each testcase, output in a single line the first day during which chef answers less than $k$ questions. 

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq $ sum of $n$ over all testcases $ \leq 10^5$
- $1 \leq k \leq 10^8$
- $0 \leq Q_i \leq 10^8$

-----Subtasks-----
- Subtask 1 - 20% points - Sum of $Q_i$ over all testcases and days $\leq 3 . 10^6$
- Subtask 2 - 80% points - Original constraints

-----Sample Input:-----
2 
6 5 
10 5 5 3 2 1 
1 1
100

-----Sample Output:-----
6
101

-----Explanation:-----
Test Case 1
On the first day, chef answers 5 questions and leaves the remaining 5 (out of the 10) for the future days.
On the second day, chef has 10 questions waiting to be answered (5 received on the second day and 5 unanswered questions from day 1). Chef answers 5 of these questions and leaves the remaining 5 for the future.
On the third day, chef has 10 questions waiting to be answered (5 received on the third day and 5 unanswered questions from earlier). Chef answers 5 of these questions and leaves the remaining 5 for later.
On the fourth day, chef has 8 questions waiting to be answered (3 received on the fourth day and 5 unanswered questions from earlier). Chef answers 5 of these questions and leaves the remaining 3 for later.
On the fifth day, chef has 5 questions waiting to be answered (2 received on the fifth day and 3 unanswered questions from earlier). Chef answers all 5 of these questions.
On the sixth day, chef has 1 question, which he answers. This is the first day he answers less than 5 questions, and so the answer is 6.
Test Case 2
Chef answers 1 question a day for the first 100 days. On day 101, he is free.
user: Due to the COVID pandemic, people have been advised to stay at least $6$ feet away from any other person. Now, people are lining up in a queue at the local shop and it is your duty to check whether they are all following this advice.
There are a total of $N$ spots (numbered $1$ through $N$) where people can stand in front of the local shop. The distance between each pair of adjacent spots is $1$ foot. Each spot may be either empty or occupied; you are given a sequence $A_1, A_2, \ldots, A_N$, where for each valid $i$, $A_i = 0$ means that the $i$-th spot is empty, while $A_i = 1$ means that there is a person standing at this spot. It is guaranteed that the queue is not completely empty.
For example, if $N = 11$ and the sequence $A$ is $(0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1)$, then this is a queue in which people are not following the advice because there are two people at a distance of just $3$ feet from each other.
You need to determine whether the people outside the local shop are following the social distancing advice or not. As long as some two people are standing at a distance smaller than 6 feet from each other, it is bad and you should report it, since social distancing is not being followed.

-----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 next 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 social distancing is being followed or "NO" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 100$
- $0 \le A_i \le 1$ for each valid $i$
- at least one spot is occupied

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

-----Example Input-----
3
3
1 0 1
7
1 0 0 0 0 0 1
11
0 1 0 0 0 0 0 1 0 0 1

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

-----Explanation-----
Example case 1: The first and third spots are occupied and the distance between them is $2$ feet.
Example case 2: The first and seventh spots are occupied and the distance between them is $6$ feet.
user: "What do you know about happiness?" — Yoda 
Chef is happy only if three conditions hold:
- Chef finished cooking a delicious meal
- Chef got AC for a programming problem with an almost correct code
- Chef got a new problem with a sequence of integers
Today, all three conditions are satisfied. Chef would like you to feel his happiness and provide him with a solution for this new problem with a sequence of integers. The problem is as follows.
You are given a sequence $A_1, A_2, \dots, A_N$. You need to determine if it is possible to choose two indices $i$ and $j$ such that $A_i \neq A_j$, but $A_{A_i}$ = $A_{A_j}$. (If it was possible, Chef would be truly happy.)

-----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 "Truly Happy" if it is possible to choose required indices or "Poor Chef" otherwise.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $1 \le A_i \le N$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $2 \cdot 10^5$

-----Subtasks-----
Subtask #1 (27 points): $1 \le N \le 1,000$
Subtask #2 (73 points): original constraints

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

-----Example Output-----
Truly Happy
Poor Chef
Poor Chef
Truly Happy

-----Explanation-----
Example case 1: Chef is truly happy because $A_{A_3} = A_{A_1}$ and $A_3 \neq A_1$.
Example case 2: There is no pair of indices which would make Chef truly happy. For instance, $A_{A_3} = A_{A_4}$, but $A_3 = A_4$,
user: Lots of geeky customers visit our chef's restaurant everyday. So, when asked to fill the feedback form, these customers represent the feedback using a binary string (i.e a string that contains only characters '0' and '1'. 

Now since chef is not that great in deciphering binary strings, he has decided the following criteria to classify the feedback as Good or Bad : 

If the string contains the substring "010" or "101", then the feedback is Good, else it is Bad. Note that, to be Good it is not necessary to have both of them as substring.

So given some binary strings, you need to output whether according to the chef, the strings are Good or Bad. 

-----Input-----
The first line contains an integer T denoting the number of feedbacks. Each of the next T lines contains a string composed of only '0'  and '1'.

-----Output-----
For every test case, print in a single line Good or Bad as per the Chef's method of classification.

-----Constraints-----
-  1 ≤  T ≤   100 
-  1  ≤  |S|   ≤  105 

Sum of length of all strings in one test file will not exceed 6*106.

-----Example-----
Input:
2
11111110
10101010101010

Output:
Bad
Good

-----Explanation-----
Example case 1.

The string doesn't contain 010 or 101 as substrings.

Example case 2.

The string contains both 010 and 101 as substrings.
user: -----Problem-----

			Nikki's latest work is writing a story of letters. However, she finds writing story so boring that, after working for three hours, she realized that all she has written are M long words consisting entirely of letters A and B. Having accepted that she will never finish the story in time, Nikki has decided to at least have some fun with it by counting bubbly words.


			Now Nikki is connecting pairs of identical letters (A with A, B with B) by drawing lines above the word. A given word is bubbly if each letter can be connected to exactly one other letter in such a way that no two lines intersect. So here is your task. Help Nikki count how many words are bubbly.

-----Input-----
- 
			The first line of input contains the positive integer M, the number of words written down by Nikki.
				
- 
			Each of the following M lines contains a single word consisting of letters A and B, with length

			between 2 and 10^5, inclusive. The sum of lengths of all words doesn't exceed 10^6.
				

-----Output-----

			The first and only line of output must contain the number of bubbly words.
		

-----Constraints-----
- 
			1 ≤ M ≤ 100
				

-----Sample Input-----

3

ABAB

AABB

ABBA

-----Sample Output-----
2

-----Explanation-----
- 
					 ABAB - It is not bubbly as A(indexed 1) will connect to A(indexed 3) by a line and when we try to connect B(indexed 2) with B(indexed 4) by a line then it will intersect with the line b/w A and A.
				
- 
					AABB - It is bubbly as line b/w A and A will not intersect with the line b/w B and B.
			
- 
ABBA -It is also bubbly as lines will not intersect. We can draw line b/w A and A above the line b/w B and B.
				 p { text-align:justify }
user: Chef would like go shopping to buy ingredients for his special dish. The local grocery store has some special discount offers. If you want to buy some set of ingredients you will pay for all ingredients except the cheapest one. Chef would like to spend as little money as possible. You have to help him. :)

The store is pretty small and stocks only one unit of each ingredients. Opposite each ingredient is a hanging price tag corresponding to it. The salesman walked away for a minute, giving Chef an opportunity to swap some price tags. He would like to swap some tags to minimize his purchase cost.

-----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 ingredients Chef needs to buy. The second line contains N space-separated integers A1, A2, ... , AN denoting the value  written on the price tags opposite the needed ingredients. The third line contains a single integer M denoting the number of special offers. The following M lines lists inventory of special offers, one offer per line. Each line contains an integer Ci followed by Ci integers denoting the indices of ingredients constituting the ith discount offer.

-----Output-----
For each test case, output a single line containing the minimal purchase cost.

-----Constraints-----
- T ≤ 5
- 1 ≤ N ≤ 15
- 1 ≤ Ai ≤ 106
- 0 ≤ M ≤ 2N-1
- 2 ≤ Ci ≤ N
- Subtask 1 (15 points):  1 ≤ N ≤  5
- Subtask 2 (25 points):  1 ≤ N ≤ 10
- Subtask 3 (60 points):  1 ≤ N ≤ 15

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

Output:
6