meetforever/GRPO_CL huggingface dataset:
user: Recently, Chef studied the binary numeral system and noticed that it is extremely simple to perform bitwise operations like AND, XOR or bit shift on non-negative integers, while it is much more complicated to perform arithmetic operations (e.g. addition, multiplication or division).
After playing with binary operations for a while, Chef invented an interesting algorithm for addition of two non-negative integers $A$ and $B$:
function add(A, B):
while B is greater than 0:
U = A XOR B
V = A AND B
A = U
B = V * 2
return A

Now Chef is wondering how fast this algorithm is. Given the initial values of $A$ and $B$ (in binary representation), he needs you to help him compute the number of times the while-loop of the algorithm is repeated.

-----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 string $A$.
- The second line contains a single string $B$.

-----Output-----
For each test case, print a single line containing one integer ― the number of iterations the algorithm will perform during addition of the given numbers $A$ and $B$.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le |A|, |B| \le 10^5$
- $A$ and $B$ contain only characters '0' and '1'
- the sum of $|A| + |B|$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (20 points): $|A|, |B| \le 30$
Subtask #2 (30 points):
- $|A|, |B| \le 500$
- the sum of $|A| + |B|$ over all test cases does not exceed $10^5$
Subtask #3 (50 points): original constraints

-----Example Input-----
3
100010
0
0
100010
11100
1010

-----Example Output-----
0
1
3

-----Explanation-----
Example case 1: The initial value of $B$ is $0$, so while-loop is not performed at all.
Example case 2: The initial values of $A$ and $B$ are $0_2 = 0$ and $100010_2 = 34$ respectively. When the while-loop is performed for the first time, we have:
- $U = 34$
- $V = 0$
- $A$ changes to $34$
- $B$ changes to $2 \cdot 0 = 0$
The while-loop terminates immediately afterwards, so it is executed only once.
Example case 3: The initial values of $A$ and $B$ are $11100_2 = 28$ and $1010_2 = 10$ respectively. After the first iteration, their values change to $22$ and $16$ respectively. After the second iteration, they change to $6$ and $32$, and finally, after the third iteration, to $38$ and $0$.
user: Dhruvil has always been a studious person and will be completing his Engineering soon. He is always kneen about solving problems and is preparing hard for his next interview at Hackerrank. He has practiced lots of problems and now he came across this problem.
Given a message containing English letters(A-Z), it is being encoded to numbers using the following mapping:
'A' -> 1,'B' -> 2 ……………… 'Z' -> 26.
Now, given a non-empty string containing only digits, help Dhruvil determine the total number of ways to decode it.
While decoding you need to choose a substring of charachters and not a subsequence. Also a chosen substring should not contain any leading "0"s, but can contain trailing "0"s. Since the output can be very large print the answer as modulo 10^9 + 7 i.e 1000000007.

-----Input:-----
The first line of the input consists of single integer T, the number of test cases.
Each test case consists of a string.

-----Output:-----
For each test case print a single integer - the total number of ways to decode the digit string.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq S \leq 10^9$

-----Sample Input:-----
2
12

226

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

3

-----EXPLANATION:-----
There are 2 possible ways. It could be decoded as "AB" {1,2} or "L" {12}.
There are 3 possible ways. It could be decoded as "BZ" {2,26}, "VF" {22,6}, or "BBF" {2,2,6}.
user: Today a plane was hijacked by a maniac. All the passengers of the flight are taken as hostage. Chef is also one of them.
He invited one of the passengers to play a game with him. If he loses the game, he will release all the passengers, otherwise he will kill all of them. A high risk affair it is.

Chef volunteered for this tough task. He was blindfolded by Hijacker. Hijacker brought a big black bag from his pockets. The contents of the bag is not visible. He tells Chef that the bag contains R red, G green and B blue colored balloons.

Hijacker now asked Chef to take out some balloons from the box such that there are at least K balloons of the same color and hand him over. If the taken out balloons does not contain at least K balloons of the same color, then the hijacker will shoot everybody. Chef is very scared and wants to leave this game as soon as possible, so he will draw the minimum number of balloons so as to save the passengers. Can you please help scared Chef to find out the minimum number of balloons he should take out.

-----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 three space-separated integers R, G and B. 

The second line contains only one integer K.

-----Output-----
For each test case, output a single line containing one integer - the minimum number of balloons Chef need to take out from the bag.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ R, G, B ≤ 109
- 1 ≤ K ≤ max{R, G, B}

-----Subtasks-----
- Subtask 1 (44 points): 1 ≤ R, G, B ≤ 10
- Subtask 2 (56 points):  No additional constraints

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

Output:
1
4

-----Explanation-----
Example case 2. In the worst-case scenario first three balloons will be of the three different colors and only after fourth balloon Chef will have two balloons of the same color. So, Chef might need to fetch 4 balloons
user: There are $N$ sabotages available in the game Among Us, initially all at level $0$. 
$N$ imposters are allotted the task to upgrade the level of the sabotages. 
The $i^{th}$ imposter $(1 \leq i \leq N)$ increases the level of $x^{th}$ sabotage $(1 \leq x \leq N)$ by one level  if $gcd(i,x)=i$.
You need to find the number of sabotages at LEVEL 5 after all the imposters have completed their tasks.

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

-----Output:-----
For each testcase, output in a single line the number of sabotages at LEVEL 5.

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

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

-----Sample Output:-----
0

-----EXPLANATION:-----
The $1^{st}$ sabotage is at level $1$, the $2^{nd}$, $3^{rd}$ and $5^{th}$ sabotages are at level $2$, the $4^{th}$ sabotage is at level $3$ and the $6^{th}$ sabotage is at level $4$.
None of them reach level $5$. Hence the output is $0$.
user: A sophomore Computer Science student is frustrated with boring college lectures. Professor X agreed to give him some questions; if the student answers all questions correctly, then minimum attendance criteria will not apply to him.
Professor X chooses a sequence $A_1, A_2, \ldots, A_N$ and asks $Q$ queries. In each query, the student is given an integer $P$; he has to construct a sequence $B_1, B_2, \ldots, B_N$, where $P \oplus A_i = B_i$ for each valid $i$ ($\oplus$ denotes bitwise XOR), and then he has to find the number of elements of this sequence which have an even number of $1$-s in the binary representation and the number of elements with an odd number of $1$-s in the binary representation. Help him answer the queries.

-----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 $A_1, A_2, \ldots, A_N$.
- $Q$ lines follow. Each of these lines contains a single integer $P$ describing a query.

-----Output-----
For each query, print a single line containing two space-separated integers ― the number of elements with an even number of $1$-s and the number of elements with an odd number of $1$-s in the binary representation.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, Q \le 10^5$
- $ T \cdot (N+Q) \leq 4 \cdot 10^6 $
- $1 \le A_i \le 10^8$ for each valid $i$
- $1 \le P \le 10^5$
The input/output is quite large, please use fast reading and writing methods.

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

-----Example Input-----
1
6 1
4 2 15 9 8 8
3

-----Example Output-----
2 4

-----Explanation-----
Example case 1: The elements of the sequence $B$ are $P \oplus 4 = 7$, $P \oplus 2 = 1$, $P \oplus 15 = 12$, $P \oplus 9 = 10$, $P \oplus 8 = 11$ and $P \oplus 8 = 11$. The elements which have an even number of $1$-s in the binary representation are $12$ and $10$, while the elements with an odd number of $1$-s are $7$, $1$, $11$ and $11$.
user: You are given an empty grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). You should fill this grid with integers in a way that satisfies the following rules:
- For any three cells $c_1$, $c_2$ and $c_3$ such that $c_1$ shares a side with $c_2$ and another side with $c_3$, the integers written in cells $c_2$ and $c_3$ are distinct.
- Let's denote the number of different integers in the grid by $K$; then, each of these integers should lie between $1$ and $K$ inclusive.
- $K$ should be minimum possible.
Find the minimum value of $K$ and a resulting (filled) grid. If there are multiple solutions, you may find any one.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $N$ and $M$.

-----Output-----
- For each test case, print $N+1$ lines.
- The first line should contain a single integer — the minimum $K$.
- Each of the following $N$ lines should contain $M$ space-separated integers between $1$ and $K$ inclusive. For each valid $i, j$, the $j$-th integer on the $i$-th line should denote the number in the $i$-th row and $j$-th column of the grid.

-----Constraints-----
- $1 \le T \le 500$
- $1 \le N, M \le 50$
- the sum of $N \cdot M$ over all test cases does not exceed $7 \cdot 10^5$

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

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

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

-----Explanation-----
Example case 1: There is only one cell in the grid, so the only valid way to fill it is to write $1$ in this cell. Note that we cannot use any other integer than $1$.
Example case 2: For example, the integers written in the neighbours of cell $(2, 2)$ are $1$, $2$ and $3$; all these numbers are pairwise distinct and the integer written inside the cell $(2, 2)$ does not matter. Note that there are pairs of neighbouring cells with the same integer written in them, but this is OK.
user: Chef's loves his dog so much! Once his dog created two strings a and b each of length n consisting of digits 1 and 2, and even a problem about them!
Chef's Dog will tell by barking if a string x (also containing only digits 1 and 2 and with length N) is good or not by performing the following actions.

- It starts at first digit of the string, i.e. at i = 1. 
- It can move from digit i to either i - 1 or i + 1 if xi equals 1 and the corresponding digits exist. 
- It can move from digit i to either i - 2 or i + 2 if xi equals 2 and the corresponding digits exist. 
- It must visit each digit exactly once. 
- It must finish at the last digit (XN). 

Chef's dog wants to make both the strings a and b good by choosing some subset S (possibly empty) of indices of set {1, 2, ..., n} and swapping each index i ϵ S between string a and b, i.e. swapping ai and bi. Can you find how many such subsets S exist out there? As the answer could be large, output it modulo 109 + 7.

-----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 contains string a.
The second line contains string b.

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

-----Constraints-----
- 1 ≤ T ≤ 20
- 1 ≤ |a| = |b| ≤ 105
- '1' ≤ ai, bi ≤ '2'

-----Subtasks-----
- Subtask #1 (30 points) |a|, |b| ≤  10
- Subtask #2 (70 points) original constraints

-----Example-----
Input:
2
1111
2211
222
111

Output:
8
0

-----Explanation-----
Test case 1.
Possible subsets are: 
{}, {1, 2}, {1, 2, 3}, {1, 2, 4}, {1, 2, 3, 4}, {3}, {4}, {3, 4}.

Test case 2. There are no possible sets S which can make both the strings good.
user: Chef solved so many hard questions, now he wants to solve some easy problems for refreshment. Chef asks Cheffina for the new question. Cheffina challanges the chef to print the total number of 1's in the binary representation of N(natural number).

-----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, $N$. 

-----Output:-----
For each test case, output in a single line answer.

-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$

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

-----Sample Output:-----
1
2

-----EXPLANATION:-----
For 1) Binary representation of 2 is 10. i.e. only one 1 present in it.
For 2) Binary representation of 5 is 101, i.e. two 1's present in it.
user: Alice's school is planning to take some students from her class on a field trip. Alice is really excited about it. There are a total of S students in her class. But due to budget constraints, the school is planning to take only N students for the trip. These students will be picked randomly. And each student has equal chance of being picked.
Alice's friend circle has M students including her. Though she is excited about the field trip, she will enjoy it only if there are atleast K of her friends with her on the trip. She is wondering what are the chances of that happening. She needs your help. Tell her the probability that she will enjoy given that she goes on the trip.

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

Each test starts with a single line having 4 space separated integers, S, N, M and K.

-----Output:-----
For each test case, output a line containing the required probability. The answer will be accepted if the relative error is not more than 10-6.

-----Constraints:-----
1 ≤ T ≤ 100
1 ≤ S ≤ 1000
1 ≤ N ≤ S
1 ≤ M ≤ S
0 ≤ K < M

-----Example:-----Input:
3
10 10 5 3
10 4 6 4
3 2 2 1

Output:
1.000000
0.000000
0.500000

-----Explanation:-----Case #1:
Every student will be taken to the trip. So all her 4 friends will accompany her to the trip no matter what. 
Case #2:
Alice wants 4 out of her 5 friends to come along with her which isn't possible because the school is willing to pick only 4 students for the trip.
user: Motu and Patlu are racing against each other on a circular track of radius $R$. Initially they are at the same point on the track and will run in same direction .The coach ordered them to run $X$ rounds of the circular field. Patlu wants to know how many times they will meet after the race starts and  before any of them finishes $X$ rounds. But he is busy in warm up so he wants you to calculate this. You are given speed of both Motu and Patlu ($A$ and $B$). 

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, four integers $X, R, A, B$. 

-----Output:-----
For each testcase, output in a single line answer the number of times whey will meet before any of them completes $X$ rounds.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq R \leq 10^9$
- $1 \leq X \leq 10^9$
- $1 \leq A \leq 10^9$
- $1 \leq B \leq 10^9$
- Speed of both are different

-----Sample Input:-----
2
3 10 2 5
2 20 5 10

-----Sample Output:-----
1
0
user: Chef changed the password of his laptop a few days ago, but he can't remember it today. Luckily, he wrote the encrypted password on a piece of paper, along with the rules for decryption.
The encrypted password is a string S consists of ASCII printable characters except space (ASCII 33 - 126, in decimal notation, the same below). Read here for more details: ASCII printable characters.
Each rule contains a pair of characters ci, pi, denoting that every character ci appears in the encrypted password should be replaced with pi. Notice that it is not allowed to do multiple replacements on a single position, see example case 1 for clarification.
After all the character replacements, the string is guaranteed to be a positive decimal number. The shortest notation of this number is the real password. To get the shortest notation, we should delete all the unnecessary leading and trailing zeros. If the number contains only non-zero fractional part, the integral part should be omitted (the shortest notation of "0.5" is ".5"). If the number contains zero fractional part, the decimal point should be omitted as well (the shortest notation of "5.00" is "5").
Please help Chef to find the real password.

-----Input-----
The first line of the input contains an interger T denoting the number of test cases.
The description of T test cases follows.
The first line of each test case contains a single interger N, denoting the number of rules.
Each of the next N lines contains two space-separated characters ci and pi,
denoting a rule.
The next line contains a string S, denoting the encrypted password.

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

-----Constraints-----
- 1 ≤ T ≤ 1000
- 0 ≤ N ≤ 94
- All characters in S and ci may be any ASCII printable character except space. (ASCII 33 - 126)
- All ci in a single test case are distinct.
- pi is a digit ("0" - "9") or a decimal point "." (ASCII 46).
- The total length of S in a single input file will not exceed 106.

-----Example-----
Input:
4
2
5 3
3 1
5
0
01800.00
0
0.00100
3
x 0
d 3
# .
0xd21#dd098x

Output:
3
1800
.001
321.33098
user: The auditorium of Stanford University is made up of L*R matrix (assume each coordinate has a chair). On the occasion of an event Chef was called as a chief guest. The auditorium was filled with males (M) and females (F), occupying one chair each. Our Chef is very curious guy, so he asks the gatekeeper some queries. The queries were as follows: Is there any K*K sub-matrix in the auditorium which contains all Males or Females.

-----Input-----
- The first line contains three space-separated integers L, R  and Q describing the dimension of the auditorium and the number of questions Chef will ask.
- Each of next L lines contains R characters (M or F).
- Next Q lines contains K and a character (M or F).

-----Output-----
- For each query output "yes" (without quotes) if there exist any K*K sub-matrix in the auditorium which contains all Males (if he asks about Male) or Females (if he asks about Female), otherwise output "no" (without quotes).

-----Constraints and Subtasks-----
- 1 <= L, R, K <= 1000
- 1 <= Q <= 1e6
Subtask 1: 30 points
- 1 <= L, R, Q <= 200
Subtask 2: 70 points
- Original Contraints

-----Example-----
Input:
4 3 3
MMF
MMM
FFM
FFM
2 F
3 M
1 M

Output:
yes
no
yes
user: Given a string s. Can you make it a palindrome by deleting exactly one character? Note that size of the string after deletion would be one less than it was before. 

-----Input-----
First line of the input contains a single integer T denoting number of test cases.
For each test case, you are given a single line containing string  s. 

-----Output-----
For each test case, print YES or NO depending on the answer of the problem. 

-----Constraints-----
Subtask 1, 35 points 
-  1 ≤ T ≤ 100
- 2 ≤  size of string s ≤ 1000
-  String s contains lowercase English alphabets (ie. from 'a' to 'z').

Subtask 2, 65 points 
- 2 ≤  size of string s ≤ 10^5
-  Sum of size of string s over all the input test cases won't exceed 10^6
-  String s contains lowercase English alphabets (ie. from 'a' to 'z').

-----Example-----
Input:
4
aaa
abc
abdbca
abba

Output:
YES
NO
YES
YES

-----Explanation-----
Example case 1. Delete any one 'a', resulting string is "aa" which is a palindrome.
Example case 2. It is not possible to delete exactly one character and having a palindrome.
Example case 3. Delete 'c', resulting string is "abdba" which is a palindrome. 
Example case 4. Delete 'b', resulting string is "aba" which is a palindrome.
user: Han Solo and Chewbacca start a space journey to planet Naboo on the Millennium Falcon. During the journey they land at a mysterious planet with high gravity where they find n diamond stones scattered all around. All the stones are of same weight. Each stone has a value according to its purity which can be detected by a special device. They choose to divide the stones fairly among themselves in two halves so that they carry almost equal weights such that the difference between the value of two halves is as small as possible. If n is even, then sizes of two halves must be strictly n/2 and if n is odd, then size of one half must be (n-1)/2 and size of the other half must be (n+1)/2. Given the value of stones, help them to divide the stones among themselves.

-----Input-----
First line consists of an integer n which denotes the number of stones.Second line consists of n space separated integers denoting the value of the stones.

-----Output-----
First line consists of the values of the stones assigned to Han Solo.Second line consists of the values of the stones assigned to Chewbacca.Assume that the set containing the first value in the input is always assigned to Han Solo.Also the values in the output sets must follow the same ordering as the input.

-----Constraints-----
The number of stones can range from 2 to 99.The values of the stones vary from 1 to 10^4.

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

Output:
1 2 4 7
3 5 6

-----Explanation-----
These 7 values must be separated into 2 sets of sizes 3 and 4.In this case, it is possible to form two sets (1,2,4,7) & (3,5,6) of equal size.The set containing the first value (i.e.) 1 must be assigned to Han Solo and the elements of the output sets have the same order as the input.
user: Raj loves to listen to songs in his free time. It’s his birthday tomorrow and his friend Neelansh wants his gift to be the most unique. Being great at making music, he decides to produce a song for him. However, Raj likes songs according to their beauty. He determines the beauty of the song as the number of times all the octave musical tones are completed in ascending order.

He begins with a jumbled tone of length N and numbers each octave tone as 1,2,3….8.

Neelansh wants to maximize the beauty of the song but since he uses the trial version of the software,
- He cannot change the size of N.
- He cannot introduce any new tone, but can choose any two tones and swap their positions

However, Neelansh just received a mail that he needs to submit all his pending assignments by tomorrow. He has tons of assignments left to do, but he doesn’t want to spoil the idea of his gift. Can you help him? 

-----INPUT-----
- The first line contains a single integer T- the number of test cases  
- The first line of each test case contains a single integer N- the length of the song  
- The second line contains N- space separated integers ai,  ai+1,.....aN 

-----OUTPUT-----
For each test case, print a single line containing one integer- the maximum possible beauty of the song  

-----CONSTRAINTS-----
1<=T<=102
1<=N<=105
1<=a<=8

-----EXAMPLE INPUT-----
2

8

1 2 3 4 5 6 7 8

16

1 2 1 2 3 3 4 4 5 5 6 6 7 8 7 8

-----EXAMPLE OUTPUT-----
1

2