meetforever/GRPO_CL huggingface dataset:
user: Santosh has a farm at Byteland. He has a very big family to look after.  His life takes a sudden turn and he runs into a financial crisis. After giving all the money he has in his hand, he decides to sell his plots. The speciality of his land is that it is rectangular in nature. Santosh comes to know that he will get more money if he sells square shaped plots. So keeping this in mind, he decides to divide his land into minimum possible number of square plots, such that each plot has the same area, and  the plots divide the land perfectly. He does this in order to get the maximum profit out of this.   
So your task is to find the minimum number of square plots with the same area, that can be formed out of the rectangular land, such that they divide it perfectly.

-----Input-----
- The first line of the input contains $T$, the number of test cases. Then $T$ lines follow.
- The first and only line of each test case contains two space-separated integers, $N$ and $M$, the length and the breadth of the land, respectively.

-----Output-----
For each test case, print the minimum number of square plots with equal area, such that they divide the farm land perfectly, in a new line.

-----Constraints-----
$1 \le T \le 20$
$1 \le M \le 10000$
$1 \le N \le 10000$ 

-----Sample Input:-----
2
10 15
4 6

-----SampleOutput:-----
6
6
user: To make Yalalovichik even more satisfied and happy, Jafar decided to invent Yalalovichik strings. A string is called a Yalalovichik string if the set of all of its distinct non-empty substrings is equal to the set of all of its distinct non-empty subsequences. 
You are given a string S$S$. You need to find the number of its distinct non-empty substrings which are Yalalovichik strings.
Note: A string A$A$ is called a subsequence of a string B$B$ if A$A$ can be formed by erasing some characters (possibly none) from B$B$. A string A$A$ is called a substring of a string B$B$ if it can be formed by erasing some characters (possibly none) from the beginning of B$B$ and some (possibly none) from the end of B$B$. Two substrings or subsequences are considered different if they are different strings.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first line of each test case contains a single integer N=|S|$N = |S|$.
- The second line contains the string S$S$.

-----Output-----
For each test case, print a single line containing one integer — the number of distinct Yalalovichik substrings of S$S$.

-----Constraints-----
- 1≤T≤100$1 \le T \le 100$
- 1≤N≤106$1 \le N \le 10^6$
- the sum of N$N$ over all test cases does not exceed 2⋅106$2 \cdot 10^6$
- S$S$ contains only lowercase English letters

-----Example Input-----
1
3
xxx

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

-----Explanation-----
Example case 1: The distinct Yalalovichik substrings are "x", "xx" and "xxx".
user: Zonal Computing Olympiad 2012, 26 Nov 2011

A sequence of opening and closing brackets is well-bracketed if we can pair up each opening bracket with a matching closing bracket in the usual sense.  For instance, the sequences (), (()) and ()(()) are well-bracketed, while (, ()), (()(), and )(  are not well-bracketed.

The nesting depth of a well-bracketed sequence tells us the maximum number of levels of inner matched brackets enclosed within outer matched brackets.  For instance, the nesting depth of () and ()()() is 1, the nesting depth of (()) and ()(()) is 2, the nesting depth of ((())) is 3, and so on.  

Given a well-bracketed sequence, we are interested in computing the following: 
-  The nesting depth, and the first position where it occurs–this will be the position of the first opening bracket at this nesting depth, where the positions are numbered starting with 1.
-  The maximum number of symbols between any pair of matched  brackets, including both the outer brackets, and the first position where this occurs–that is, the position of the first opening bracket of this segment

For instance, the nesting depth of ()(())()(()())(()()) is 2 and the first position where this occurs is 4.  The opening bracket at position 10 is also at nesting depth 2 but we have to report the first position where this occurs, which is 4.

In this sequence, the maximum number of symbols between a pair of matched bracket is 6, starting at position 9. There is another such sequence of length 6 starting at position 15, but this is not the first such position.

-----Input format-----
The input consists of two lines. The first line is a single integer N, the length of the bracket sequence. Positions in the sequence are numbered 1,2,…,N. The second line is a sequence of N space-separated integers that encode the bracket expression as follows: 1 denotes an opening bracket ( and 2 denotes a closing bracket ).  Nothing other than 1 or 2 appears in the second line of input and the corresponding expression is guaranteed to be well-bracketed.

-----Output format-----
Your program should print 4 space-separated integers in a line, denoting the four quantities asked for in the following order: nesting depth, first position that achieves the nesting depth, length of the maximum sequence between matching brackets and the first position where such a maximum length sequence occurs.  

-----Testdata-----

You may assume that 2 ≤ N ≤ 105.  In 30% of the test cases, 2 ≤ N ≤ 103.

- Subtask 1 (30 marks)
- Subtask 2 (70 marks)

-----Sample Input-----
20
1 2 1 1 2 2 1 2 1 1 2 1 2 2 1 1 2 1 2 2

-----Sample Output-----
2 4 6 9
user: Cherry has a binary matrix $A$ consisting of $N$ rows and $M$ columns. The rows are numbered from $1$ to $N$, columns are numbered from $1$ to $M$. Element at row $i$ ($1$ ≤ $i$ ≤ $N$) and column $j$ ($1$ ≤ $j$ ≤ $M$) is denoted as $A_{ij}$. All elements of $A$ are either $0$ or $1$.
He performs $Q$ queries on matrix. Each query is provided by four integers $x_{1}$, $y_{1}$, $x_{2}$, $y_{2}$ which define the rectangle, where ($x_{1}$, $y_{1}$) stands for the coordinates of the top left cell of the rectangle, while ($x_{2}$, $y_{2}$) stands for the coordinates of the bottom right cell. You need to flip all the bits i.e. ($0$ to $1$, $1$ to $0$) that are located fully inside the query rectangle.
Finally, print the matrix after performing all the queries.
Note: $x_{1}$ represents the row number while $y_{1}$ represents the column number.

-----Input:-----
- The first line of the input contains two integers $N$ and $M$ — the number of rows and the number of columns in the matrix.
- Each of the next $N$ lines contains a string of length $M$, where the $j^{th}$ character of $i^{th}$ line denotes the value of $A_{i,j}$. 
- Next line contains an integer $Q$ — the number of queries.
- Then follow $Q$ lines with queries descriptions. Each of them contains four space-seperated integers $x_{1}$, $y_{1}$, $x_{2}$, $y_{2}$ — coordinates of the up left and bottom right cells of the query rectangle.

-----Output:-----
Print the matrix, in the form of $N$ strings, after performing all the queries.

-----Constraints-----
- $1 \leq N,M \leq 1000$
- $0 \leq  A_{ij}  \leq 1$
- $1 \leq Q \leq 10^6$
- $1 \leq x_{1} \leq x_{2} \leq N$
- $1 \leq y_{1} \leq y_{2} \leq M$

-----Sample Input:-----
2 2
00
00
3
1 1 1 1
2 2 2 2
1 1 2 2 

-----Sample Output:-----
01
10

-----Explanation:-----
Example case 1:
After processing the 1st query 1 1 1 1, matrix becomes:
[1000][1000]\begin{bmatrix} 10 \\ 00  \end{bmatrix}
After processing the 2nd query 2 2 2 2, the matrix becomes:
[1001][1001]\begin{bmatrix} 10 \\ 01  \end{bmatrix}
After processing the 3rd query 1 1 2 2, matrix becomes:
[0110][0110]\begin{bmatrix} 01 \\ 10  \end{bmatrix}
We need to output the matrix after processing all queries.
user: You are given a grid with dimension $n$ x $m$ and two points with coordinates $X(x1,y1)$ and $Y(x2,y2)$ . Your task is to find the number of ways in which one can go from point $A(0, 0)$ to point $B (n, m)$ using the $shortest$ possible path such that the shortest path neither passes through $X$ nor through $Y$. 

Consider the above 4 x 4 grid . Our shortest path can't pass through points (1,3) and (3,3) (marked by yellow dots). One of the possible shortest path is from $A$ to $C$ and then from $C$ to $B$.

-----Input:-----
- First line contains $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, six space separated integers $n, m, x1, y1, x2, y2$. 

-----Output:-----
- For each testcase, output in a single line number of ways modulo $998244353$.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $3 \leq n,m \leq 10^5$
- $1 \leq x1, x2 \leq n - 1$
- $1 \leq y1, y2 \leq m - 1$
- $x1 \leq x2$
- $y1 \leq y2$
- $X$ and $Y$ never coincide.

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

-----Sample Output:-----
5
user: The chef is trying to decode 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:-----
4
1
2
3
4

-----Sample Output:-----
0
01
10
012
101
210
0123
1012
2101
3210

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: The Siruseri amusement park has a new attraction. It consists of a rectangular array of discs. Each disc is divided into four equal sectors and the four sectors are coloured with the colours Red, Blue, Green and Yellow (in some order). The ordering may be different in different discs. Here is a possible arrangment of the discs:

You start at the top left disc. Your task is to walk down to the bottom right disc. In each step, you can rotate the current disc by $90$ degrees in the clockwise direction or move to a neighbouring disc. However, you can move to a neighbouring disc only if adjacent sectors of these two discs have the same colour. For example, in the figure above, you can move from the disc at position ($1$, $1$) to either of its neighbours. However, from the disc at position ($1$, $2$) you can only move to the disc at position ($1$, $1$). If you wish to move from ($1$, $2$) to ($1$, $3$) then you would have to rotate this disc three times so that the colour (red) on the adjacent sectors are the same.
For each rotate move, a penalty point is added to the score. The aim is to reach the bottom right with as few penalty points as possible. For example, in the arrangement described in the above figure, the best possible score is $2$, corresponding to the following path: Move from ($1$, $1$) to ($2$, $1$). Move from ($2$, $1$) to ($2$, $2$). Rotate. Rotate. Move from ($2$, $2$) to ($2$, $3$). Move from ($2$, $3$) to ($1$, $3$). Move from ($1$, $3$) to ($1$, $4$). Finally, move from ($1$, $4$) to ($2$, $4$).
Your task is to determine the minimum number of penalty points required to go from the top left disc to the bottom right disc for the given arrangement of discs.

-----Input:-----
The first line contains two integers $M$ and $N$. $M$ is the number of rows and $N$ is the number of columns in the given arrangment. This is followed by $M \times N$ lines of input. Lines $2$ to $N+1$, describe the colours on the discs on the first row, Lines $N+2$ to $2 \cdot N+1$ describe the colours on discs in the second row and so on. Each of these lines contain a permutation of the set {R, G, B, Y} giving the colours in the top, right, bottom and left sectors in that order.

-----Output:-----
A single integer on a single line indicating the minimum number of penalty points required to go from the top left disc to the bottom right disc for the given arrangement of discs.

-----Constraints:-----
- In $80 \%$ of the input, $1 \leq M,N \leq 60$.
- In all the inputs $1 \leq M,N \leq 1000$.

-----Sample Input-----
2 4
G Y B R
B G R Y
G Y B R
G R B Y
B Y G R
G B R Y
B R G Y
B R G Y

-----Sample Output-----
2
user: You are playing a game where you have been sent in a town to collect 10 types of coin and their symbol are defined with $A, B, C, D, E, F, G, H , I, J$. In that town every enemy have a coin. By killing one you will get a coin from that enemy. Each enemy have only a unique coin.
The challange of the game is You have to collect all the coin and only then you will get the victory. You are a brave gamer so you took this hard challange and successfully finished it. After finishing, you are thinking of the game. You know the order off collecting coin. Now you are thinking how many enemy did you have killed?
Can you solve that out?

-----Input:-----
First line of the input is an integer $T$.Next T line consists of a string which denotes the order of your collecting coins. The string consists of Uppercase latin latter only and from A to J.

-----Output:-----
Print T line, in each line an integer with the number of enemy you have killed in the operation.

-----Constraints-----
- $1 \leq T \leq 5000$

-----Sample Input:-----
1
ABCDEFGHIJ

-----Sample Output:-----
10
user: Chef loves to play with iron (Fe) and magnets (Ma). He took a row of $N$ cells (numbered $1$ through $N$) and placed some objects in some of these cells. You are given a string $S$ with length $N$ describing them; for each valid $i$, the $i$-th character of $S$ is one of the following:
- 'I' if the $i$-th cell contains a piece of iron
- 'M' if the $i$-th cell contains a magnet
- '_' if the $i$-th cell is empty
- ':' if the $i$-th cell contains a conducting sheet
- 'X' if the $i$-th cell is blocked
If there is a magnet in a cell $i$ and iron in a cell $j$, the attraction power between these cells is $P_{i,j} = K+1 - |j-i| - S_{i,j}$, where $S_{i,j}$ is the number of cells containing sheets between cells $i$ and $j$. This magnet can only attract this iron if $P_{i, j} > 0$ and there are no blocked cells between the cells $i$ and $j$.
Chef wants to choose some magnets (possibly none) and to each of these magnets, assign a piece of iron which this magnet should attract. Each piece of iron may only be attracted by at most one magnet and only if the attraction power between them is positive and there are no blocked cells between them. Find the maximum number of magnets Chef can choose.

-----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 a single string $S$ with length $N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum number of magnets that can attract iron.

-----Constraints-----
- $1 \le T \le 2,000$
- $1 \le N \le 10^5$
- $0 \le K \le 10^5$
- $S$ contains only characters 'I', 'M', '_', ':' and 'X'
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^6$

-----Subtasks-----
Subtask #1 (30 points): there are no sheets, i.e. $S$ does not contain the character ':'
Subtask #2 (70 points): original constraints

-----Example Input-----
2
4 5
I::M
9 10
MIM_XII:M

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

-----Explanation-----
Example case 1: The attraction power between the only magnet and the only piece of iron is $5+1-3-2 = 1$. Note that it decreases with distance and the number of sheets.
Example case 2:
The magnets in cells $1$ and $3$ can attract the piece of iron in cell $2$, since the attraction power is $10$ in both cases. They cannot attract iron in cells $6$ or $7$ because there is a wall between them.
The magnet in cell $9$ can attract the pieces of iron in cells $7$ and $6$; the attraction power is $8$ and $7$ respectively.
user: Tuzik and Vanya are playing the following game.
They have an N × M board and a chip to indicate the current game position. The chip can be placed on any one cell of the game board, each of which is uniquely identified by an ordered pair of positive integers (r, c), where 1 ≤ r ≤ N is the row number and 1 ≤ c ≤ M is the column number.
Initially, the chip is placed at the cell identified as (1, 1). For his move, a player can move it either 1, 2 or 3 cells up, or 1 or 2 cells to the right. The player who can not move the chip loses. In other words, a player suffers defeat if the chip is placed in the cell (N, M) at the start of his turn.
Tuzik starts the game. You have to determine who will win the game if both players play optimally.

-----Input-----
The first line contains an integer T denoting the number of tests. Each of the following T lines contain two integers N and M.

-----Output-----
For each test output "Tuzik" or "Vanya" on a separate line, indicating who will win the game.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N, M ≤ 106

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

Output:
Tuzik
Vanya


-----Explanation-----Test case 1: On his first turn Tuzik moves chip 3 cells up to the cell (4, 1). On his turn Vanya can move chip only right to the cell (4, 2) or to the cell (4, 3) and after that Tuzik moves it to (4, 4) and finishes the game.

Test case 2: On his first Turn Tuzik can move chip to the cell (2, 1) or (1, 2), but on his next turn Vanya moves it to (2, 2) and wins the game.
user: Ishank lives in a country in which there are N$N$ cities and N−1$N-1$ roads. All the cities are connected via these roads. Each city has been assigned a unique number from 1 to N$N$. The country can be assumed as a tree, with nodes representing the cities and edges representing the roads. The tree is rooted at 1.Every Time, when a traveler through a road, he will either gain some amount or has to pay some amount.
Abhineet is a traveler and wishes to travel to various cities in this country. There's a law in the country for travelers, according to which, when a traveler moves from the city A$A$ to city B$B$, where city A$A$ and B$B$ are connected by a road then the traveler is either paid or has to pay the amount of money equal to profit or loss respectively. When he moves from A$A$ to B$B$, he hires a special kind of vehicle which can reverse its direction at most once. Reversing the direction means earlier the vehicle is going towards the root, then away from the root or vice versa. Abhineet is analyzing his trip and therefore gave Q$Q$ queries to his friend, Ishank, a great coder. In every query, he gives two cities A$A$ and B$B$. Ishank has to calculate the maximum amount he can gain (if he cannot gain, then the minimum amount he will lose) if he goes from the city A$A$ to city B$B$.

-----Input:-----
-The first line of the input contains a two space-separated integers N and Q.
-The next N-1 line contains 3 space-separated integers Xi and Yi and Zi denoting that cities Xi and Yi are connected by a road which gives profit Zi (Negative Zi represents loss).
-The next Q contains 2 space-separated integers A and B denoting two cities.

-----Output:-----
Print a single line corresponding to each query — the maximum amount he can gain (if he cannot gain, then the minimum amount he will lose with negative sign) if he goes from city A to city B.

-----Constraints-----
- 2≤N≤105$2 \leq N \leq 10^5$
- 1≤Q≤105$1 \leq Q \leq 10^5$
- 1≤Xi,Yi,A,B≤N$1 \leq Xi, Yi, A, B \leq N$
- abs(Zi)≤109$ abs(Zi) \leq 10^9$

-----Sample Input:-----
9 5
1 2 8
1 3 -9
2 4 1
2 5 -6
3 6 7
3 7 6
6 8 3
6 9 4
1 2
2 7
4 3
3 2
8 9

-----Sample Output:-----
10
5
0
-1
21

-----EXPLANATION:-----
In the first query, he goes from 1 to 2, 2 to 4, takes a turn and go to 2. Therefore profit=8+1+1=10.
user: Raj is a math pro and number theory expert. One day, he met his age-old friend Chef. Chef claimed to be better at number theory than Raj, so Raj gave him some fuzzy problems to solve. In one of those problems, he gave Chef a 3$3$-tuple of non-negative integers (a0,b0,c0)$(a_0, b_0, c_0)$ and told Chef to convert it to another tuple (x,y,z)$(x, y, z)$.
Chef may perform the following operations any number of times (including zero) on his current tuple (a,b,c)$(a, b, c)$, in any order:
- Choose one element of this tuple, i.e. a$a$, b$b$ or c$c$. Either add 1$1$ to that element or subtract 1$1$ from it. The cost of this operation is 1$1$.
- Merge: Change the tuple to (a−1,b−1,c+1)$(a-1, b-1, c+1)$, (a−1,b+1,c−1)$(a-1, b+1, c-1)$ or (a+1,b−1,c−1)$(a+1, b-1, c-1)$, i.e. add 1$1$ to one element and subtract 1$1$ from the other two. The cost of this operation is 0$0$.
- Split: Change the tuple to (a−1,b+1,c+1)$(a-1, b+1, c+1)$, (a+1,b−1,c+1)$(a+1, b-1, c+1)$ or (a+1,b+1,c−1)$(a+1, b+1, c-1)$, i.e. subtract 1$1$ from one element and add 1$1$ to the other two. The cost of this operation is also 0$0$.
After each operation, all elements of Chef's tuple must be non-negative. It is not allowed to perform an operation that would make one or more elements of this tuple negative.
Can you help Chef find the minimum cost of converting the tuple (a0,b0,c0)$(a_0, b_0, c_0)$ to the tuple (x,y,z)$(x, y, z)$? It can be easily proved that it is always possible to convert any tuple of non-negative integers to any other.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first and only line of each test case contains six space-separated integers a0$a_0$, b0$b_0$, c0$c_0$, x$x$, y$y$ and z$z$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum cost.

-----Constraints-----
- 1≤T≤105$1 \le T \le 10^5$
- 0≤a0,b0,c0,x,y,z≤1018$0 \le a_0, b_0, c_0, x, y, z \le 10^{18}$

-----Subtasks-----
Subtask #1 (20 points): 0≤a0,b0,c0,x,y,z≤100$0 \le a_0, b_0, c_0, x, y, z \le 100$
Subtask #2 (80 points): original constraints

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

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

-----Explanation-----
Example case 1: The tuple (1,1,1)$(1, 1, 1)$ can be converted to (2,2,2)$(2, 2, 2)$ using only three Split operations, with cost 0$0$: (1,1,1)→(2,0,2)→(1,1,3)→(2,2,2)$(1, 1, 1) \rightarrow (2, 0, 2) \rightarrow (1, 1, 3) \rightarrow (2, 2, 2)$.
Example case 2: We can use one addition operation and one Split operation: (1,2,3)→(1,3,3)→(2,4,2)$(1, 2, 3) \rightarrow (1, 3, 3) \rightarrow (2, 4, 2)$.
user: Chefina  is  always interested to play with string. But due to exam pressure she has no time to solve a string problem. She wants your help. Can you help her to solve that problem?
You are given a string. You have to find out the $Wonder$ $Sum$ of the string. $Wonder$ $Sum$ of a string is defined as the sum of the value of each character of the string. 
The value of each character means:
- If the string is started with "a" , then the value of each character of the string is like "a"=100, "b"=101, "c"="102" ………"z"=125.
- If the string is started with "z" , then the value of each character of the string is like "a"=2600, "b"=2601, "c"="2602" ………"z"=2625.
Since even the $Wonder$ $Sum$ can be large, output $Wonder$ $Sum$ modulo  ($10^9 + 7$).

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, a string $S$ with lower case alphabet 
only.

-----Output:-----
For each testcase, output in a single line integer i.e.  $Wonder$ $Sum$ modulo  ($10^9 + 7$).

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq |S| \leq 10^5$

-----Sample Input:-----
$2$$cab$
$sdef$

-----Sample Output:-----
$903$
$7630$

-----EXPLANATION:-----
i) For the first test case, since the string is started with "$c$", so output is ($302$+$300$+$301$)=$903$
ii)For the second test case, since the string is started with "$s$", so output is ($1918$+$1903$+$1904$+$1905$)=$7630$