meetforever/GRPO_CL huggingface dataset:
user: A star is a figure of the following type: an asterisk character '*' in the center of the figure and four rays (to the left, right, top, bottom) of the same positive length. The size of a star is the length of its rays. The size of a star must be a positive number (i.e. rays of length $0$ are not allowed).

Let's consider empty cells are denoted by '.', then the following figures are stars:

 [Image] The leftmost figure is a star of size $1$, the middle figure is a star of size $2$ and the rightmost figure is a star of size $3$. 

You are given a rectangular grid of size $n \times m$ consisting only of asterisks '*' and periods (dots) '.'. Rows are numbered from $1$ to $n$, columns are numbered from $1$ to $m$. Your task is to draw this grid using any number of stars or find out that it is impossible. Stars can intersect, overlap or even coincide with each other. The number of stars in the output can't exceed $n \cdot m$. Each star should be completely inside the grid. You can use stars of same and arbitrary sizes.

In this problem, you do not need to minimize the number of stars. Just find any way to draw the given grid with at most $n \cdot m$ stars.


-----Input-----

The first line of the input contains two integers $n$ and $m$ ($3 \le n, m \le 100$) — the sizes of the given grid.

The next $n$ lines contains $m$ characters each, the $i$-th line describes the $i$-th row of the grid. It is guaranteed that grid consists of characters '*' and '.' only.


-----Output-----

If it is impossible to draw the given grid using stars only, print "-1".

Otherwise in the first line print one integer $k$ ($0 \le k \le n \cdot m$) — the number of stars needed to draw the given grid. The next $k$ lines should contain three integers each — $x_j$, $y_j$ and $s_j$, where $x_j$ is the row index of the central star character, $y_j$ is the column index of the central star character and $s_j$ is the size of the star. Each star should be completely inside the grid.


-----Examples-----
Input
6 8
....*...
...**...
..*****.
...**...
....*...
........

Output
3
3 4 1
3 5 2
3 5 1

Input
5 5
.*...
****.
.****
..**.
.....

Output
3
2 2 1
3 3 1
3 4 1

Input
5 5
.*...
***..
.*...
.*...
.....

Output
-1

Input
3 3
*.*
.*.
*.*

Output
-1



-----Note-----

In the first example the output 2

3 4 1

3 5 2



is also correct.
user: Let's call (yet again) a string good if its length is even, and every character in odd position of this string is different from the next character (the first character is different from the second, the third is different from the fourth, and so on). For example, the strings good, string and xyyx are good strings, and the strings bad, aa and aabc are not good. Note that the empty string is considered good.

You are given a string $s$, you have to delete minimum number of characters from this string so that it becomes good.


-----Input-----

The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of characters in $s$.

The second line contains the string $s$, consisting of exactly $n$ lowercase Latin letters.


-----Output-----

In the first line, print one integer $k$ ($0 \le k \le n$) — the minimum number of characters you have to delete from $s$ to make it good.

In the second line, print the resulting string $s$. If it is empty, you may leave the second line blank, or not print it at all.


-----Examples-----
Input
4
good

Output
0
good

Input
4
aabc

Output
2
ab

Input
3
aaa

Output
3
user: You are given a connected undirected graph consisting of $n$ vertices and $m$ edges. There are no self-loops or multiple edges in the given graph.

You have to direct its edges in such a way that the obtained directed graph does not contain any paths of length two or greater (where the length of path is denoted as the number of traversed edges).


-----Input-----

The first line contains two integer numbers $n$ and $m$ ($2 \le n \le 2 \cdot 10^5$, $n - 1 \le m \le 2 \cdot 10^5$) — the number of vertices and edges, respectively.

The following $m$ lines contain edges: edge $i$ is given as a pair of vertices $u_i$, $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$). There are no multiple edges in the given graph, i. e. for each pair ($u_i, v_i$) there are no other pairs ($u_i, v_i$) and ($v_i, u_i$) in the list of edges. It is also guaranteed that the given graph is connected (there is a path between any pair of vertex in the given graph).


-----Output-----

If it is impossible to direct edges of the given graph in such a way that the obtained directed graph does not contain paths of length at least two, print "NO" in the first line.

Otherwise print "YES" in the first line, and then print any suitable orientation of edges: a binary string (the string consisting only of '0' and '1') of length $m$. The $i$-th element of this string should be '0' if the $i$-th edge of the graph should be directed from $u_i$ to $v_i$, and '1' otherwise. Edges are numbered in the order they are given in the input.


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

Output
YES
10100



-----Note-----

The picture corresponding to the first example: [Image]

And one of possible answers: $\text{of}$
user: You are given a set of $n$ segments on the axis $Ox$, each segment has integer endpoints between $1$ and $m$ inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le m$) — coordinates of the left and of the right endpoints. 

Consider all integer points between $1$ and $m$ inclusive. Your task is to print all such points that don't belong to any segment. The point $x$ belongs to the segment $[l; r]$ if and only if $l \le x \le r$.


-----Input-----

The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 100$) — the number of segments and the upper bound for coordinates.

The next $n$ lines contain two integers each $l_i$ and $r_i$ ($1 \le l_i \le r_i \le m$) — the endpoints of the $i$-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that $l_i=r_i$, i.e. a segment can degenerate to a point.


-----Output-----

In the first line print one integer $k$ — the number of points that don't belong to any segment.

In the second line print exactly $k$ integers in any order — the points that don't belong to any segment. All points you print should be distinct.

If there are no such points at all, print a single integer $0$ in the first line and either leave the second line empty or do not print it at all.


-----Examples-----
Input
3 5
2 2
1 2
5 5

Output
2
3 4 

Input
1 7
1 7

Output
0




-----Note-----

In the first example the point $1$ belongs to the second segment, the point $2$ belongs to the first and the second segments and the point $5$ belongs to the third segment. The points $3$ and $4$ do not belong to any segment.

In the second example all the points from $1$ to $7$ belong to the first segment.
user: You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

-----Constraints-----
 - 1\leq A\leq B\leq 10^{18}
 - 1\leq C,D\leq 10^9
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
A B C D

-----Output-----
Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

-----Sample Input-----
4 9 2 3

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

5 and 7 satisfy the condition.
user: An integer N is a multiple of 9 if and only if the sum of the digits in the decimal representation of N is a multiple of 9.
Determine whether N is a multiple of 9.

-----Constraints-----
 - 0 \leq N < 10^{200000}
 - N is an integer.

-----Input-----
Input is given from Standard Input in the following format:
N

-----Output-----
If N is a multiple of 9, print Yes; otherwise, print No.

-----Sample Input-----
123456789

-----Sample Output-----
Yes

The sum of these digits is 1+2+3+4+5+6+7+8+9=45, which is a multiple of 9, so 123456789 is a multiple of 9.
user: To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:
 - 1 yen (the currency of Japan)
 - 6 yen, 6^2(=36) yen, 6^3(=216) yen, ...
 - 9 yen, 9^2(=81) yen, 9^3(=729) yen, ...
At least how many operations are required to withdraw exactly N yen in total?
It is not allowed to re-deposit the money you withdrew.

-----Constraints-----
 - 1 \leq N \leq 100000
 - N is an integer.

-----Input-----
Input is given from Standard Input in the following format:
N

-----Output-----
If at least x operations are required to withdraw exactly N yen in total, print x.

-----Sample Input-----
127

-----Sample Output-----
4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.
user: You are given string S and T consisting of lowercase English letters.
Determine if S equals T after rotation.
That is, determine if S equals T after the following operation is performed some number of times:
Operation: Let S = S_1 S_2 ... S_{|S|}. Change S to S_{|S|} S_1 S_2 ... S_{|S|-1}.
Here, |X| denotes the length of the string X.

-----Constraints-----
 - 2 \leq |S| \leq 100
 - |S| = |T|
 - S and T consist of lowercase English letters.

-----Input-----
Input is given from Standard Input in the following format:
S
T

-----Output-----
If S equals T after rotation, print Yes; if it does not, print No.

-----Sample Input-----
kyoto
tokyo

-----Sample Output-----
Yes

 - In the first operation, kyoto becomes okyot.
 - In the second operation, okyot becomes tokyo.
user: Given are two strings S and T.
Let us change some of the characters in S so that T will be a substring of S.
At least how many characters do we need to change?
Here, a substring is a consecutive subsequence. For example, xxx is a substring of yxxxy, but not a substring of xxyxx.

-----Constraints-----
 - The lengths of S and T are each at least 1 and at most 1000.
 - The length of T is at most that of S.
 - S and T consist of lowercase English letters.

-----Input-----
Input is given from Standard Input in the following format:
S
T

-----Output-----
Print the minimum number of characters in S that need to be changed.

-----Sample Input-----
cabacc
abc

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

For example, changing the fourth character a in S to c will match the second through fourth characters in S to T.
Since S itself does not have T as its substring, this number of changes - one - is the minimum needed.
user: You are given positive integers A and B.
Find the K-th largest positive integer that divides both A and B.
The input guarantees that there exists such a number.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq A, B \leq 100
 - The K-th largest positive integer that divides both A and B exists.
 - K \geq 1

-----Input-----
Input is given from Standard Input in the following format:
A B K

-----Output-----
Print the K-th largest positive integer that divides both A and B.

-----Sample Input-----
8 12 2

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

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.
user: Takahashi loves gold coins. He gains 1000 happiness points for each 500-yen coin he has and gains 5 happiness points for each 5-yen coin he has. (Yen is the currency of Japan.)
Takahashi has X yen. If he exchanges his money so that he will gain the most happiness points, how many happiness points will he earn?
(We assume that there are six kinds of coins available: 500-yen, 100-yen, 50-yen, 10-yen, 5-yen, and 1-yen coins.)

-----Constraints-----
 - 0 \leq X \leq 10^9
 - X is an integer.

-----Input-----
Input is given from Standard Input in the following format:
X

-----Output-----
Print the maximum number of happiness points that can be earned.

-----Sample Input-----
1024

-----Sample Output-----
2020

By exchanging his money so that he gets two 500-yen coins and four 5-yen coins, he gains 2020 happiness points, which is the maximum number of happiness points that can be earned.
user: There are N people living on a number line.
The i-th person lives at coordinate X_i.
You are going to hold a meeting that all N people have to attend.
The meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.
Find the minimum total points of stamina the N people have to spend.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq N \leq 100
 - 1 \leq X_i \leq 100

-----Input-----
Input is given from Standard Input in the following format:
N
X_1 X_2 ... X_N

-----Output-----
Print the minimum total stamina the N people have to spend.

-----Sample Input-----
2
1 4

-----Sample Output-----
5

Assume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.
Note that you can hold the meeting only at an integer coordinate.
user: Takahashi's house has only one socket.
Takahashi wants to extend it with some number of power strips, each with A sockets, into B or more empty sockets.
One power strip with A sockets can extend one empty socket into A empty sockets.
Find the minimum number of power strips required.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq A \leq 20
 - 1 \leq B \leq 20

-----Input-----
Input is given from Standard Input in the following format:
A B

-----Output-----
Print the minimum number of power strips required.

-----Sample Input-----
4 10

-----Sample Output-----
3

3 power strips, each with 4 sockets, extend the socket into 10 empty sockets.
user: You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.

-----Constraints-----
 - S and T are strings of length 3 each.
 - S and T consist of S, C, and R.

-----Input-----
Input is given from Standard Input in the following format:
S
T

-----Output-----
Print the number of days for which the forecast was correct.

-----Sample Input-----
CSS
CSR

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

 - For the first day, it was forecast to be cloudy, and it was indeed cloudy.
 - For the second day, it was forecast to be sunny, and it was indeed sunny.
 - For the third day, it was forecast to be sunny, but it was rainy.
Thus, the forecast was correct for two days in this case.
user: We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.
Print the number of elements p_i (1 < i < n) that satisfy the following condition:
 - p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

-----Constraints-----
 - All values in input are integers.
 - 3 \leq n \leq 20
 - p is a permutation of {1,\ 2,\ ...,\ n}.

-----Input-----
Input is given from Standard Input in the following format:
n
p_1 p_2 ... p_n

-----Output-----
Print the number of elements p_i (1 < i < n) that satisfy the condition.

-----Sample Input-----
5
1 3 5 4 2

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

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.
user: -----Input-----

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of points on a plane.

Each of the next n lines contains two real coordinates x_{i} and y_{i} of the $i^{\text{th}}$ point, specified with exactly 2 fractional digits. All coordinates are between  - 1000 and 1000, inclusive.


-----Output-----

Output a single real number θ — the answer to the problem statement. The absolute or relative error of your answer should be at most 10^{ - 2}.


-----Examples-----
Input
8
-2.14 2.06
-1.14 2.04
-2.16 1.46
-2.14 0.70
-1.42 0.40
-0.94 -0.48
-1.42 -1.28
-2.16 -1.62

Output
5.410

Input
5
2.26 1.44
2.28 0.64
2.30 -0.30
1.58 0.66
3.24 0.66

Output
5.620

Input
8
6.98 2.06
6.40 1.12
5.98 0.24
5.54 -0.60
7.16 0.30
7.82 1.24
8.34 0.24
8.74 -0.76

Output
5.480

Input
5
10.44 2.06
10.90 0.80
11.48 -0.48
12.06 0.76
12.54 2.06

Output
6.040

Input
8
16.94 2.42
15.72 2.38
14.82 1.58
14.88 0.50
15.76 -0.16
16.86 -0.20
17.00 0.88
16.40 0.92

Output
6.040

Input
7
20.62 3.00
21.06 2.28
21.56 1.36
21.66 0.56
21.64 -0.52
22.14 2.32
22.62 3.04

Output
6.720
user: You are given an array $s$ consisting of $n$ integers.

You have to find any array $t$ of length $k$ such that you can cut out maximum number of copies of array $t$ from array $s$.

Cutting out the copy of $t$ means that for each element $t_i$ of array $t$ you have to find $t_i$ in $s$ and remove it from $s$. If for some $t_i$ you cannot find such element in $s$, then you cannot cut out one more copy of $t$. The both arrays can contain duplicate elements.

For example, if $s = [1, 2, 3, 2, 4, 3, 1]$ and $k = 3$ then one of the possible answers is $t = [1, 2, 3]$. This array $t$ can be cut out $2$ times.   To cut out the first copy of $t$ you can use the elements $[1, \underline{\textbf{2}}, 3, 2, 4, \underline{\textbf{3}}, \underline{\textbf{1}}]$ (use the highlighted elements). After cutting out the first copy of $t$ the array $s$ can look like $[1, 3, 2, 4]$.  To cut out the second copy of $t$ you can use the elements $[\underline{\textbf{1}}, \underline{\textbf{3}}, \underline{\textbf{2}}, 4]$. After cutting out the second copy of $t$ the array $s$ will be $[4]$. 

Your task is to find such array $t$ that you can cut out the copy of $t$ from $s$ maximum number of times. If there are multiple answers, you may choose any of them.


-----Input-----

The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \cdot 10^5$) — the number of elements in $s$ and the desired number of elements in $t$, respectively.

The second line of the input contains exactly $n$ integers $s_1, s_2, \dots, s_n$ ($1 \le s_i \le 2 \cdot 10^5$).


-----Output-----

Print $k$ integers — the elements of array $t$ such that you can cut out maximum possible number of copies of this array from $s$. If there are multiple answers, print any of them. The required array $t$ can contain duplicate elements. All the elements of $t$ ($t_1, t_2, \dots, t_k$) should satisfy the following condition: $1 \le t_i \le 2 \cdot 10^5$.


-----Examples-----
Input
7 3
1 2 3 2 4 3 1

Output
1 2 3 

Input
10 4
1 3 1 3 10 3 7 7 12 3

Output
7 3 1 3

Input
15 2
1 2 1 1 1 2 1 1 2 1 2 1 1 1 1

Output
1 1 



-----Note-----

The first example is described in the problem statement.

In the second example the only answer is $[7, 3, 1, 3]$ and any its permutations. It can be shown that you cannot choose any other array such that the maximum number of copies you can cut out would be equal to $2$.

In the third example the array $t$ can be cut out $5$ times.
user: You are given a matrix $a$, consisting of $n$ rows and $m$ columns. Each cell contains an integer in it.

You can change the order of rows arbitrarily (including leaving the initial order), but you can't change the order of cells in a row. After you pick some order of rows, you traverse the whole matrix the following way: firstly visit all cells of the first column from the top row to the bottom one, then the same for the second column and so on. During the traversal you write down the sequence of the numbers on the cells in the same order you visited them. Let that sequence be $s_1, s_2, \dots, s_{nm}$. 

The traversal is $k$-acceptable if for all $i$ ($1 \le i \le nm - 1$) $|s_i - s_{i + 1}| \ge k$.

Find the maximum integer $k$ such that there exists some order of rows of matrix $a$ that it produces a $k$-acceptable traversal.


-----Input-----

The first line contains two integers $n$ and $m$ ($1 \le n \le 16$, $1 \le m \le 10^4$, $2 \le nm$) — the number of rows and the number of columns, respectively.

Each of the next $n$ lines contains $m$ integers ($1 \le a_{i, j} \le 10^9$) — the description of the matrix.


-----Output-----

Print a single integer $k$ — the maximum number such that there exists some order of rows of matrix $a$ that it produces an $k$-acceptable traversal.


-----Examples-----
Input
4 2
9 9
10 8
5 3
4 3

Output
5

Input
2 4
1 2 3 4
10 3 7 3

Output
0

Input
6 1
3
6
2
5
1
4

Output
3



-----Note-----

In the first example you can rearrange rows as following to get the $5$-acceptable traversal:

5 3

10 8

4 3

9 9



Then the sequence $s$ will be $[5, 10, 4, 9, 3, 8, 3, 9]$. Each pair of neighbouring elements have at least $k = 5$ difference between them.

In the second example the maximum $k = 0$, any order is $0$-acceptable.

In the third example the given order is already $3$-acceptable, you can leave it as it is.
user: You can not just take the file and send it. When Polycarp trying to send a file in the social network "Codehorses", he encountered an unexpected problem. If the name of the file contains three or more "x" (lowercase Latin letters "x") in a row, the system considers that the file content does not correspond to the social network topic. In this case, the file is not sent and an error message is displayed.

Determine the minimum number of characters to remove from the file name so after that the name does not contain "xxx" as a substring. Print 0 if the file name does not initially contain a forbidden substring "xxx".

You can delete characters in arbitrary positions (not necessarily consecutive). If you delete a character, then the length of a string is reduced by $1$. For example, if you delete the character in the position $2$ from the string "exxxii", then the resulting string is "exxii".


-----Input-----

The first line contains integer $n$ $(3 \le n \le 100)$ — the length of the file name.

The second line contains a string of length $n$ consisting of lowercase Latin letters only — the file name.


-----Output-----

Print the minimum number of characters to remove from the file name so after that the name does not contain "xxx" as a substring. If initially the file name dost not contain a forbidden substring "xxx", print 0.


-----Examples-----
Input
6
xxxiii

Output
1

Input
5
xxoxx

Output
0

Input
10
xxxxxxxxxx

Output
8



-----Note-----

In the first example Polycarp tried to send a file with name contains number $33$, written in Roman numerals. But he can not just send the file, because it name contains three letters "x" in a row. To send the file he needs to remove any one of this letters.
user: It is known that the area of a regular dodecagon inscribed in a circle of radius a is 3a^2.
Given an integer r, find the area of a regular dodecagon inscribed in a circle of radius r.

-----Constraints-----
 - 1 \leq r \leq 100
 - r is an integer.

-----Input-----
Input is given from Standard Input in the following format:
r

-----Output-----
Print an integer representing the area of the regular dodecagon.

-----Sample Input-----
4

-----Sample Output-----
48

The area of the regular dodecagon is 3 \times 4^2 = 48.
user: There are S sheep and W wolves.
If the number of wolves is greater than or equal to that of sheep, the wolves will attack the sheep.
If the wolves will attack the sheep, print unsafe; otherwise, print safe.

-----Constraints-----
 - 1 \leq S \leq 100
 - 1 \leq W \leq 100

-----Input-----
Input is given from Standard Input in the following format:
S W

-----Output-----
If the wolves will attack the sheep, print unsafe; otherwise, print safe.

-----Sample Input-----
4 5

-----Sample Output-----
unsafe

There are four sheep and five wolves. The number of wolves is not less than that of sheep, so they will attack them.