meetforever/GRPO_CL huggingface dataset:
user: You are given an integer array of length $n$.

You have to choose some subsequence of this array of maximum length such that this subsequence forms a increasing sequence of consecutive integers. In other words the required sequence should be equal to $[x, x + 1, \dots, x + k - 1]$ for some value $x$ and length $k$.

Subsequence of an array can be obtained by erasing some (possibly zero) elements from the array. You can erase any elements, not necessarily going successively. The remaining elements preserve their order. For example, for the array $[5, 3, 1, 2, 4]$ the following arrays are subsequences: $[3]$, $[5, 3, 1, 2, 4]$, $[5, 1, 4]$, but the array $[1, 3]$ is not.


-----Input-----

The first line of the input containing integer number $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array. The second line of the input containing $n$ integer numbers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) — the array itself.


-----Output-----

On the first line print $k$ — the maximum length of the subsequence of the given array that forms an increasing sequence of consecutive integers.

On the second line print the sequence of the indices of the any maximum length subsequence of the given array that forms an increasing sequence of consecutive integers.


-----Examples-----
Input
7
3 3 4 7 5 6 8

Output
4
2 3 5 6 

Input
6
1 3 5 2 4 6

Output
2
1 4 

Input
4
10 9 8 7

Output
1
1 

Input
9
6 7 8 3 4 5 9 10 11

Output
6
1 2 3 7 8 9 



-----Note-----

All valid answers for the first example (as sequences of indices):   $[1, 3, 5, 6]$  $[2, 3, 5, 6]$ 

All valid answers for the second example:   $[1, 4]$  $[2, 5]$  $[3, 6]$ 

All valid answers for the third example:   $[1]$  $[2]$  $[3]$  $[4]$ 

All valid answers for the fourth example:   $[1, 2, 3, 7, 8, 9]$
user: You are given integers A and B, each between 1 and 3 (inclusive).
Determine if there is an integer C between 1 and 3 (inclusive) such that A \times B \times C is an odd number.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq A, B \leq 3

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

-----Output-----
If there is an integer C between 1 and 3 that satisfies the condition, print Yes; otherwise, print No.

-----Sample Input-----
3 1

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

Let C = 3. Then, A \times B \times C = 3 \times 1 \times 3 = 9, which is an odd number.
user: There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?

-----Constraints-----
 - 1 \leq X,Y \leq 100
 - Y is an even number.
 - All values in input are integers.

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

-----Output-----
If it costs x yen to travel from Station A to Station C, print x.

-----Sample Input-----
81 58

-----Sample Output-----
110

 - The train fare is 81 yen.
 - The train fare is 58 ⁄ 2=29 yen with the 50% discount.
Thus, it costs 110 yen to travel from Station A to Station C.
user: Takahashi is going to set a 3-character password.
How many possible passwords are there if each of its characters must be a digit between 1 and N (inclusive)?

-----Constraints-----
 - 1 \leq N \leq 9
 - N is an integer.

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

-----Output-----
Print the number of possible passwords.

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

-----Sample Output-----
8

There are eight possible passwords: 111, 112, 121, 122, 211, 212, 221, and 222.
user: Shichi-Go-San (literally "Seven-Five-Three") is a traditional event in a certain country to celebrate the growth of seven-, five- and three-year-old children.
Takahashi is now X years old. Will his growth be celebrated in Shichi-Go-San this time?

-----Constraints-----
 - 1 ≤ X ≤ 9
 - X is an integer.

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

-----Output-----
If Takahashi's growth will be celebrated, print YES; if it will not, print NO.

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

-----Sample Output-----
YES

The growth of a five-year-old child will be celebrated.
user: Decades have passed since the beginning of AtCoder Beginner Contest.
The contests are labeled as ABC001, ABC002, ... from the first round, but after the 999-th round ABC999, a problem occurred: how the future rounds should be labeled?
In the end, the labels for the rounds from the 1000-th to the 1998-th are decided: ABD001, ABD002, ..., ABD999.
You are given an integer N between 1 and 1998 (inclusive). Print the first three characters of the label of the N-th round of AtCoder Beginner Contest.

-----Constraints-----
 - 1 \leq N \leq 1998
 - N is an integer.

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

-----Output-----
Print the first three characters of the label of the N-th round of AtCoder Beginner Contest.

-----Sample Input-----
999

-----Sample Output-----
ABC

The 999-th round of AtCoder Beginner Contest is labeled as ABC999.
user: In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.

Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.

Determine if there exists a pair of antennas that cannot communicate directly.

Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.  

-----Constraints-----
 - a, b, c, d, e and k are integers between 0 and 123 (inclusive).
 - a < b < c < d < e

-----Input-----
Input is given from Standard Input in the following format:
a
b
c
d
e
k

-----Output-----
Print :( if there exists a pair of antennas that cannot communicate directly, and print Yay! if there is no such pair.

-----Sample Input-----
1
2
4
8
9
15

-----Sample Output-----
Yay!

In this case, there is no pair of antennas that cannot communicate directly, because:
 - the distance between A and B is 2 - 1 = 1
 - the distance between A and C is 4 - 1 = 3
 - the distance between A and D is 8 - 1 = 7
 - the distance between A and E is 9 - 1 = 8
 - the distance between B and C is 4 - 2 = 2
 - the distance between B and D is 8 - 2 = 6
 - the distance between B and E is 9 - 2 = 7
 - the distance between C and D is 8 - 4 = 4
 - the distance between C and E is 9 - 4 = 5
 - the distance between D and E is 9 - 8 = 1
and none of them is greater than 15. Thus, the correct output is Yay!.
user: You will be given an integer a and a string s consisting of lowercase English letters as input.
Write a program that prints s if a is not less than 3200 and prints red if a is less than 3200.

-----Constraints-----
 - 2800 \leq a < 5000
 - s is a string of length between 1 and 10 (inclusive).
 - Each character of s is a lowercase English letter.

-----Input-----
Input is given from Standard Input in the following format:
a
s

-----Output-----
If a is not less than 3200, print s; if a is less than 3200, print red.

-----Sample Input-----
3200
pink

-----Sample Output-----
pink

a = 3200 is not less than 3200, so we print s = pink.
user: A programming competition site AtCode regularly holds programming contests.
The next contest on AtCode is called ABC, which is rated for contestants with ratings less than 1200.
The contest after the ABC is called ARC, which is rated for contestants with ratings less than 2800.
The contest after the ARC is called AGC, which is rated for all contestants.
Takahashi's rating on AtCode is R. What is the next contest rated for him?

-----Constraints-----
 - 0 ≤ R ≤ 4208
 - R is an integer.

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

-----Output-----
Print the name of the next contest rated for Takahashi (ABC, ARC or AGC).

-----Sample Input-----
1199

-----Sample Output-----
ABC

1199 is less than 1200, so ABC will be rated.
user: Cat Snuke is learning to write characters.
Today, he practiced writing digits 1 and 9, but he did it the other way around.
You are given a three-digit integer n written by Snuke.
Print the integer obtained by replacing each digit 1 with 9 and each digit 9 with 1 in n.

-----Constraints-----
 - 111 \leq n \leq 999
 - n is an integer consisting of digits 1 and 9.

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

-----Output-----
Print the integer obtained by replacing each occurrence of 1 with 9 and each occurrence of 9 with 1 in n.

-----Sample Input-----
119

-----Sample Output-----
991

Replace the 9 in the ones place with 1, the 1 in the tens place with 9 and the 1 in the hundreds place with 9. The answer is 991.
user: Alice guesses the strings that Bob made for her.

At first, Bob came up with the secret string $a$ consisting of lowercase English letters. The string $a$ has a length of $2$ or more characters. Then, from string $a$ he builds a new string $b$ and offers Alice the string $b$ so that she can guess the string $a$.

Bob builds $b$ from $a$ as follows: he writes all the substrings of length $2$ of the string $a$ in the order from left to right, and then joins them in the same order into the string $b$.

For example, if Bob came up with the string $a$="abac", then all the substrings of length $2$ of the string $a$ are: "ab", "ba", "ac". Therefore, the string $b$="abbaac".

You are given the string $b$. Help Alice to guess the string $a$ that Bob came up with. It is guaranteed that $b$ was built according to the algorithm given above. It can be proved that the answer to the problem is unique.


-----Input-----

The first line contains a single positive integer $t$ ($1 \le t \le 1000$) — the number of test cases in the test. Then $t$ test cases follow.

Each test case consists of one line in which the string $b$ is written, consisting of lowercase English letters ($2 \le |b| \le 100$) — the string Bob came up with, where $|b|$ is the length of the string $b$. It is guaranteed that $b$ was built according to the algorithm given above.


-----Output-----

Output $t$ answers to test cases. Each answer is the secret string $a$, consisting of lowercase English letters, that Bob came up with.


-----Example-----
Input
4
abbaac
ac
bccddaaf
zzzzzzzzzz

Output
abac
ac
bcdaf
zzzzzz



-----Note-----

The first test case is explained in the statement.

In the second test case, Bob came up with the string $a$="ac", the string $a$ has a length $2$, so the string $b$ is equal to the string $a$.

In the third test case, Bob came up with the string $a$="bcdaf", substrings of length $2$ of string $a$ are: "bc", "cd", "da", "af", so the string $b$="bccddaaf".
user: You are given two positive integers $a$ and $b$. In one move you can increase $a$ by $1$ (replace $a$ with $a+1$). Your task is to find the minimum number of moves you need to do in order to make $a$ divisible by $b$. It is possible, that you have to make $0$ moves, as $a$ is already divisible by $b$. You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$).


-----Output-----

For each test case print the answer — the minimum number of moves you need to do in order to make $a$ divisible by $b$.


-----Example-----
Input
5
10 4
13 9
100 13
123 456
92 46

Output
2
5
4
333
0
user: The heat during the last few days has been really intense. Scientists from all over the Berland study how the temperatures and weather change, and they claim that this summer is abnormally hot. But any scientific claim sounds a lot more reasonable if there are some numbers involved, so they have decided to actually calculate some value which would represent how high the temperatures are.

Mathematicians of Berland State University came up with a special heat intensity value. This value is calculated as follows:

Suppose we want to analyze the segment of $n$ consecutive days. We have measured the temperatures during these $n$ days; the temperature during $i$-th day equals $a_i$.

We denote the average temperature of a segment of some consecutive days as the arithmetic mean of the temperature measures during this segment of days. So, if we want to analyze the average temperature from day $x$ to day $y$, we calculate it as $\frac{\sum \limits_{i = x}^{y} a_i}{y - x + 1}$ (note that division is performed without any rounding). The heat intensity value is the maximum of average temperatures over all segments of not less than $k$ consecutive days. For example, if analyzing the measures $[3, 4, 1, 2]$ and $k = 3$, we are interested in segments $[3, 4, 1]$, $[4, 1, 2]$ and $[3, 4, 1, 2]$ (we want to find the maximum value of average temperature over these segments).

You have been hired by Berland State University to write a program that would compute the heat intensity value of a given period of days. Are you up to this task?


-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 5000$) — the number of days in the given period, and the minimum number of days in a segment we consider when calculating heat intensity value, respectively.

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le 5000$) — the temperature measures during given $n$ days.


-----Output-----

Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than $k$ consecutive days.

Your answer will be considered correct if the following condition holds: $|res - res_0| < 10^{-6}$, where $res$ is your answer, and $res_0$ is the answer given by the jury's solution.


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

Output
2.666666666666667
user: You are given an array $a$ of length $n$.

You are also given a set of distinct positions $p_1, p_2, \dots, p_m$, where $1 \le p_i < n$. The position $p_i$ means that you can swap elements $a[p_i]$ and $a[p_i + 1]$. You can apply this operation any number of times for each of the given positions.

Your task is to determine if it is possible to sort the initial array in non-decreasing order ($a_1 \le a_2 \le \dots \le a_n$) using only allowed swaps.

For example, if $a = [3, 2, 1]$ and $p = [1, 2]$, then we can first swap elements $a[2]$ and $a[3]$ (because position $2$ is contained in the given set $p$). We get the array $a = [3, 1, 2]$. Then we swap $a[1]$ and $a[2]$ (position $1$ is also contained in $p$). We get the array $a = [1, 3, 2]$. Finally, we swap $a[2]$ and $a[3]$ again and get the array $a = [1, 2, 3]$, sorted in non-decreasing order.

You can see that if $a = [4, 1, 2, 3]$ and $p = [3, 2]$ then you cannot sort the array.

You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 100$) — the number of test cases.

Then $t$ test cases follow. The first line of each test case contains two integers $n$ and $m$ ($1 \le m < n \le 100$) — the number of elements in $a$ and the number of elements in $p$. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 100$). The third line of the test case contains $m$ integers $p_1, p_2, \dots, p_m$ ($1 \le p_i < n$, all $p_i$ are distinct) — the set of positions described in the problem statement.


-----Output-----

For each test case, print the answer — "YES" (without quotes) if you can sort the initial array in non-decreasing order ($a_1 \le a_2 \le \dots \le a_n$) using only allowed swaps. Otherwise, print "NO".


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

Output
YES
NO
YES
YES
NO
YES
user: Polycarp loves ciphers. He has invented his own cipher called repeating.

Repeating cipher is used for strings. To encrypt the string $s=s_{1}s_{2} \dots s_{m}$ ($1 \le m \le 10$), Polycarp uses the following algorithm:

  he writes down $s_1$ ones,  he writes down $s_2$ twice,  he writes down $s_3$ three times,  ...  he writes down $s_m$ $m$ times. 

For example, if $s$="bab" the process is: "b" $\to$ "baa" $\to$ "baabbb". So the encrypted $s$="bab" is "baabbb".

Given string $t$ — the result of encryption of some string $s$. Your task is to decrypt it, i. e. find the string $s$.


-----Input-----

The first line contains integer $n$ ($1 \le n \le 55$) — the length of the encrypted string. The second line of the input contains $t$ — the result of encryption of some string $s$. It contains only lowercase Latin letters. The length of $t$ is exactly $n$.

It is guaranteed that the answer to the test exists.


-----Output-----

Print such string $s$ that after encryption it equals $t$.


-----Examples-----
Input
6
baabbb

Output
bab
Input
10
ooopppssss

Output
oops
Input
1
z

Output
z
user: You are given an undirected weighted connected graph with $n$ vertices and $m$ edges without loops and multiple edges.

The $i$-th edge is $e_i = (u_i, v_i, w_i)$; the distance between vertices $u_i$ and $v_i$ along the edge $e_i$ is $w_i$ ($1 \le w_i$). The graph is connected, i. e. for any pair of vertices, there is at least one path between them consisting only of edges of the given graph.

A minimum spanning tree (MST) in case of positive weights is a subset of the edges of a connected weighted undirected graph that connects all the vertices together and has minimum total cost among all such subsets (total cost is the sum of costs of chosen edges).

You can modify the given graph. The only operation you can perform is the following: increase the weight of some edge by $1$. You can increase the weight of each edge multiple (possibly, zero) times.

Suppose that the initial MST cost is $k$. Your problem is to increase weights of some edges with minimum possible number of operations in such a way that the cost of MST in the obtained graph remains $k$, but MST is unique (it means that there is only one way to choose MST in the obtained graph).

Your problem is to calculate the minimum number of operations required to do it.


-----Input-----

The first line of the input contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5, n - 1 \le m \le 2 \cdot 10^5$) — the number of vertices and the number of edges in the initial graph.

The next $m$ lines contain three integers each. The $i$-th line contains the description of the $i$-th edge $e_i$. It is denoted by three integers $u_i, v_i$ and $w_i$ ($1 \le u_i, v_i \le n, u_i \ne v_i, 1 \le w \le 10^9$), where $u_i$ and $v_i$ are vertices connected by the $i$-th edge and $w_i$ is the weight of this edge.

It is guaranteed that the given graph doesn't contain loops and multiple edges (i.e. for each $i$ from $1$ to $m$ $u_i \ne v_i$ and for each unordered pair of vertices $(u, v)$ there is at most one edge connecting this pair of vertices). It is also guaranteed that the given graph is connected.


-----Output-----

Print one integer — the minimum number of operations to unify MST of the initial graph without changing the cost of MST.


-----Examples-----
Input
8 10
1 2 1
2 3 2
2 4 5
1 4 2
6 3 3
6 1 3
3 5 2
3 7 1
4 8 1
6 2 4

Output
1

Input
4 3
2 1 3
4 3 4
2 4 1

Output
0

Input
3 3
1 2 1
2 3 2
1 3 3

Output
0

Input
3 3
1 2 1
2 3 3
1 3 3

Output
1

Input
1 0

Output
0

Input
5 6
1 2 2
2 3 1
4 5 3
2 4 2
1 4 2
1 5 3

Output
2



-----Note-----

The picture corresponding to the first example: [Image]

You can, for example, increase weight of the edge $(1, 6)$ or $(6, 3)$ by $1$ to unify MST.

The picture corresponding to the last example: $\$ 8$

You can, for example, increase weights of edges $(1, 5)$ and $(2, 4)$ by $1$ to unify MST.
user: You have a garland consisting of $n$ lamps. Each lamp is colored red, green or blue. The color of the $i$-th lamp is $s_i$ ('R', 'G' and 'B' — colors of lamps in the garland).

You have to recolor some lamps in this garland (recoloring a lamp means changing its initial color to another) in such a way that the obtained garland is nice.

A garland is called nice if any two lamps of the same color have distance divisible by three between them. I.e. if the obtained garland is $t$, then for each $i, j$ such that $t_i = t_j$ should be satisfied $|i-j|~ mod~ 3 = 0$. The value $|x|$ means absolute value of $x$, the operation $x~ mod~ y$ means remainder of $x$ when divided by $y$.

For example, the following garlands are nice: "RGBRGBRG", "GB", "R", "GRBGRBG", "BRGBRGB". The following garlands are not nice: "RR", "RGBG".

Among all ways to recolor the initial garland to make it nice you have to choose one with the minimum number of recolored lamps. If there are multiple optimal solutions, print any of them.


-----Input-----

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

The second line of the input contains the string $s$ consisting of $n$ characters 'R', 'G' and 'B' — colors of lamps in the garland.


-----Output-----

In the first line of the output print one integer $r$ — the minimum number of recolors needed to obtain a nice garland from the given one.

In the second line of the output print one string $t$ of length $n$ — a nice garland obtained from the initial one with minimum number of recolors. If there are multiple optimal solutions, print any of them.


-----Examples-----
Input
3
BRB

Output
1
GRB

Input
7
RGBGRBB

Output
3
RGBRGBR
user: Takahashi received otoshidama (New Year's money gifts) from N of his relatives.
You are given N values x_1, x_2, ..., x_N and N strings u_1, u_2, ..., u_N as input. Each string u_i is either JPY or BTC, and x_i and u_i represent the content of the otoshidama from the i-th relative.
For example, if x_1 = 10000 and u_1 = JPY, the otoshidama from the first relative is 10000 Japanese yen; if x_2 = 0.10000000 and u_2 = BTC, the otoshidama from the second relative is 0.1 bitcoins.
If we convert the bitcoins into yen at the rate of 380000.0 JPY per 1.0 BTC, how much are the gifts worth in total?

-----Constraints-----
 - 2 \leq N \leq 10
 - u_i = JPY or BTC.
 - If u_i = JPY, x_i is an integer such that 1 \leq x_i \leq 10^8.
 - If u_i = BTC, x_i is a decimal with 8 decimal digits, such that 0.00000001 \leq x_i \leq 100.00000000.

-----Input-----
Input is given from Standard Input in the following format:
N
x_1 u_1
x_2 u_2
:
x_N u_N

-----Output-----
If the gifts are worth Y yen in total, print the value Y (not necessarily an integer).
Output will be judged correct when the absolute or relative error from the judge's output is at most 10^{-5}.

-----Sample Input-----
2
10000 JPY
0.10000000 BTC

-----Sample Output-----
48000.0

The otoshidama from the first relative is 10000 yen. The otoshidama from the second relative is 0.1 bitcoins, which is worth 38000.0 yen if converted at the rate of 380000.0 JPY per 1.0 BTC. The sum of these is 48000.0 yen.
Outputs such as 48000 and 48000.1 will also be judged correct.
user: There is an N-car train.
You are given an integer i. Find the value of j such that the following statement is true: "the i-th car from the front of the train is the j-th car from the back."

-----Constraints-----
 - 1 \leq N \leq 100
 - 1 \leq i \leq N

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

-----Output-----
Print the answer.

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

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

The second car from the front of a 4-car train is the third car from the back.