vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Everybody knows that the $m$-coder Tournament will happen soon. $m$ schools participate in the tournament, and only one student from each school participates.

There are a total of $n$ students in those schools. Before the tournament, all students put their names and the names of their schools into the Technogoblet of Fire. After that, Technogoblet selects the strongest student from each school to participate. 

Arkady is a hacker who wants to have $k$ Chosen Ones selected by the Technogoblet. Unfortunately, not all of them are the strongest in their schools, but Arkady can make up some new school names and replace some names from Technogoblet with those. You can't use each made-up name more than once. In that case, Technogoblet would select the strongest student in those made-up schools too.

You know the power of each student and schools they study in. Calculate the minimal number of schools Arkady has to make up so that $k$ Chosen Ones would be selected by the Technogoblet.


-----Input-----

The first line contains three integers $n$, $m$ and $k$ ($1 \le n \le 100$, $1 \le m, k \le n$) — the total number of students, the number of schools and the number of the Chosen Ones.

The second line contains $n$ different integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$), where $p_i$ denotes the power of $i$-th student. The bigger the power, the stronger the student.

The third line contains $n$ integers $s_1, s_2, \ldots, s_n$ ($1 \le s_i \le m$), where $s_i$ denotes the school the $i$-th student goes to. At least one student studies in each of the schools. 

The fourth line contains $k$ different integers $c_1, c_2, \ldots, c_k$ ($1 \le c_i \le n$)  — the id's of the Chosen Ones.


-----Output-----

Output a single integer  — the minimal number of schools to be made up by Arkady so that $k$ Chosen Ones would be selected by the Technogoblet.


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

Output
1

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

Output
2



-----Note-----

In the first example there's just a single Chosen One with id $3$. His power is equal to $3$, but in the same school $1$, there's a student with id $5$ and power $6$, and that means inaction would not lead to the latter being chosen. If we, however, make up a new school (let its id be $4$) for the Chosen One, Technogoblet would select students with ids $2$ (strongest in $3$), $5$ (strongest in $1$), $6$ (strongest in $2$) and $3$ (strongest in $4$).

In the second example, you can change the school of student $3$ to the made-up $5$ and the school of student $4$ to the made-up $6$. It will cause the Technogoblet to choose students $8$, $7$, $6$, $5$, $3$ and $4$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Da Vinci Powers

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
The input contains a single integer *a* (0<=≤<=*a*<=≤<=35).

Output a single integer.

Input Specification:
The input contains a single integer *a* (0<=≤<=*a*<=≤<=35).

Output Specification:
Output a single integer.

Demo Input:
['3\n', '10\n']

Demo Output:
['8\n', '1024\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Some scientists are working on protein recombination, and during their research, they have found a remarkable fact: there are 4 proteins in the protein ring that mutate after every second according to a fixed pattern. For simplicity, proteins are called $A,B,C,D$ (you know, protein names can be very complicated). A protein mutates into another one depending on itself and the protein right after it. Scientists determined that the mutation table goes like this:  

    A   B   C   D
    _   _   _   _
A|  A   B   C   D
B|  B   A   D   C
C|  C   D   A   B
D|  D   C   B   A

Here rows denote the protein at current position, while columns denote the protein at the next position. And the corresponding value in the table denotes the new protein that will emerge. So for example, if protein i is A, and protein i + 1 is B, protein i will change to B. All mutations take place simultaneously. The protein ring is seen as a circular list, so last protein of the list mutates depending on the first protein. 

Using this data, they have written a small simulation software to get mutations second by second. The problem is that the protein rings can be very long (up to 1 million proteins in a single ring) and they want to know the state of the ring after upto $\mathbf{10^{9}}$ seconds. Thus their software takes too long to report the  results. They ask you for your help.  

Input Format

Input contains 2 lines. 

First line has 2 integers $N$ and $\mbox{K}$, $N$ being the length of the protein ring and $\mbox{K}$ the desired number of seconds. 

Second line contains a string of length $N$ containing uppercase letters $\mbox{A}$,$\mbox{B}$, $\mbox{C}$ or $\mbox{D}$ only, describing the ring. 

Constraints

$1\leq N\leq10^6$ 

$1\leq K\leq10^9$ 

Output Format

Output a single line with a string of length $N$, describing the state of the ring after $\mbox{K}$ seconds.

Sample Input 0
5 15
AAAAD

Sample Output 0
DDDDA

Explanation 0

The complete sequence of mutations is:

AAADD
AADAD
ADDDD
DAAAD
DAADA
DADDD
DDAAA
ADAAD
DDADD
ADDAA
DADAA
DDDAD
AADDA
ADADA
DDDDA

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The city’s local subway service S.L., Super Lag, are currently being blamed that their displays, showing the expected wait time until the next train arrives, are faulty. Too many commuters have the experience of coming to the subway station, and then having to wait many more minutes than the display showed when they got there. 

The American Commuter Movement and the International Commuting Peoples’ Community have had it with this. Especially Johan, a young student, who has decided to investigate this matter further. Johan went to one of the stations, and studied the behaviour of the displays. Each time the display showed a new number, Johan carefully measured the number of seconds that passed from that moment until the train arrived. As soon as that train left again, he did the same thing for the next train and so on. He remembered all the displayed minutes, and the wait time for each such in seconds. Although Johan has a very good memory, he does not know what to do with his measurements. He needs your help!

Your task is to help Johan calculate the average length of an S.L. minute (the length of a minute according to the display). You may assume that when the display shows a new number $M$, the expected S.L. wait time in that moment is exactly $M$ minutes.

-----Input-----
The first line contains an integer $1 \le N \le 1000$ – the number of observations Johan did. The following $N$ lines contain two positive integers $M \le 60$ and $S \le 3600$ – the number of minutes displayed, and the number of seconds Johan had to wait for his train.

-----Output-----
Output should consist of a single real number: the average length of an S.L. minute, measured in real minutes. A relative or absolute error of at most $10^{-7}$ will be considered correct. If the average length of an S.L. minute is shorter than or equal to a normal minute, print the message "measurement error" instead.

-----Examples-----
Sample Input:
1
1 61
Sample Output:
1.016666667

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Master Oogway has forseen that a panda named Po will be the dragon warrior, and the master of Chi. But he did not tell anyone about the spell that would make him the master of Chi, and has left Po confused. Now Po has to defeat Kai, who is the super villian, the strongest of them all. Po needs to master Chi, and he finds a spell which unlocks his powerful Chi. But the spell is rather strange. It asks Po to calculate the factorial of a number! Po is very good at mathematics, and thinks that this is very easy. So he leaves the spell, thinking it's a hoax. But little does he know that this can give him the ultimate power of Chi. Help Po by solving the spell and proving that it's not a hoax.

-----Input-----
First line of input contains an integer T denoting the number of test cases.
The next T lines contain an integer N.

-----Output-----
For each test case, print a single line containing the solution to the spell which is equal to factorial of N, i.e. N!. Since the output could be large, output it modulo 1589540031(Grand Master Oogway's current age).

-----Constraints-----
- 1 ≤ T ≤ 100000
- 1 ≤ N ≤ 100000

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

Output:
1
2
6
24

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess the current position of the ball.

Bomboslav noticed that guys are not very inventive, so the operator always swaps the left shell with the middle one during odd moves (first, third, fifth, etc.) and always swaps the middle shell with the right one during even moves (second, fourth, etc.).

Let's number shells from 0 to 2 from left to right. Thus the left shell is assigned number 0, the middle shell is 1 and the right shell is 2. Bomboslav has missed the moment when the ball was placed beneath the shell, but he knows that exactly n movements were made by the operator and the ball was under shell x at the end. Now he wonders, what was the initial position of the ball?


-----Input-----

The first line of the input contains an integer n (1 ≤ n ≤ 2·10^9) — the number of movements made by the operator.

The second line contains a single integer x (0 ≤ x ≤ 2) — the index of the shell where the ball was found after n movements.


-----Output-----

Print one integer from 0 to 2 — the index of the shell where the ball was initially placed.


-----Examples-----
Input
4
2

Output
1

Input
1
1

Output
0



-----Note-----

In the first sample, the ball was initially placed beneath the middle shell and the operator completed four movements.  During the first move operator swapped the left shell and the middle shell. The ball is now under the left shell.  During the second move operator swapped the middle shell and the right one. The ball is still under the left shell.  During the third move operator swapped the left shell and the middle shell again. The ball is again in the middle.  Finally, the operators swapped the middle shell and the right shell. The ball is now beneath the right shell.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Your friend Claire has dragged you along to a speedcubing event that is happening in Eindhoven. These events are all about solving the Rubik’s cube and similar twisty puzzles as quickly as possible. The attendants of the event can enter into various competitions based on the type and size of the puzzle, and there are even special competitions where the puzzles need to be solved one-handed or blindfolded. 

Claire is competing in the most popular competition: speedsolving the $3\times 3\times 3$ Rubik’s cube, pictured on the right. Each contestant needs to solve the cube five times, each time with a different random scramble. After all solves are completed, the best and the worst times are discarded and the final score is the average of the remaining three times. The contestant with the smallest final score wins.

Claire has done well in the competition so far and is among the contenders for the overall victory. All the other contestants have already finished their five solves, but Claire has one solve remaining. By looking at the final scores of the other contestants, she has deduced her own target final score. As long as her final score is less than or equal to this target score, she will be declared the overall winner. Is it possible for her to win the competition, and if so, what is the worst time she can have on her last solve in order to do so?

-----Input-----
The input consists of:
 - One line with four real numbers $t_1$, $t_2$, $t_3$ and $t_4$, the times Claire got on her first four solves.
 - One line with a real number $t$, Claire’s target final score, the worst final score she can have in order to be declared the overall winner.

Each number is between $1$ and $20$, inclusive, and is given with exactly two decimal places.

-----Output-----
If it is not possible for Claire to win the event, output “impossible”. If she will win regardless of the time she gets on her last solve, output “infinite”. Otherwise, output the worst time she can have on her last solve in order to be declared the overall winner. Output the number to exactly two decimal places.

-----Examples-----
Sample Input 1:
6.38 7.20 6.95 8.11
7.53
Sample Output 1:
infinite

Sample Input 2:
6.38 7.20 6.95 8.11
6.99
Sample Output 2:
6.82

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Round Table Knights

Time Limit: 0 seconds

Memory Limit: 256 megabytes

Problem Description:
There are *n* knights sitting at the Round Table at an equal distance from each other. Each of them is either in a good or in a bad mood.

Merlin, the wizard predicted to King Arthur that the next month will turn out to be particularly fortunate if the regular polygon can be found. On all vertices of the polygon knights in a good mood should be located. Otherwise, the next month will bring misfortunes.

A convex polygon is regular if all its sides have same length and all his angles are equal. In this problem we consider only regular polygons with at least 3 vertices, i. e. only nondegenerated.

On a picture below some examples of such polygons are present. Green points mean knights in a good mood. Red points mean ones in a bad mood.

King Arthur knows the knights' moods. Help him find out if the next month will be fortunate or not.

Input Specification:
The first line contains number *n*, which is the number of knights at the round table (3<=≤<=*n*<=≤<=105). The second line contains space-separated moods of all the *n* knights in the order of passing them around the table. "1" means that the knight is in a good mood an "0" means that he is in a bad mood.

Output Specification:
Print "YES" without the quotes if the following month will turn out to be lucky. Otherwise, print "NO".

Demo Input:
['3\n1 1 1\n', '6\n1 0 1 1 1 0\n', '6\n1 0 0 1 0 1\n']

Demo Output:
['YES', 'YES', 'NO']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Nobody outside the cooking community knows that Chef is a big fan of Chefgram™ — a social network where chefs and cooks upload their secret kitchen photos.
Recently Chef clicked a beautiful photo, which is represented using 10 pixels in a single row. Respecting Chefgram™'s boolean roots, every pixel is either white or black.

Chefgram™ has N filters. Every filter is a string containing 10 symbols. Every symbol is either '+' or '-'.

- A '+' at the ith position in a filter means that if Chef applies this filter to his photo, the ith pixel will be inverted: it becomes black if it was originally white, and vice versa. 
- A '-' at the ith position in a filter string means that if Chef applies this filter to his photo, the ith pixel will remain unchanged.

Chef can apply as many filters as he wants from a list. He can pick any subset of filters and consequently apply them to a photo.

For example:

- Imagine that Chef has a photo "bbwwbbwwbb" (where 'b' stands for black and 'w' stands for white).
- He applies filters "++--++--++", "-+-+-+-+-+".
- Applying the first filter will transform his picture to "wwwwwwwwww". 
- Applying the second filter on the transformed picture will give Chef the picture "wbwbwbwbwb".

Even if Chefgram™ has two or more identical filters, they are still considered different!

Chef is extremely interested in knowing how many different subsets of all the Chefgram™ filters can he apply to transform his photo into 10 black pixels?

-----Input-----
- The first line of input contains a single integer T — the number of test cases.
- First line of each test case contains a string S. Each symbol is either 'b' or 'w'. This is Chef's photo.
- Second line of each test case contains a single integer N — the number of Chefgram™ filters.
- Each of the next N lines contains a single string Fi, each symbol of which is either '+' or '-'. This string is the ith Chefgram™ filter.

-----Output-----
- For each test case, output a single line containing a single integer — answer to Chef's question modulo 109+7.

-----Constraints-----
- 1 ≤ T ≤ 5
- |S| = 10
- 1 ≤ N ≤ 10^5
- |Fi| = 10

-----Subtasks-----
- Subtask 1: T ≤ 5; N ≤ 20; Points: 20
- Subtask 2: T ≤ 5; N ≤ 10^3; Points: 30
- Subtask 3: T ≤ 5; N ≤ 10^5; Points: 50

-----Example-----
Input:
3
wwwwwwwwww
3
+-+-+-+-+-
----------
+---------
wbwbwbwbwb
3
+-+-+-+-+-
+-+-------
----+-+-+-
bbbbbbbbbb
2
----------
----------

Output:
0
2
4

-----Explanation-----
Example case 1. There is no filter or combination of filters transforming the picture to whole black. 
Example case 2. Chef can either apply the first filter (and invert all whites) or apply the second and third filters in any order.
Example case 3. Picture is already fully black, and we have two different identity filters. Chef can either apply the empty subset of filters, the first filter only, the second filter only, or both.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The chef is very expert in coding, so to keep his password safe from the hackers. He always enters a decoded code of his password. You are a hacker and your work is to find the maximum number of possible ways to unlock his password in encoded form.

The encoded message containing only letters from A-Z is being encoded with numbers using the following mapping: 

'A' -> 1 

'B' -> 2 ... 

'Z' -> 26

You have given a non-empty string containing only digits, determine the total number of ways to encode it. 

If the total number of ways are even then you are able to unlock the password. 

Input: 
The first line has a single integer T, denoting the number of test cases. The first line of each test case contains string “S” decoded number.

Output:
For each test case, in a new line, print 'YES' if number of maximum ways are even, otherwise
'NO'. (without quotes)

Constraints:
1 ≤ T ≤ 50

1 ≤ S ≤ 30

Sample Input:
2

12

223

Sample Output:
YES

NO

Explanation:
For first test case, It could be encoded as "AB" (1 2) or "L" (12), hence the number of
maximum possible ways are 2 so output is “YES”.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Serval soon said goodbye to Japari kindergarten, and began his life in Japari Primary School.

In his favorite math class, the teacher taught him the following interesting definitions.

A parenthesis sequence is a string, containing only characters "(" and ")".

A correct parenthesis sequence is a parenthesis sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, parenthesis sequences "()()", "(())" are correct (the resulting expressions are: "(1+1)+(1+1)", "((1+1)+1)"), while ")(" and ")" are not. Note that the empty string is a correct parenthesis sequence by definition.

We define that $|s|$ as the length of string $s$. A strict prefix $s[1\dots l]$ $(1\leq l< |s|)$ of a string $s = s_1s_2\dots s_{|s|}$ is string $s_1s_2\dots s_l$. Note that the empty string and the whole string are not strict prefixes of any string by the definition.

Having learned these definitions, he comes up with a new problem. He writes down a string $s$ containing only characters "(", ")" and "?". And what he is going to do, is to replace each of the "?" in $s$ independently by one of "(" and ")" to make all strict prefixes of the new sequence not a correct parenthesis sequence, while the new sequence should be a correct parenthesis sequence.

After all, he is just a primary school student so this problem is too hard for him to solve. As his best friend, can you help him to replace the question marks? If there are many solutions, any of them is acceptable.


-----Input-----

The first line contains a single integer $|s|$ ($1\leq |s|\leq 3 \cdot 10^5$), the length of the string.

The second line contains a string $s$, containing only "(", ")" and "?".


-----Output-----

A single line contains a string representing the answer.

If there are many solutions, any of them is acceptable.

If there is no answer, print a single line containing ":(" (without the quotes).


-----Examples-----
Input
6
(?????

Output
(()())
Input
10
(???(???(?

Output
:(



-----Note-----

It can be proved that there is no solution for the second sample, so print ":(".

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Escape Through Leaf

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given a tree with *n* nodes (numbered from 1 to *n*) rooted at node 1. Also, each node has two values associated with it. The values for *i*-th node are *a**i* and *b**i*.

You can jump from a node to any node in its subtree. The cost of one jump from node *x* to node *y* is the product of *a**x* and *b**y*. The total cost of a path formed by one or more jumps is sum of costs of individual jumps. For every node, calculate the minimum total cost to reach any leaf from that node. Pay attention, that root can never be leaf, even if it has degree 1.

Note that you cannot jump from a node to itself.

Input Specification:
The first line of input contains an integer *n* (2<=≤<=*n*<=≤<=105) — the number of nodes in the tree.

The second line contains *n* space-separated integers *a*1,<=<=*a*2,<=<=...,<=<=*a**n*(<=-<=105<=<=≤<=<=*a**i*<=<=≤<=<=105).

The third line contains *n* space-separated integers *b*1,<=<=*b*2,<=<=...,<=<=*b**n*(<=-<=105<=<=≤<=<=*b**i*<=<=≤<=<=105).

Next *n*<=<=-<=<=1 lines contains two space-separated integers *u**i* and *v**i* (1<=≤<=*u**i*,<=<=*v**i*<=≤<=<=*n*) describing edge between nodes *u**i* and *v**i* in the tree.

Output Specification:
Output *n* space-separated integers, *i*-th of which denotes the minimum cost of a path from node *i* to reach any leaf.

Demo Input:
['3\n2 10 -1\n7 -7 5\n2 3\n2 1\n', '4\n5 -10 5 7\n-8 -80 -3 -10\n2 1\n2 4\n1 3\n']

Demo Output:
['10 50 0 ', '-300 100 0 0 ']

Note:
In the first example, node 3 is already a leaf, so the cost is 0. For node 2, jump to node 3 with cost *a*<sub class="lower-index">2</sub> × *b*<sub class="lower-index">3</sub> = 50. For node 1, jump directly to node 3 with cost *a*<sub class="lower-index">1</sub> × *b*<sub class="lower-index">3</sub> = 10.

In the second example, node 3 and node 4 are leaves, so the cost is 0. For node 2, jump to node 4 with cost *a*<sub class="lower-index">2</sub> × *b*<sub class="lower-index">4</sub> = 100. For node 1, jump to node 2 with cost *a*<sub class="lower-index">1</sub> × *b*<sub class="lower-index">2</sub> =  - 400 followed by a jump from 2 to 4 with cost *a*<sub class="lower-index">2</sub> × *b*<sub class="lower-index">4</sub> = 100.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.