vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Santa puts all the presents into the huge sack. In order to let his reindeers rest a bit, he only takes as many reindeers with him as he is required to do. The others may take a nap.

Two reindeers are always required for the sleigh and Santa himself. Additionally he needs 1 reindeer per 30 presents. As you know, Santa has 8 reindeers in total, so he can deliver up to 180 presents at once (2 reindeers for Santa and the sleigh + 6 reindeers with 30 presents each).

Complete the function `reindeers()`, which takes a number of presents and returns the minimum numbers of required reindeers. If the number of presents is too high, throw an error.

Examles:

```python
reindeer(0) # must return 2
reindeer(1) # must return 3
reindeer(30) # must return 3
reindeer(200) # must throw an error
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Circle of Numbers

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
*n* evenly spaced points have been marked around the edge of a circle. There is a number written at each point. You choose a positive real number *k*. Then you may repeatedly select a set of 2 or more points which are evenly spaced, and either increase all numbers at points in the set by *k* or decrease all numbers at points in the set by *k*. You would like to eventually end up with all numbers equal to 0. Is it possible?

A set of 2 points is considered evenly spaced if they are diametrically opposed, and a set of 3 or more points is considered evenly spaced if they form a regular polygon.

Input Specification:
The first line of input contains an integer *n* (3<=≤<=*n*<=≤<=100000), the number of points along the circle.

The following line contains a string *s* with exactly *n* digits, indicating the numbers initially present at each of the points, in clockwise order.

Output Specification:
Print "YES" (without quotes) if there is some sequence of operations that results in all numbers being 0, otherwise "NO" (without quotes).

You can print each letter in any case (upper or lower).

Demo Input:
['30\n000100000100000110000000001100\n', '6\n314159\n']

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

Note:
If we label the points from 1 to *n*, then for the first test case we can set *k* = 1. Then we increase the numbers at points 7 and 22 by 1, then decrease the numbers at points 7, 17, and 27 by 1, then decrease the numbers at points 4, 10, 16, 22, and 28 by 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Vova is again playing some computer game, now an RPG. In the game Vova's character received a quest: to slay the fearsome monster called Modcrab.

After two hours of playing the game Vova has tracked the monster and analyzed its tactics. The Modcrab has h_2 health points and an attack power of a_2. Knowing that, Vova has decided to buy a lot of strong healing potions and to prepare for battle.

Vova's character has h_1 health points and an attack power of a_1. Also he has a large supply of healing potions, each of which increases his current amount of health points by c_1 when Vova drinks a potion. All potions are identical to each other. It is guaranteed that c_1 > a_2.

The battle consists of multiple phases. In the beginning of each phase, Vova can either attack the monster (thus reducing its health by a_1) or drink a healing potion (it increases Vova's health by c_1; Vova's health can exceed h_1). Then, if the battle is not over yet, the Modcrab attacks Vova, reducing his health by a_2. The battle ends when Vova's (or Modcrab's) health drops to 0 or lower. It is possible that the battle ends in a middle of a phase after Vova's attack.

Of course, Vova wants to win the fight. But also he wants to do it as fast as possible. So he wants to make up a strategy that will allow him to win the fight after the minimum possible number of phases.

Help Vova to make up a strategy! You may assume that Vova never runs out of healing potions, and that he can always win.


-----Input-----

The first line contains three integers h_1, a_1, c_1 (1 ≤ h_1, a_1 ≤ 100, 2 ≤ c_1 ≤ 100) — Vova's health, Vova's attack power and the healing power of a potion.

The second line contains two integers h_2, a_2 (1 ≤ h_2 ≤ 100, 1 ≤ a_2 < c_1) — the Modcrab's health and his attack power.


-----Output-----

In the first line print one integer n denoting the minimum number of phases required to win the battle.

Then print n lines. i-th line must be equal to HEAL if Vova drinks a potion in i-th phase, or STRIKE if he attacks the Modcrab.

The strategy must be valid: Vova's character must not be defeated before slaying the Modcrab, and the monster's health must be 0 or lower after Vova's last action.

If there are multiple optimal solutions, print any of them.


-----Examples-----
Input
10 6 100
17 5

Output
4
STRIKE
HEAL
STRIKE
STRIKE

Input
11 6 100
12 5

Output
2
STRIKE
STRIKE



-----Note-----

In the first example Vova's character must heal before or after his first attack. Otherwise his health will drop to zero in 2 phases while he needs 3 strikes to win.

In the second example no healing needed, two strikes are enough to get monster to zero health and win with 6 health left.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array A of N integers, sort them in non-decreasing order.
Input Format

The first line of the input file contains a positive integer <N.
Then, N lines follow, each containing a single integer Ai, which is the i^th element of A.

Output Format

The output must contain exactly N lines, each line containing a single integer from the list, and sorted in non-increasing order.

Constraints

1 ≤ N ≤ 10,000
-10^6 ≤ Ai ≤ 10^6

SAMPLE INPUT
8
567
23
-10982
1000000
-999999
-3456
1729
65535

SAMPLE OUTPUT
-999999
-10982
-3456
23
567
1729
65535
1000000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You need to find a binary tree of size n that satisfies a given set of c constraints. Suppose that the nodes of the unknown binary tree are labeled using a pre-order traversal starting with 1. For the i-th constraint you are given two labels, ai and bi and a direction, left or right. In case of left direction, bi is an element of the subtree rooted at ai's left child. Similarly in the case of right direction bi is an element of the subtree rooted at ai's right child.

Input

The first line of input contains two integers n and c. The next c lines contain 2 integers ai, bi (1 ≤ ai, bi ≤ n) and either "LEFT" or "RIGHT" denoting whether b is in the subtree rooted at ai's left child or in the subtree rooted at ai's right child.

The problem consists of multiple subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.

  * In subproblem D1 (9 points), the constraints 1 ≤ n ≤ 100, 1 ≤ c ≤ 50 will hold. 
  * In subproblem D2 (8 points), the constraints 1 ≤ n ≤ 1000000, 1 ≤ c ≤ 100000 will hold. 

Output

Output will be on a single line.

Any binary tree that satisfies the constraints will be accepted. The tree's nodes should be printed out as n space separated labels representing an in-order traversal, using the pre-order numbers as labels of vertices.

If there are no trees that satisfy the constraints, print "IMPOSSIBLE" (without quotes).

Examples

Input

3 2
1 2 LEFT
1 3 RIGHT


Output

2 1 3


Input

3 2
1 2 RIGHT
1 3 LEFT


Output

IMPOSSIBLE

Note

Consider the first sample test. We need to find a tree with 3 nodes that satisfies the following two constraints. The node labeled 2 with pre-order traversal should be in the left subtree of the node labeled 1 with pre-order traversal; the node labeled 3 with pre-order traversal should be in the right subtree of the node labeled 1. There is only one tree with three nodes that satisfies these constraints and its in-order traversal is (2, 1, 3).

Pre-order is the "root – left subtree – right subtree" order. In-order is the "left subtree – root – right subtree" order.

For other information regarding in-order and pre-order, see <http://en.wikipedia.org/wiki/Tree_traversal>.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: 4-point polyline

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given a rectangular grid of lattice points from (0,<=0) to (*n*,<=*m*) inclusive. You have to choose exactly 4 different points to build a polyline possibly with self-intersections and self-touching. This polyline should be as long as possible.

A polyline defined by points *p*1,<=*p*2,<=*p*3,<=*p*4 consists of the line segments *p*1<=*p*2,<=*p*2<=*p*3,<=*p*3<=*p*4, and its length is the sum of the lengths of the individual line segments.

Input Specification:
The only line of the input contains two integers *n* and *m* (0<=≤<=*n*,<=*m*<=≤<=1000). It is guaranteed that grid contains at least 4 different points.

Output Specification:
Print 4 lines with two integers per line separated by space — coordinates of points *p*1,<=*p*2,<=*p*3,<=*p*4 in order which represent the longest possible polyline.

Judge program compares your answer and jury's answer with 10<=-<=6 precision.

Demo Input:
['1 1\n', '0 10\n']

Demo Output:
['1 1\n0 0\n1 0\n0 1\n', '0 1\n0 10\n0 0\n0 9\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A policeman wants to catch a thief. Both the policeman and the thief can only move on a line on integer coordinates between $0$ and $N$ (inclusive).
Initially, the policeman is at a coordinate $x$ and the thief is at a coordinate $y$. During each second, each of them must move to the left or right (not necessarily both in the same direction) by distance $\textbf{exactly}$ equal to $K$. No one may go to the left of the coordinate $0$ or to the right of $N$. Both the policeman and the thief move simultaneously and they cannot meet while moving, only at the end of each second.
Will the policeman be able to catch the thief if they both move optimally? The thief is caught as soon as the policeman and thief meet at the same position at the same time.

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

-----Output-----
For each test case, print a single line containing the string "Yes" if the thief can be caught or "No" if the thief cannot be caught (without quotes).

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^9$
- $1 \le K \le N$
- $0 \le x, y \le N$
- $x \neq y$

-----Example Input-----
5
0 1 1 1
1 4 1 5
4 2 1 7
3 7 2 10
8 2 3 15

-----Example Output-----
No
No
Yes
Yes
Yes

-----Explanation-----
Example case 1: The policeman is at $0$ and the thief is at $1$. After the $1$-st second, the policeman is at $1$ and the thief is at $0$. After the next second, the policeman is again at $0$ and the thief at $1$. They cannot end up at the same coordinate.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Vanya and his friend Vova play a computer game where they need to destroy n monsters to pass a level. Vanya's character performs attack with frequency x hits per second and Vova's character performs attack with frequency y hits per second. Each character spends fixed time to raise a weapon and then he hits (the time to raise the weapon is 1 / x seconds for the first character and 1 / y seconds for the second one). The i-th monster dies after he receives a_{i} hits. 

Vanya and Vova wonder who makes the last hit on each monster. If Vanya and Vova make the last hit at the same time, we assume that both of them have made the last hit.


-----Input-----

The first line contains three integers n,x,y (1 ≤ n ≤ 10^5, 1 ≤ x, y ≤ 10^6) — the number of monsters, the frequency of Vanya's and Vova's attack, correspondingly.

Next n lines contain integers a_{i} (1 ≤ a_{i} ≤ 10^9) — the number of hits needed do destroy the i-th monster.


-----Output-----

Print n lines. In the i-th line print word "Vanya", if the last hit on the i-th monster was performed by Vanya, "Vova", if Vova performed the last hit, or "Both", if both boys performed it at the same time.


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

Output
Vanya
Vova
Vanya
Both

Input
2 1 1
1
2

Output
Both
Both



-----Note-----

In the first sample Vanya makes the first hit at time 1 / 3, Vova makes the second hit at time 1 / 2, Vanya makes the third hit at time 2 / 3, and both boys make the fourth and fifth hit simultaneously at the time 1.

In the second sample Vanya and Vova make the first and second hit simultaneously at time 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have a playlist consisting of $n$ songs. The $i$-th song is characterized by two numbers $t_i$ and $b_i$ — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied by the minimum beauty among them. For example, the pleasure of listening to a set of $3$ songs having lengths $[5, 7, 4]$ and beauty values $[11, 14, 6]$ is equal to $(5 + 7 + 4) \cdot 6 = 96$.

You need to choose at most $k$ songs from your playlist, so the pleasure of listening to the set of these songs them is maximum possible.


-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 3 \cdot 10^5$) – the number of songs in the playlist and the maximum number of songs you can choose, respectively.

Each of the next $n$ lines contains two integers $t_i$ and $b_i$ ($1 \le t_i, b_i \le 10^6$) — the length and beauty of $i$-th song.


-----Output-----

Print one integer — the maximum pleasure you can get.


-----Examples-----
Input
4 3
4 7
15 1
3 6
6 8

Output
78

Input
5 3
12 31
112 4
100 100
13 55
55 50

Output
10000



-----Note-----

In the first test case we can choose songs ${1, 3, 4}$, so the total pleasure is $(4 + 3 + 6) \cdot 6 = 78$.

In the second test case we can choose song $3$. The total pleasure will be equal to $100 \cdot 100 = 10000$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
To pass the series of gates guarded by the owls, Kenneth needs to present them each with a highly realistic portrait of one.  Unfortunately, he is absolutely rubbish at drawing, and needs some code to return a brand new portrait with a moment's notice.

All owl heads look like this:

    ''0v0''

Such beautiful eyes!
However, they differ in their plumage, which is always symmetrical, eg.:

       VVHVAV''0v0''VAVHVV

or
 
    YYAYAH8XH''0v0''HX8HAYAYY

So Kenneth needs a method that will take a garble of text generated by mashing at his keyboard (numbers and letters, but he knows how to avoid punctuation etc.) for a bit and give him a symmetrical owl with a lovely little face, with a truly symmetrical plumage made of uppercase letters and numbers.

(To be clear, the acceptable characters for the plumage are 8,W,T,Y,U,I,O,A,H,X,V and M.)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Even though she saw Zvonko steal Mirko’s microprocessor in the second task, Mirko’s sister Ivana did not tell Mirko because she likes Zvonko. She suggested to him that they go see a movie together so that she would “forget” about the incident.

Zvonko does not care much for girls because they take away precious time he usually spends practicing his math-fu. He suggested that the two of them play a game and, if Ivana wins, they will go see a movie together. Ivana agreed, being good at jump rope and she sometimes even kicks a football around with her two brothers.

Zvonko laid $N$ positive integers in a circle on the floor and explained the rules:
 - The first player takes any number.
 - The second player takes either of the two numbers adjacent to the one the first player took.
 - The next player takes a number adjacent to any of the numbers taken so far, and so on until they run out of numbers. The player to take more odd numbers (not divisible by 2) wins.

Zvonko plays optimally; he always looks for a strategy that leads to certain victory or a draw. Zvonko does not know how well Ivana plays. Being a true cavalier, he let Ivana have the first move. But Ivana only cares about sitting next to Zvonko in front of the big screen so she seeks help playing.

Write a program that finds how many different first moves Ivana can make, so that she has a chance of winning afterwards.

-----Input-----
The first line of input contains an integer $N$ $(1 \leq N \leq 100)$, how many numbers there are in the circle. The second line contains $N$ integers separated by single spaces. All numbers will be between $1$ and $1000$ (inclusive). No two numbers will be the same.

-----Output-----
Output the desired number on a single line.

-----Examples-----
Sample Input 1:
3
3 1 5
Sample Output 1:
3

Sample Input 2:
4
1 2 3 4
Sample Output 2:
2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Silver Fox is fighting with N monsters.
The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.
Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.
Silver Fox wins when all the monsters' healths become 0 or below.
Find the minimum number of bombs needed to win.

-----Constraints-----
 - 1 \leq N \leq 2 \times 10^5
 - 0 \leq D \leq 10^9
 - 1 \leq A \leq 10^9
 - 0 \leq X_i \leq 10^9
 - 1 \leq H_i \leq 10^9
 - X_i are distinct.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N D A
X_1 H_1
:
X_N H_N

-----Output-----
Print the minimum number of bombs needed to win.

-----Sample Input-----
3 3 2
1 2
5 4
9 2

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

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.
Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.
Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).
Consider a sequence A satisfying the following conditions:
 - A is a sequence of N positive integers.
 - 1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.
Let us define a score of this sequence as follows:
 - The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)
Find the maximum possible score of A.

-----Constraints-----
 - All values in input are integers.
 - 2 ≤ N ≤ 10
 - 1 \leq M \leq 10
 - 1 \leq Q \leq 50
 - 1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )
 - 0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )
 - (a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)
 - 1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

-----Input-----
Input is given from Standard Input in the following format:
N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

-----Output-----
Print the maximum possible score of A.

-----Sample Input-----
3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

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

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
### Background
In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. It was invented by Lester S. Hill in 1929.



### Task


This cipher involves a text key which has to be turned into a matrix and text which needs to be encoded. The text key can be of any perfect square length but for the sake of this kata we will focus on keys of length 4 forming a 2x2 matrix.

To encrypt a message using the hill cipher, first of all you need to convert the text key into a key matrix. To do that you will convert the key row wise into a 2x2 matrix. Then you will substitute the letters with their respective positions on the alphabet: A=0, B=1,C=2 and so on till Z=25. So for example if we get the key text as ```cats```, the key matrix will be:
    
    [[ 2  0]
     [19 18]]
     
Now the next step is to break the text into pairs of two and convert those pairs into 2x1 matrices. If your text has an odd number of letters then just add a Z next to your last letter. Now again convert those letters into their respective position in the alphabet as above. So for example the text ```Hi``` would be converted into:

    [[7]
     [8]]
     
Now we need to [multiply](https://www.mathsisfun.com/algebra/matrix-multiplying.html) the key matrix by the text matrix to get our encrypted matrix and then find out the encrypted matrix [modulo](https://en.wikipedia.org/wiki/Modulo_operation) 26:

    [[ 2  0]  *  [[7]  =  [[14]   =  [[14]  mod 26
     [19 18]]     [8]]     [277]]     [17]]
     
For the final step we just find out the letters at the alphabet position of 14 and 17 which are ```O``` and ```R```. So ```OR``` is our encrypted message for the message ```Hi```


In this kata you will be given a function named ```encrypt``` with the parameters ```text``` and ```key``` and you have to return the encrypted message in all uppercase letters

``` python
encrypt('','azyb') → ''
encrypt('Hi','cats') → 'OR'
encrypt('This is a good day','bbaa') → 'AAAAAAGACAGAYA'
```

Note:
- The text to encrypt will contain characters other than the alphabets, its your job to clean them before converting text to matrices. Spaces also need to be removed
- The text may contain both uppercase and lowercase alphabets. Its your job to standardize them, the encrypted text however should be returned in uppercase letters.
- The key will always contain 4 lowercase alphabet.

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