apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Kolya has a string s of length n consisting of lowercase and uppercase Latin letters and digits.

He wants to rearrange the symbols in s and cut it into the minimum number of parts so that each part is a palindrome and all parts have the same lengths. A palindrome is a string which reads the same backward as forward, such as madam or racecar.

Your task is to help Kolya and determine the minimum number of palindromes of equal lengths to cut s into, if it is allowed to rearrange letters in s before cuttings.

## Input Format
The first line contains an integer n (1 ≤ n ≤ 4·105) — the length of string s.

The second line contains a string s of length n consisting of lowercase and uppercase Latin letters and digits.

## Output Format
Print to the first line an integer k — minimum number of palindromes into which you can cut a given string.

Print to the second line k strings — the palindromes themselves. Separate them by a space. You are allowed to print palindromes in arbitrary order. All of them should have the same length.

## Examples
```input
6
aabaac
```
```output
2
aba aca
```
-----
```input
8
0rTrT022
```
```output
1
02TrrT20
```
-----
```input
2
aA
```
```output
2
a A
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Evlampiy has found one more cool application to process photos. However the application has certain limitations.

Each photo i has a contrast vi. In order for the processing to be truly of high quality, the application must receive at least k photos with contrasts which differ as little as possible.

Evlampiy already knows the contrast vi for each of his n photos. Now he wants to split the photos into groups, so that each group contains at least k photos. As a result, each photo must belong to exactly one group.

He considers a processing time of the j-th group to be the difference between the maximum and minimum values of vi in the group. Because of multithreading the processing time of a division into groups is the maximum processing time among all groups.

Split n photos into groups in a such way that the processing time of the division is the minimum possible, i.e. that the the maximum processing time over all groups as least as possible.

## Input Format
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3·105) — number of photos and minimum size of a group.

The second line contains n integers v1, v2, ..., vn (1 ≤ vi ≤ 109), where vi is the contrast of the i-th photo.

## Output Format
Print the minimal processing time of the division into groups.

## Examples
```input
5 2
50 110 130 40 120
```
```output
20
```
-----
```input
4 1
2 3 4 1
```
```output
0
```

## Note
In the first example the photos should be split into 2 groups: [40, 50] and [110, 120, 130]. The processing time of the first group is 10, and the processing time of the second group is 20. Maximum among 10 and 20 is 20. It is impossible to split the photos into groups in a such way that the processing time of division is less than 20.

In the second example the photos should be split into four groups, each containing one photo. So the minimal possible processing time of a division is 0.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Mayor of city S just hates trees and lawns. They take so much space and there could be a road on the place they occupy!

The Mayor thinks that one of the main city streets could be considerably widened on account of lawn nobody needs anyway. Moreover, that might help reduce the car jams which happen from time to time on the street.

The street is split into n equal length parts from left to right, the i-th part is characterized by two integers: width of road si and width of lawn gi.

For each of n parts the Mayor should decide the size of lawn to demolish. For the i-th part he can reduce lawn width by integer xi (0 ≤ xi ≤ gi). After it new road width of the i-th part will be equal to s'i = si + xi and new lawn width will be equal to g'i = gi - xi.

On the one hand, the Mayor wants to demolish as much lawn as possible (and replace it with road). On the other hand, he does not want to create a rapid widening or narrowing of the road, which would lead to car accidents. To avoid that, the Mayor decided that width of the road for consecutive parts should differ by at most 1, i.e. for each i (1 ≤ i < n) the inequation |s'i + 1 - s'i| ≤ 1 should hold. Initially this condition might not be true.

You need to find the the total width of lawns the Mayor will destroy according to his plan.

## Input Format
The first line contains integer n (1 ≤ n ≤ 2·105) — number of parts of the street.

Each of the following n lines contains two integers si, gi (1 ≤ si ≤ 106, 0 ≤ gi ≤ 106) — current width of road and width of the lawn on the i-th part of the street.

## Output Format
In the first line print the total width of lawns which will be removed.

In the second line print n integers s'1, s'2, ..., s'n (si ≤ s'i ≤ si + gi) — new widths of the road starting from the first part and to the last.

If there is no solution, print the only integer -1 in the first line.

## Examples
```input
3
4 5
4 5
4 10
```
```output
16
9 9 10
```
-----
```input
4
1 100
100 1
1 100
100 1
```
```output
202
101 101 101 101
```
-----
```input
3
1 1
100 100
1 1
```
```output
-1
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:

- start the race from some point of a field,
- go around the flag,
- close cycle returning back to the starting point.

Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarp’s quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).

Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.

The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).

What is the minimal length of the quadcopter path?

## Input Format
The first line contains two integer numbers x1 and y1 ( - 100 ≤ x1, y1 ≤ 100) — coordinates of the quadcopter starting (and finishing) point.

The second line contains two integer numbers x2 and y2 ( - 100 ≤ x2, y2 ≤ 100) — coordinates of the flag.

It is guaranteed that the quadcopter starting point and the flag do not coincide.

## Output Format
Print the length of minimal path of the quadcopter to surround the flag and return back.

## Examples
```input
1 5
5 2
```
```output
18
```
-----
```input
0 1
0 0
```
```output
8
```

Now solve the problem and return the code.