Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.util.ArrayList;
import java.util.List;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    List<Long> list = new ArrayList<>();
    int n = sc.nextInt();
    for(int i = 0; i < n; i++){
      list.add(sc.nextLong() - i);
    }
    
    Collections.sort(list);
    long size = list.get((int)(list.size() / 2));
	
    long ans1 = 0L;
    long ans2 = 0L;
    for(int i = 0; i < n; i++){
       ans1 += Math.abs(list.get(i) - size);
    }
    
    size = list.get((int)(list.size() / 2) + 1);
    for(int i = 0; i < n; i++){
       ans2 += Math.abs(list.get(i) - size);
    }

    
    System.out.println((int)((ans1 < ans2) ? ans1 : ans2));
    return;
  }
}