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: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] a2 = new int[n];
        long sum = 0;
        for(int i=0; i<n; i++){
            a[i] = sc.nextInt();
            a2[i] = a[i] - i - 1;
            sum += a[i];
        }
        sc.close();

        Arrays.sort(a2);

        

        //long s = (sum - (long)(n+1)*(long)(n+2)/2) / n;
        long s = a2[n/2];
        long l = s + 1;
        long ss = s - 1;

        long ans1 = 0, ans2 = 0, ans3 = 0;
        for(int i=0; i<n; i++){
            ans1 += Math.abs(a[i] - s - i - 1);
            ans2 += Math.abs(a[i] - l - i - 1);
            ans3 += Math.abs(a[i] - ss - i - 1);
        }
        System.out.println(Math.min(Math.min(ans1, ans2), ans3));
    }
}