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.

Examples

Input

5
2 2 3 5 5


Output

2


Input

9
1 2 3 4 5 6 7 8 9


Output

0


Input

6
6 5 4 3 2 1


Output

18


Input

7
1 1 1 1 2 3 4


Output

6


import java.util.Arrays;
import java.util.Scanner;

/*
絶対値の和の最小
|x−B1|+|x−B2|+⋯+|x−BN| を最小にする x は、B1,B2,…,BN のメディアン *式変形
 */
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[(int)N];
        int[] b = new int[(int)N];
        for(int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
            b[i] = a[i] - i;
        }
        Arrays.sort(b);
        int mid = b[N/2];
        long min = 0;
        for(int i = 0; i < N; i++) {
            min += Math.max(mid - b[i], - mid + b[i]);
        }
        System.out.println(min);

    }
}
