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.*;

public class Main {

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        int l = -2000000000;
        int r = 2000000000;
        long anss = 0;
        while (l < r) {

            int tmp = (l + r) / 2;

            int b = tmp;
            long ans = 0;
            for (int i = 0; i < n; i++) {
                ans += Math.abs(a[i] - 1 - i - b);
            }

            b = tmp + 1;
            long ans2 = 0;
            for (int i = 0; i < n; i++) {
                ans2 += Math.abs(a[i] - 1 - i - b);
            }

            b = tmp - 1;
            long ans3 = 0;
            for (int i = 0; i < n; i++) {
                ans3 += Math.abs(a[i] - 1 - i - b);
            }

            if (ans3 >= ans && ans2 >= ans) {
                anss = ans;
                break;
            }
            if (ans2 < ans) {
                l = tmp;
            } else if (ans3 < ans) {
                r = tmp;
            }

            if (l >= r) {
                anss = Math.min(ans, Math.min(ans2, ans3));
            }
        }

        System.out.println(anss);

    }

}
