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;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        long[] a = new long[n];
        long[] sub = new long[n];
        for (int i = 0; i < n; i++) {
            long temp = Long.parseLong(sc.next());
            a[i] = temp;
            sub[i] = temp - (i + 1);
        }
        Arrays.sort(sub);
        long center = 0;
        if (n % 2 != 0) {
            center = sub[n / 2];
        } else {
            center = (sub[n / 2] + sub[n / 2 - 1]) / 2;
        }
        long ans = 0;
        for (int i = 0; i < n; i++) {
            ans += Math.abs(a[i] - (center + i + 1));
        }
        System.out.println(ans);
    }
}