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 scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int a[] = new int[n];
		for (int i=0; i<n; i++){
			a[i] = scanner.nextInt()-(i+1);
		}
		Arrays.sort(a);
		int center;
		if (n%2==0){
			center = (a[n/2-1]+a[n/2])/2;
		}else {
			center = a[(n+1)/2-1];
		}
		long ans = Long.MAX_VALUE;
		for (int d=-2; d<=2; d++){
			long anscand = 0;
			for (int i=0; i<n; i++) {
				anscand += Math.abs(a[i]-(center+d));
			}
			ans = Math.min(ans, anscand);
		}
		System.out.println(ans);
	}
}