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 = sc.nextInt();
		int []a = new int [n];
		long sum = 0;
		
		for(int i = 0 ; i < n ; i++) {
			a[i] = sc.nextInt();
			a[i] = a[i] - i - 1 ;
		}
		Arrays.sort(a);
		int b = 0;
		
		if(n % 2 == 0) {
			 b = (a[n/2] + a[n/2 - 1])/2;
		}
		if(n % 2 == 1){
			b = a[(n-1)/2];
		}
		long ans = 0;
		for(int i = 0; i < n ; i++) {
			ans += Math.abs(a[i] - b);
		}
		System.out.println(ans);

	}

}
