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];
		for(int i=1;i<n+1;i++) {
			a[i-1]=sc.nextInt()-i;
		}
		Arrays.sort(a);

		int chuuou0=a[n/2];
		long summary0=0;
		for(int i=0;i<n;i++) {
			summary0+=zettaichi(a[i]-chuuou0);
		}
		if(n>=2) {
			int chuuou1=a[n/2+1];
			long summary1=0;

			for(int i=0;i<n;i++) {
				summary1+=zettaichi(a[i]-chuuou1);
			}
			if(summary0>summary1) {
				summary0=summary1;
			}
		}
		if(n>=3) {
			int chuuou2=a[n/2+1];
			long summary2=0;

			for(int i=0;i<n;i++) {
				summary2+=zettaichi(a[i]-chuuou2);
			}
			if(summary0>summary2) {
				summary0=summary2;
			}
		}

		System.out.print(summary0);


	}



	public static int zettaichi(int a) {
		if(a>=0)
			return a;
		else
			return -a;
	}


}
