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.*;
import static java.lang.Integer.*;
import static java.lang.Long.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) {
		int i,j;
		Scanner sc = new Scanner(in);
		int n = parseInt(sc.next());
		long[] a = new long[n];
		for(i=0;i<n;i++) {
			a[i] = parseLong(sc.next()) - i -1;
		}
		sc.close();
		Arrays.sort(a);
		long b0 = 0;
		long b1 = 0;
		if(n%2==1) {
			b0 = a[n/2];
			b1 = a[n/2];
		} else {
			b0 = a[n/2-1];
			b1 = a[n/2];
		}
		long ans0 = 0;
		long ans1 = 0;
		for(i=0;i<n;i++) {
			ans0 += abs(a[i]-b0);
			ans1 += abs(a[i]-b1);
		}
		out.println(ans0<ans1?ans0:ans1);
	}
}
