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 scn = new Scanner(System.in);
		int N = scn.nextInt();
		long[] A = new long[N];
		long buf,ave = 0,up = 0,down = 0;
		for(int i = 1; i <= N ;i++) {
			buf = scn.nextLong() - i;
			A[i-1] = buf;
			//ave += buf;
		}
		Arrays.sort(A);
		up = A[N/2];
		down = A[(N-1)/2];
		long ans1 = 0,ans2 = 0;
		for(int i = 0;i < N;i++) {
			ans1 += Math.abs(A[i]-up);
			ans2 += Math.abs(A[i]-down);
		}
		System.out.println(Math.min(ans1, ans2));
		scn.close();
	}
}
