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();
		long[] a = new long[N];
		for (int i = 0; i < N; i++)
			a[i] = sc.nextLong() - i - 1;
		Arrays.sort(a);
		long[] s = new long[N + 1];
		for (int i = 0; i < N; i++)
			s[i] = i == 0 ? a[i] : s[i - 1] + a[i];
		long total = s[N - 1];
		long min = Long.MAX_VALUE;
		for (int i = 0; i < N; i++) {
			if (i > 0 && a[i] == a[i - 1])
				continue;
			long l = a[i] * (i + 1) - s[i];
			long h = (total - s[i]) - a[i] * (N - i - 1);
			min = Math.min(min, l + h);
		}
		System.out.println(min);
	}
}
