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 {

		static long mod = 1000000007;

		public static void main(String[] args) {

			Scanner sc = new Scanner(System.in);
			String[] t = sc.nextLine().split(" ");
			int n  	   = Integer.parseInt(t[0]);
			//long k = Long.parseLong(t[1].replaceAll("\\.", ""));

			String[] r = sc.nextLine().split(" ");
			long[] bist = new long[n];

			for(int i  = 0; i < n; i ++) {
				bist[i] = Long.parseLong(r[i]) - i - 1;
			}

			Arrays.sort(bist);

			long ans = 0;
			long mid = n % 2 == 0 ? (bist[n / 2] + bist[n / 2 - 1]) / 2 : bist[(n - 1)/ 2];

			for(int i  = 0; i < n; i ++) {
				ans += Math.abs(bist[i] - mid);
			}

			System.out.println(ans);

		}
	}
