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 scan = new Scanner(System.in);
		int N = scan.nextInt();
		int []B = new int[N];
		for(int i = 0; i < N; i++) {
			B[i] = scan.nextInt() - i - 1;
		}
		scan.close();
		if(N == 1) {
			System.out.println(0);
			System.exit(0);
		}
		Arrays.sort(B);
		long sum = 0;
		long min = 10000000000000000L;
		int k[] = {B[0] - 1,B[N/2], B[N/2 + 1],B[N - 1] + 1};
		for(int i = 0; i < 4; i++) {
			sum = 0;
			for(int j = 0; j < N; j++) {
				sum += abs(k[i], B[j]);
			}
			if(min > sum) {
				min = sum;
			}
		}
		System.out.println(min);

	}
	static int abs(int a, int b) {
		if(a > b) {
			return a - b;
		}else {
			return b - a;
		}
	}
}