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 in = new Scanner(System.in);
		int n = in.nextInt();
		
		long[] a = new long[n];
		
		for(int i=0;i<n;i++) {
			a[i] = in.nextLong() - 1 - i;
		}
		
		Arrays.sort(a);
		
		int half = n/2;
		long b = a[half];
		
		long sum1 = 0;
		long sum2 = 0;
		
		for(int i=0;i<half;i++) {
			sum1 = sum1 + a[i];
		}
		for(int i=half;i<n;i++) {
			sum2 = sum2 + a[i];
		}
		
		long sumB = (half - n + half )* b;
		
		System.out.println(sum2 - sum1 + sumB);

	}

}