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.*;
public class Main {

  public static void main(String[] args) { 
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int[] arr = new int[n];
      int max = -1;
      for(int i = 0; i < n; i++) {
        arr[i] = sc.nextInt() - i - 1;
        max = Math.max(max, arr[i] + i + 1);
      }
      int left = -1 * max;
      int right = max;

      while(left < right) {
        int mid1 = left + (right - left) / 3;
        int mid2 = right - (right - left) / 3;
        long leftRes = cal(arr, mid1);
        long rightRes = cal(arr, mid2);
        if(leftRes < rightRes)
          right = mid2 - 1;
        else if (leftRes > rightRes)
          left = mid1 + 1;
        else {
          left = mid1 + 1;
          right = mid2;
        }
      }
      
      System.out.println(cal(arr, left));
  }

  private static long cal(int[] arr, int b) {
    long sum = 0;
    for(int a : arr) {
      sum += Math.abs(a - b);
    }
    return sum;
  }
}