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();
      long[] a = new long[n];
      for(int i = 0;i < n;i++){
        a[i]=sc.nextLong()-i-1;
      }
      Arrays.sort(a);
      long b = 0;
      if(n%2==1)b = a[n/2];
      else b = (a[n/2-1]+a[n/2])/2;
      long sum = 0;
      for(int i = 0;i < n;i++)sum+=Math.abs(a[i]-b);
      System.out.println(sum);
    }
}
