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.Scanner;
import java.util.Arrays;

public class Main { 
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    long[] A = new long[N];
    long[] B = new long[N];
    for (int i =0; i<N; i++) {
      A[i] = sc.nextLong();
      B[i] = A[i] - i;
    }
    Arrays.sort(B);
    if (N == 1) {
      System.out.println(0);
      return;
    }
    long c1 = B[N/2 - 1]; 
    long c2 = B[N/2];
    long ans1 =0;long ans2 =0; long ans;
    for (int i =0; i<N; i++) {
      ans1 += Math.abs(B[i] - c1);
    }
    for (int i =0; i<N; i++) {
      ans2 += Math.abs(B[i] - c2);
    }
    ans = Math.min(ans1,ans2);
    System.out.println(ans);
  }
}