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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Silviase
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    Scanner in = new Scanner(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    ABC102LinearApproximation solver = new ABC102LinearApproximation();
    solver.solve(1, in, out);
    out.close();
  }

  static class ABC102LinearApproximation {

    public void solve(int testNumber, Scanner in, PrintWriter out) {
      int n = in.nextInt();
      int[] ar = new int[n];
      long res = 0;
      for (int i = 0; i < n; i++) {
        ar[i] = in.nextInt() - (i + 1);
      }
      Arrays.sort(ar);
      int mode = ar[n / 2];
      for (int i = 0; i < n; i++) {
        res += Math.abs(ar[i] - mode);
      }
      out.println(res);
    }

  }
}