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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] arr = new int[N];
        for (int i = 0; i < N; ++i)
            arr[i] = in.nextInt();

        int lo = -(int)1e9;
        int hi = (int)1e9;

        while (Math.abs(hi - lo) > 1) {
            int mid1 = lo + (hi - lo + 1) / 3;
            int mid2 = hi - (hi - lo + 1) / 3;

            long sum1 = computeSadness(arr, mid1);
            long sum2 = computeSadness(arr, mid2);

            // System.err.println(lo + " " + mid1 + " " + mid2 + " "+ hi);

            if (sum1 < sum2) hi = mid2;
            else lo = mid1;
        }

        System.out.println(Math.min(computeSadness(arr, lo), computeSadness(arr, hi)));
    }

    private static long computeSadness(int[] arr, int b) {
        long s = 0;
        for (int i = 0; i < arr.length; ++i) {
            s += Math.abs(arr[i] - (b + i + 1));
        }
        return s;
    }
}