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.ArrayList;
import java.util.Comparator;

class Main {
    public static long kanacy(long b, long[] a) {
        long sum=0;
        for(int i=0; i<a.length; i++) {
            sum += Math.abs(a[i] - (b+i+1));
        }
        return sum;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long a[] = new long[n];
        ArrayList<Long> offset = new ArrayList<>();
        for(int i=0; i<n; i++) {
            a[i] = sc.nextInt();
            offset.add(a[i] - (i+1));
        }
        sc.close();

        offset.sort(Comparator.naturalOrder());

        long b = offset.get(offset.size()/2);
        
        System.out.println(kanacy(b, a));
    }
}