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);
        ArrayList<Integer> List = new ArrayList<>();
        int N = sc.nextInt();
        for(int i=0;i<N;i++){
            int num = sc.nextInt();
            int b_num = num - (i+1);
            List.add(b_num);
        }
        Collections.sort(List);
        int mid = List.get((int)Math.ceil(N/2));
        long sum = 0;
        for(int i=0;i<List.size();i++) sum+= Math.abs(List.get(i)-mid);
        System.out.println(sum);
    }
}