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.util.ArrayList;
import java.util.Collections;

class Main{
    public static void main(String[] args){
        
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] A = new int[N];
        ArrayList<Integer> list = new ArrayList<Integer>();

        for(int i=0; i<N; i++){
            A[i] = sc.nextInt();
            list.add(A[i] - i - 1);
        }

        Collections.sort(list);
        long ans = 0; 
        int b = 0;
        if(N%2!=0){
            b = list.get(N / 2);
        }
        else{
            b = (list.get(N / 2) + list.get(N / 2 - 1)) / 2;
        }
        for(int i=0; i<N; i++){
            ans += Math.abs(A[i] - (b + i + 1));
        }
        System.out.println(ans);
    }
}