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);
        int[] nums = new int[sc.nextInt()];
        for (int i = 0; i < nums.length; i++) {
            nums[i] = sc.nextInt();
        }
        long output = 0;
        for(int i=0;i<nums.length;i++){
            nums[i]-=i;
        }
        Arrays.sort(nums);
        int c=nums[(int)((nums.length+1)/2)-1];
        
        for(int i=0;i<nums.length;i++){
            if(nums[i]-c>=0){
                output+=nums[i]-c;
            }else{
               output-=nums[i]-c; 
            }
        }
        System.out.println(output);

    }

}