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 {
    static private Scanner sc = new Scanner(System.in);
    static int n = 0;
    static ArrayList<Integer> a = new ArrayList<>(20000);
    static ArrayList<Integer> b = new ArrayList<>(20000);
    
    public static void main(String[] args) {
        n = sc.nextInt();
        for(int i = 1; i <= n; ++i) {
            a.add(sc.nextInt());
            b.add(a.get(i - 1) - i);
        }
        
        Collections.sort(b);
        
        long median = (n % 2 == 1) ? b.get(n / 2) : b.get(n / 2) + (b.get(n / 2 - 1) - b.get(n / 2)) / 2;
        long ans = 0;
        for(int i = 0; i < n; ++i) {
            ans += Math.abs(b.get(i) - median);
        }
        System.out.println(ans);
    }
}
