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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        A = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            A.add(sc.nextInt());
        }

        solve();
    }

    static int N;
    static List<Integer> A;

    static void solve() {

        // An - nの中央値を求める
        List<Integer> calcList = new ArrayList<>();
        for (int i = 0;i < N; i++) {
            calcList.add(A.get(i) - (i+1));
        }


        Collections.sort(calcList);


        if (calcList.size() % 2 == 0) {
            int i1 = calcList.size() / 2 - 1;
            int m1 = calcList.get(i1);
            
            int i2 = calcList.size() / 2;
            int m2 = calcList.get(i2);
            
            System.out.println(Math.min(calc(m1), calc(m2)));
        } else {
            int i = calcList.size() / 2;
            int m = calcList.get(i);

            System.out.println(calc(m));
        }
    }
    
    static long calc(int b) {
        long sum = 0;
        for (int i = 0; i < A.size(); i++) {

            sum += Math.abs(A.get(i) - (b + i + 1) );

        }

        return sum;
    }
}
