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.Scanner;
import java.util.stream.IntStream;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
 
        int N = sc.nextInt();
        int[] A = new int[N];
        for (int i = 0; i < A.length; ++i) {
            A[i] = sc.nextInt();
        }
 
        System.out.println(solve(A));
 
        sc.close();
    }
 
    static long solve(int[] A) {
        int[] regulated = IntStream.range(0, A.length).map(i -> A[i] - i - 1).sorted().toArray();
 
        return IntStream.range(0, A.length / 2).map(i -> regulated[A.length - 1 - i] - regulated[i]).asLongStream()
                .sum();
    }
}