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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		//ArrayList<Integer> numArray = new ArrayList<>();
		long numArray[] = new long[N];

		long ans1 = 0,ans2 = 0,up=0,down=0;
		for(int i = 0; i < N; i++){
			numArray[i] = sc.nextLong() - i;
			}

		Arrays.sort(numArray);
		up = numArray[N/2];
		down = numArray[(N-1)/2];

		for(int i = 0; i < N; i++){
			ans1 += Math.abs(numArray[i]-up);
			ans2 += Math.abs(numArray[i]-down);
		}

		System.out.println(Math.min(ans1, ans2));
		sc.close();

	}

}
