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;
import java.util.stream.IntStream;

/**
 * 解説どおりに作成したソースコード
 */
public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int[] a = new int[n];
			IntStream.range(0, n).forEach(i -> a[i] = scanner.nextInt() - 1 - i);
			Arrays.sort(a);
			// 中央値を求める
			int middle = (0 == (1 & n)) ? (a[n / 2] + a[n / 2 - 1]) / 2 : a[n / 2];
			System.out.println(IntStream.range(0, n).mapToLong(i -> Math.abs(a[i] - middle)).sum());
		}
	}
}
