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.*;
import java.util.stream.Collectors;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	int N;
	long[] A;

	Main(BufferedReader in) throws IOException {
		N = Integer.parseInt(in.readLine());
		A = new long[N];
		String[] tokens = in.readLine().split(" ");
		for (int i = 0; i < N; ++i) {
			A[i] = Long.parseLong(tokens[i]) - (long) (i + 1);
		}
		Arrays.sort(A);
		long med = getMedium();

		long result = Long.MAX_VALUE / 2;
		for (long b = med - 5; b <= med + 5; ++b) {
			result = Math.min(result, sub(b));
		}
		System.out.println(result);
	}

	long getMedium() {
		if (A.length == 1) {
			return A[0];
		} else if (A.length % 2 == 1) {
			return A[A.length / 2];
		} else {
			return (A[A.length / 2 - 1] + A[A.length / 2]) / 2;
		}
	}

	long sub(long b) {
		long result = 0;
		for (int i = 0; i < N; ++i) {
			result += Math.abs(A[i] - b);
		}
		return result;
	}

	void calc() {
	}

	void showResult() {
	}
}