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.io.*;

public class Main {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	
	public static void main(String[] args) throws Exception {
		int N = Integer.parseInt(br.readLine());
		
		long[] yarra = new long[N];
		String[] split = br.readLine().split(" ");
		
		for(int i = 0; i < yarra.length; i++)
			yarra[i] = Long.parseLong(split[i]) - i - 1;
		
		Arrays.sort(yarra);
		
		long left = yarra[0] - 1, right = yarra[N-1] + 1;
		long mid = -1;
		
		while(right - left >= 2) {
			mid = (left + right)/2;
			long val = 0;
			long val2 = 0;
			for(int i = 0; i < yarra.length; i++) {
				val += (long) Math.abs(yarra[i] - mid);
				val2 += (long) Math.abs(yarra[i] - (mid-1));
			}
			
			if(val2 < val)
				right = mid;
			else
				left = mid;
		}
		
		long val = 0;
		long val2 = 0;
		long val3 = 0;
		
		for(int i = 0; i < yarra.length; i++) {
			val += (long) Math.abs(yarra[i] - left);
			val2 += (long) Math.abs(yarra[i] - mid);
			val3 += (long) Math.abs(yarra[i] - right);
		}
		pw.println(Math.min(val, Math.min(val2, val3)));
		
		pw.close();
	}
}





