Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		try (Scanner sc = new Scanner(System.in);) {

			int n = Integer.parseInt(sc.nextLine());
			String a = sc.nextLine();
			String[] b = a.split(" ");
			List<Integer> list = new ArrayList<>();
			List<Integer> max = new ArrayList<>();

			for (int i = 0; i < b.length; i++) {
				list.add(Integer.parseInt(b[i]));
				max.add(Integer.parseInt(b[i]));
			}

			Collections.sort(max);
			int judge = max.get(max.size() - 1);
			int all1 = 0;
			int num = 1;
			if (judge < n) {
				for (int i = -(n / 2); i < n - (n / 2); i++, num++) {
					all1 += Math.abs(list.get(num - 1) - (-(n / 2) + num));
				}
			} else {

				for (int i = 0; i < n; i++) {
					all1 += Math.abs(list.get(i) - (i + 1));
				}
			}

			System.out.println(all1);
		}
	}
}