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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) {
		try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in));) {

			int n = Integer.parseInt(br.readLine());
			String[] str = br.readLine().split(" ");
			int[] a = new int[n];
			int total = 0;
			for (int i = 0; i < n; i++) {
				a[i] = Integer.parseInt(str[i]);
				total += Math.abs(a[i] - (i + 1));
			}
			int b = total / n;
			int sad = Integer.MAX_VALUE;
			for (int i = 0; i <= b; i++) {
				int tmpSad = 0;
				for (int j = 0; j < n; j++) {
					tmpSad += Math.abs(a[j] - (i + (j + 1)));
				}
				sad = Math.min(tmpSad, sad);

			}
			System.out.println(sad);

		} catch (IOException e) {

		}
	}

}