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: Time Limit Exceeded)

import java.util.Scanner;


public class Main {
	int[] arr = null;
	public int sad(int b) {
		int total = 0;
		for (int i=0; i<arr.length; i++) {
			total += Math.abs(arr[i]-(b+i+1));
		}
		return total;
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		Main m = new Main();
		m.arr = new int[n];
		int min = Integer.MAX_VALUE;
		int max = Integer.MIN_VALUE;

		for (int i=0; i<n; i++) {
			m.arr[i] = scan.nextInt();
			if (m.arr[i]<min) {
				min = m.arr[i];
			}
			if (m.arr[i]>max) {
				max = m.arr[i];
			}
		}
		int ans = Integer.MAX_VALUE;
		for (int i=min-n; i<=max+n; i++) {
			int j=m.sad(i);
			if (j<ans) {
				ans=j;
			}
		}

		System.out.println(ans);
		scan.close();
	}
}