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.util.Scanner;

public class Main {

	static Scanner scan = new Scanner(System.in);

	public static void main(String[] args) {
		int n = scan.nextInt();
		int[] a = new int[n];

		long ave = 0;
		for(int i = 0; i < n; i++) {
			a[i] = scan.nextInt() - (i + 1);
			ave += a[i];
		}
		ave /= n;

		long ans_sum = Long.MAX_VALUE;
		boolean p = true;
		boolean m = true;
		for(long b = (long)Math.abs(ave) - 1; ; b++) {
			long sum_m = 0;
			long sum_p = 0;
			for(int j = 0; j < n; j++) {
				if(p) sum_p += Math.abs(a[j] - b);
				if(m) sum_m += Math.abs(a[j] + b);
			}

			if(ans_sum < sum_p) p = false;
			if(ans_sum < sum_m) m = false;
			if(!p && !m) break;

			if(p && ans_sum > sum_p) ans_sum = sum_p;
			if(m && ans_sum > sum_m) ans_sum = sum_m;
		}

		System.out.println(ans_sum);
    }
}