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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

	import java.util.Arrays;
import java.util.Scanner;

	public class Main {

		static long mod = 1000000007;

		public static void main(String[] args) {

			Scanner sc = new Scanner(System.in);
			String[] t = sc.nextLine().split(" ");
			int n  	   = Integer.parseInt(t[0]);
			//long k = Long.parseLong(t[1].replaceAll("\\.", ""));

			String[] r = sc.nextLine().split(" ");
			int[] bist = new int[n];

			for(int i  = 0; i < n; i ++) {
				bist[i] = Integer.parseInt(r[i]) - i - 1;
			}

			Arrays.sort(bist);

			int ans = 0;
			int mid = n % 2 == 0 ? (bist[n / 2] + bist[n / 2 - 1]) / 2 : bist[n / 2];

			for(int i  = 0; i < n; i ++) {
				ans += Math.abs(bist[i] - mid);
			}

			System.out.println(ans);

		}
	}