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 {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		int[] a = new int[N];

		int sum = 0;


		for(int i=0;i<N;i++) {

			a[i] = sc.nextInt();

			sum += a[i] -(i+1);
		}

		int b = sum/N;

		int c = b+1;

		int e = b-1;


		int ansB = 0;

		int ansC = 0;

		int ansE = 0;

		int d = 0;

		for(int i=0;i<N;i++) {

			d = Math.abs(a[i]-((i+1)+b));

			ansB += d;
		}

		for(int i=0;i<N;i++) {

			d = Math.abs(a[i]-((i+1)+c));

			ansC += d;
		}




		for(int i=0;i<N;i++) {

			d = Math.abs(a[i]-((i+1)+e));

			ansE += d;
		}

		int f = Math.min(ansC, ansB);
		System.out.println(Math.min(f, ansE));
	}
}