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

		double heikin=sum/n;
		int mannnaka1=(int)(heikin+0.5);
		int mannnaka2=(int)(heikin-0.5);
		long summary1=0;
		long summary2=0;
		for(int i=0;i<n;i++) {
			summary1+=zettaichi(a[i]-mannnaka1);
			summary2+=zettaichi(a[i]-mannnaka2);
		}
		long min=summary1;

		if(summary1<summary2) {
			System.out.print(summary1);
		}
		else{
			System.out.print(summary2);
		}
    }



	public static int zettaichi(int a) {
		if(a>=0)
			return a;
		else
			return -a;
	}

}