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.*;

class Main{
	
	public static void main(String args[]){

		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int arr[] = new int[N];
		int sum = 0;
		for(int n=0;n<N;n++){
			arr[n] = sc.nextInt();
			sum += arr[n]-n-1;
		}

		if(sum%N==0){
			int s=0;
			for(int n=0;n<N;n++){
				if(sum>0)
					s += Math.abs(arr[n]-n-1-sum/N);
				else
					s += Math.abs(arr[n]-n-1+sum/N);
			}
			System.out.println(s);
		}
		else{
			int s=0,t=0;
			for(int n=0;n<N;n++){
				s += Math.abs(arr[n]-n-1-sum/N);
				t += Math.abs(arr[n]-n-1-sum/N+1);
			}
			System.out.println(Math.min(s,t));
		}
	}
}