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: Runtime Error)

import java.io.*;
import java.util.*;

public class Main {
    public static void main(String args[]) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] arr = new int[n];
        String[] tokens = br.readLine().split(" ");
        for(int i = 0; i < n; ++i)
            arr[i] = Integer.parseInt(tokens[i]) - (i+1);
        Arrays.sort(arr);
        if(n%2==1)
            System.out.println(got(arr, arr[n/2]));
        else {
            int res = (int)((long)arr[n/2] + arr[n+1/2])/2;
            System.out.println(got(arr, res));
        }
    }
    private static long got(int[] arr, int b){
        long res = 0;
        for(int i = 0, n = arr.length; i < n; ++i)
            res += Math.abs(arr[i] - b);
        return res;
    }
}