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.*;

import static java.lang.System.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();

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

        Arrays.sort(a);

        // determine the median
        int median;
        if (a.length % 2 == 0) {
            median = a[a.length / 2 - 1];
        } else {
            median = a[a.length / 2];
        }

        long ans = Long.MAX_VALUE;
        for (int j : new int[]{-1, 0, 1}) {
            int tmpAns = 0;
            for (int i = 0; i < N; i++) {
                tmpAns += Math.abs(a[i] - (median + j));
            }
            ans = Math.min(ans, tmpAns);
        }

        out.println(ans);
    }
}