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: Accepted)


import java.util.Arrays;
import java.util.Scanner;

/*
絶対値の和の最小
|x−B1|+|x−B2|+⋯+|x−BN| を最小にする x は、B1,B2,…,BN のメディアン *式変形
 */
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[(int)N];
        int[] b = new int[(int)N];
        for(int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
            b[i] = a[i] - i;
        }
        Arrays.sort(b);
        int mid = b[N/2];
        long min = 0;
        for(int i = 0; i < N; i++) {
            min += Math.abs(mid - b[i]);
        }
        System.out.println(min);

    }
}