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: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int[] A = new int[N];
            for (int i = 0; i < A.length; i++) {
                A[i] = in.nextInt();
            }

            long min = (long) 1e18;
            long l = -(int) 1e18, r = (int) 1e18;
            for (; l + 1 < r;) {
                long c = (l + r) / 2;
                // long snukeL = snuke(A, l);
                // long snukeR = snuke(A, r);
                long snuke = snuke(A, c);
                long snukeP = snuke(A, c + 1);
                long snukeM = snuke(A, c - 1);
                if (snukeP < snuke) {
                    l = c;
                } else if (snukeM < snuke) {
                    r = c;
                } else {
                    min = Math.min(min, snuke);
                    break;
                }
            }
            long snukeL = snuke(A, l);
            long snukeR = snuke(A, r);
            min = Math.min(min, snukeL);
            min = Math.min(min, snukeR);
            System.out.println(min);
        }
    }

    private static long snuke(int[] a, long c) {
        long value = 0;
        for (int i = 0; i < a.length; i++) {
            value += Math.abs(a[i] - (c + i + 1));
        }
        return value;
    }
}