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.Arrays;
import java.util.Scanner;

public class Main {
    static long[] arr;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        arr = new long[n];
        for(int i = 0; i < n; i++) {
            arr[i] = sc.nextLong() - (i+1);
        }

        Arrays.sort(arr);

        long right = 1000000000;
        long left = -1000000000;
        while(Math.abs(left - right) > 2) {
            //System.err.println(left+" "+right);
            long midLeft = left + (right - left)/3;
            long midRight = left + (right - left)*2/3;
            long midLeftResult = calc(midLeft);
            long midRightResult = calc(midRight);
            if(midLeftResult > midRightResult) {
                left = midLeft;
            } else {
                right = midRight;
            }
        }
       // System.err.println(left+" "+right);
        long[] results = new long[3];
        results[0] = calc(left);
        results[1] = calc(left+1);
        results[2] = calc(left+2);
        Arrays.sort(results);
        System.out.println(results[0]);
    }

    static long calc(long b) {
        long result = 0;
        for(long num : arr) {
            result += Math.abs(num - b);
        }
        return result;
    }
}