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) {
        Scanner sc = new Scanner(System.in);
        int n  =sc.nextInt();
        int [] x = new int[n];
        long min  = (long)1e18;
        for(int i = 1;i<=n;++i)
            min += Math.abs(x[i-1] = sc.nextInt() - i);
        min  = (long)1e18;
        int lo = (int)-1e9;
        int hi = (int)1e9;
        while(lo<=hi){
            int mid = (lo + hi) / 2;
            long sum = 0;
            long sum2 = 0;
            for(int i = 0;i<n;++i) {
                sum += Math.abs(x[i] - mid);
                sum2 += Math.abs(x[i] - mid +1);
            }
            if(sum<sum2){
                min = Math.min(sum2,sum);
                lo = mid + 1;
            }
            else{
                min = Math.min(sum,sum2);
                hi = mid - 1;
            }
            if(min == 15)
                System.out.println(mid);

        }
        System.out.println(min);

    }
}