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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;


public class MyProgram
{	

    public static void Main()
	{
        int N = int.Parse(Console.ReadLine());
	    int[] n = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        int[] dif = new int[N];
        long Sum = 0;
        long B = 0;
        for(int i = 0 ; i < N ; i++)
        {
            dif[i] = (n[i]-(i+1));
        }
        Array.Sort(dif);
        
        B = Math.Abs(n[0] - (dif[0]+1));
        if(N > 1)
        {
            if(N % 2 == 1)
            {
                B = dif[N / 2];
            }
            else
            {
                B = (dif[N/2 +1] + dif[N/2])/2;
            }
            
        }

        
        for(int i = 0 ; i < N ; i++)
        {
            Sum += Math.Abs(n[i] - (B+i+1));
        }
        Console.WriteLine(Sum);
	}
}