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: Accepted)

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

class Solution
{
    static double Median(long[] x)
    {
        x = x.OrderBy(xx => xx).ToArray();
        var n = x.Length;
        if (n % 2 == 0)
        {
            return (x[n / 2 - 1] + x[n / 2]) / 2;
        }
        else
        {
            return x[n / 2];
        }
    }

    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        a = a.Select((aa, i) => aa - (i + 1)).ToArray();
        var b = (int)Median(a);
        var min = long.MaxValue;
        for (int i = -1; i <= 1; i++)
        {
            var sad = a.Sum(aa => Math.Abs(aa - (b + i)));
            min = Math.Min(min, sad);
        }
        Console.WriteLine(min);
    }
}