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;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line, int.Parse);
        var b = new int[n];
        for (int i = 0; i < n; i++) b[i] = a[i] - (i + 1);
        //if (n % 2 == 1)
        {
            var med = getMed(b);
            Console.WriteLine(getSum(a, med));
        }
        //else
        //{
        //    var med1 = b[n / 2];
        //    var ret1 = getSum(b, med1);
        //    var med2 = b[n / 2 - 1];
        //    var ret2 = getSum(b, med2);
        //    Console.WriteLine(Math.Min(ret1, ret2));
        //}
    }
    public static int getMed(int[] a)
    {
        Array.Sort(a);
        return a[a.Length / 2];
    }
    public static long getSum(int[] a, int b)
    {
        var n = a.Length;
        var ret = 0L;
        for (int i = 0; i < n; i++)
            ret += Math.Abs(a[i] - b - i - 1);
        return ret;
    }
}