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.Linq;
class Program
{
    static void Main(string[] args)
    {
        var N = long.Parse(Console.ReadLine());
        var array = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        for (int i = 0; i < array.Length; i++)
        {
            array[i] -= i+1;
        }
        var j = 0;
        var min = abs(0, N, array);
        var cont = true;
        while (cont)//減っている間
        {
            var current = abs(--j, N, array);
            if (min > current)
            {
                min = current;
            }
            else cont = false;
        }
        j = 0;
        while (cont)//減っている間
        {
            var current = abs(++j, N, array);
            if (min > current)
            {
                min = current;
            }
            else cont = false;
        }
        Console.WriteLine(min);
        //for (int i = -100; i < 100; i++)
        //{
        //    Console.WriteLine(i.ToString() + ": " + abs(i, N, array).ToString());
        //}
        //var avgL = (long)Math.Floor((double)array.Sum() / array.Length);
        //var avgH = avgL + 1;
        //var valL = abs(avgL, N, array);
        //var valH = abs(avgH, N, array);
        //Console.WriteLine("best: "+Math.Min(valL, valH));
    }
    static long abs(long b,long N, long[] array)
    {
        long res = 0;
        for (long i = 0; i < N; i++)
        {
            res += Math.Abs(array[i]-b);
        }
        return res;
    }
}