Problem:
Score : 400 points

Problem Statement

You are given N integers; the i-th of them is A_i.
Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

2 \leq N \leq 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_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Sample Input 1

5
6
8
1
2
3

Sample Output 1

21

When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9

Sample Output 2

25

Sample Input 3

3
5
5
1

Sample Output 3

8

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

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        var num = ToInt32(ReadLine());
        var array = new int[num];
        var left = new Stack<int>();
        var right = new Stack<int>();
        for (var i = 0; i < num; i++)
        {
            array[i] = ToInt32(ReadLine());
        }
        Array.Sort(array);
        for(var i = 0; i < num; i++)
        {
            if (i < num / 2) left.Push(array[num/2-i-1]);
            else right.Push(array[i]);
        }
        var l = left.Pop();
        var r = right.Pop();
        WriteLine(Get(left, right,l, r, r-l,0));
    }

    private static long Get(Stack<int> left,Stack<int> right,int l,int r,long result,int i)
    {
        var w = 0L;
        while(left.Count!=0||right.Count!=0)
        {
            var s = 0;
            if (i % 2 == 0) s = right.Pop();
            else s = left.Pop();
            i++;
            if (Abs(l - s) == Abs(r - s))
            {
                var nu = Get(left, right,s, r, result + Abs(l - s),i);
                if (nu > w) w = nu;
            }

            if (Abs(l - s) > Abs(r - s))
            {
                result += Abs(l - s); l = s;
            }
            else
            {
                result += Abs(r - s); r = s;
            }
        }
        return Max(w, result);
    }
}