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: Time Limit Exceeded)

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

class Solution
{
    static long Calc(IEnumerable<long> array)
    {
        var list = new LinkedList<long>();
        var a = new LinkedList<long>(array);
        list.AddFirst(a.First());
        a.RemoveFirst();
        while (a.Count > 0)
        {
            list.AddLast(a.Last());
            a.RemoveLast();
            if (a.Count == 0)
            {
                break;
            }
            list.AddFirst(a.Last());
            a.RemoveLast();

            if (a.Count == 0)
            {
                break;
            }
            list.AddLast(a.First());
            a.RemoveFirst();
            if (a.Count == 0)
            {
                break;
            }
            list.AddFirst(a.First());
            a.RemoveFirst();
        }

        long sum = 0;
        var prev = list.First();
        foreach (var x in list.Skip(1))
        {
            sum += Math.Abs(x - prev);
            prev = x;
        }

        return sum;
    }

    static void Main()
    {
        var input = Console.In.ReadToEnd().Split(new string[] { Environment.NewLine }, StringSplitOptions.None).Where(s => s != "").Select(long.Parse).ToArray();
        var N = input[0];
        var A = input.Skip(1).ToArray();

        Array.Sort(A);
        var a = Calc(A);
        var b = Calc(A.AsEnumerable().Reverse());

        var sum = Math.Max(a, b);
        Console.WriteLine(sum);
    }
}