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: Accepted)

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

class Cmondai
{
    static void Main()
    {
        var n=Int32.Parse(Console.ReadLine());
        var list = new List<long>();
        for (int i = 0; i < n; ++i) list.Add(Int64.Parse(Console.ReadLine()));
        var line=list.OrderBy(x=>x).ToArray();
        var ans = 0L;
        var m = n / 2;
        if (n % 2 == 0)
        {         
            for (int i=0;i<n;++i)
            {
                if (i < m - 1) ans += (-2) * line[i];
                else if (i == m - 1) ans -= line[i];
                else if (i == m) ans += line[i];
                else ans += 2 * line[i];
            }
        }
        else
        {
            var a = 0L;
            var b = 0L;
            for (int i=0;i<n;++i)
            {
                if (i == m || i == m + 1) a += line[i];
                else if (i < m) a -= 2 * line[i];
                else a += 2 * line[i];
            }
            for (int i=0;i<n;++i)
            {
                if (i == m - 1 || i == m) b -= line[i];
                else if (i < m - 1) b -= 2 * line[i];
                else b += 2 * line[i];
            }
            ans = Math.Max(a,b);
        }
        Console.WriteLine(ans);
    }
}