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;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var N = Sarray()[0];
            var A = new long[N];
            for (var i = 0; i < N; ++i)
                A[i] = Sarray()[0];
            Array.Sort(A);
            var An = new long[2 * N + 1];
            var left = N;
            var right = N;
            An[right] = A[N - 1];
            var b = 0; var e = N - 2;
            for (var i = 0; i < N - 1; ++i)
            {
                var b1 = Abs(A[b] - An[left]);
                var b2 = Abs(A[b] - An[right]);
                var e1 = Abs(A[e] - An[left]);
                var e2 = Abs(A[e] - An[right]);
                if (Max(b1, b2) < Max(e1, e2))
                {
                    if (e1 < e2)
                        An[++right] = A[e--];
                    else
                        An[--left] = A[e--];
                }
                else
                {
                    if (b1 < b2)
                        An[++right] = A[b++];
                    else
                        An[--left] = A[b++];
                }
            }
            var ans = 0L;
            for (var i = left; i < right; ++i)
                ans += Abs(An[i + 1] - An[i]);
            WriteLine(ans);
            //Out.Flush();
        }
    }
}