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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static long Solve(int N, long[] A)
        {
            var k1 = new int[N];
            var k2 = new int[N];
            for (int i = 0; i < N; ++i)
            {
                var k = (i == 0 || i == N - 1) ? 1 : 2;
                if (i % 2 == 0)
                {
                    k1[i] = -k;
                    k2[i] =  k;
                }
                else
                {
                    k1[i] =  k;
                    k2[i] = -k;
                }
            }
            Array.Sort(k1);
            Array.Sort(k2);
            Array.Sort(A);
            long sum1 = 0;
            long sum2 = 0;
            for (int i = 0; i < N; ++i)
            {
                sum1 += A[i] * k1[i];
                sum2 += A[i] * k2[i];
            }
            return Math.Max(sum1, sum2);
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            var A = new long[N];
            for (int i = 0; i < N; ++i) { A[i] = ReadLong(); }
            Console.WriteLine(Solve(N, A));
        }
    }
}