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 System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication7
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] A = new int[N];
            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(Console.ReadLine());
            }
            //
            Array.Sort(A);
            int fromMin = 0;
            int fromMax = N - 1;
            long output = 0;
            List<int> array = new List<int>();
            array.Add(A[0]);
            array.Add(A[fromMax]);
            fromMin++;
            fromMax--;
            while (array.Count!=N)
            {
                int insert0 = Math.Abs(array[0] - A[fromMin]);
                int add = Math.Abs(array[array.Count - 1] - A[fromMin]);
                if (add > insert0) array.Add(A[fromMin]);
                else array.Insert(0, A[fromMin]);
                fromMin++;
                if (fromMax < fromMin) break;

                insert0 = Math.Abs(array[0] - A[fromMax]);
                add = Math.Abs(array[array.Count - 1] - A[fromMax]);

                if (add > insert0) array.Add(A[fromMax]);
                else array.Insert(0, A[fromMax]);
                fromMax--;
                if (fromMax < fromMin) break;

                /*
                array.Add(A[fromMax]);
                fromMax--;
                if (fromMax < fromMin) break;

                array.Add(A[fromMin]);
                fromMin++;
                if (fromMax < fromMin) break;

                array.Insert(0,A[fromMax]);
                fromMax--;
                if (fromMax < fromMin) break;

                array.Insert(0, A[fromMin]);
                fromMin++;
                if (fromMax < fromMin) break;
                */
            }

            for (int i = 0; i < N-1; i++)
            {
                long bigger = long.Parse(Math.Max(array[i],array[i+1]).ToString());
                long smaller = long.Parse(Math.Min(array[i], array[i + 1]).ToString());

                output += bigger - smaller;
            }
            Console.WriteLine(output);
        }
    }
}