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.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N;
        public long[] A;
        public long MOD = 1000000007;

        public void Run()
        {
            N = Input.ReadInt();
            A = new long[N];
            for (int i = 0; i < N; i++)
            {
                A[i] = Input.ReadLong();
            }

            Array.Sort(A);

            long r1 = 0;
            long r2;
            {
                long[] R = new long[N];
                int u = N - 1;
                int d = 0;
            
                for (int i = 1; i < N - 1; i+= 2)
                {
                    R[i] = A[u];
                    u--;
                }
                for (int i = 2; i < N - 1; i += 2)
                {
                    R[i] = A[d];
                    d++;
                }

                R[0] = A[d];
                R[N - 1] = A[d + 1];

                long r = 0;
                for (int i = 0; i < N - 1; i++)
                {
                    r += Math.Abs(R[i + 1] - R[i]);
                }

                r1 = r;
            }

            {
                long[] R = new long[N];
                int u = N - 1;
                int d = 0;

                for (int i = 1; i < N - 1; i += 2)
                {
                    R[i] = A[d];
                    d++;
                }
                for (int i = 2; i < N - 1; i += 2)
                {
                    R[i] = A[u];
                    u--;
                }

                R[0] = A[d];
                R[N - 1] = A[d + 1];

                long r = 0;
                for (int i = 0; i < N - 1; i++)
                {
                    r += Math.Abs(R[i + 1] - R[i]);
                }

                r2 = r;
            }

            Console.WriteLine(Math.Max(r1, r2));
        }
    }

    // libs ----------


    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}