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);

            var l1 = new List<long>();
            var l2 = new List<long>();

            var l = 0;
            var r = N - 1;

            for (int t = 0; t < N / 2; t++)
            {
                if (t % 2 == 0)
                {
                    l1.Add(A[l]);
                    l2.Add(A[r]);
                }
                else
                {
                    l1.Add(A[r]);
                    l2.Add(A[l]);
                }
                l++;
                r--;
            }

            long ret = 0;
            ret += Math.Abs(l1[0] - l2[0]);
            for (int i = 1; i < l1.Count; i++)
            {
                ret += Math.Abs(l1[i - 1] - l1[i]);
            }
            for (int i = 1; i < l2.Count; i++)
            {
                ret += Math.Abs(l2[i - 1] - l2[i]);
            }

            if (N % 2 == 1)
            {
                int m = N / 2;
                ret += Math.Max(Math.Abs(l1.Last() - A[m]), Math.Abs(l2.Last() - A[m]));
            }

            Console.WriteLine(ret);
        }
    }

    // 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();
        }
    }
}