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;

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 int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }

        static long Solve(int N, int[] A)
        {
            var ranks = new int[N];
            int m = N / 2;
            int min = 1;
            int max = N - 1;
            ranks[m] = 0;
            for (int i = 1; true;)
            {
                if (min <= max) { ranks[m - i] = max--; } else { break; }
                if (min <= max) { ranks[m + i] = max--; } else { break; }
                ++i;
                if (min <= max) { ranks[m - i] = min++; } else { break; }
                if (min <= max) { ranks[m + i] = min++; } else { break; }
                ++i;
            }
            Array.Sort(A);
            long sum = 0;
            for (int i = 1; i < N; ++i)
            {
                int p = ranks[i];
                int q = ranks[i - 1];
                sum += Math.Abs(A[q] - A[p]);
            }
            return sum;
        }
        static void Main(string[] args)
        {
            int N = ReadInt();
            var A = new int[N];
            for (int i = 0; i < N; ++i) { A[i] = ReadInt(); }
            Console.WriteLine(Solve(N, A));
        }
    }
}