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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
  public static void Main()
  {
    var n = int.Parse(Console.ReadLine());
    var xs = new long[n];
    for (int i = 0; i < xs.Length; i++)
    {
      xs[i] = int.Parse(Console.ReadLine());
    }

    Array.Sort(xs);
    var ys = new LinkedList<long>(xs);
    var zs = new LinkedList<long>();
    var actions = new Action[]
    {
        () => {
            zs.AddFirst(ys.First.Value);
            ys.RemoveFirst();
        },
        () => {
            zs.AddLast(ys.Last.Value);
            ys.RemoveLast();
        },
        () => {
            zs.AddFirst(ys.Last.Value);
            ys.RemoveLast();
        },
        () => {
            zs.AddLast(ys.First.Value);
            ys.RemoveFirst();
        }
    };
    for (int i = 0; ys.Any(); i = (i + 1) % actions.Length)
    {
        actions[i]();
    }
    var k = 0L;
    xs = zs.ToArray();
    for (int i = 1; i < xs.Length; i++)
    {
        k += Math.Abs(xs[i] - xs[i - 1]);
    }
    Console.WriteLine(k);
  }
}