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;

public class Test
{
	public static void Main()
	{
		int n = int.Parse(Console.ReadLine());
		int[] x = new int[n];
		for (int i = 0; i < n; i++) x[i] = int.Parse(Console.ReadLine());
		long ret = 0;
		for (int z = 0; z < 2; z++)
		{
			int c = (n + z) / 2;
			Array.Sort(x);
			LinkedList<int> small = new LinkedList<int>();
			for (int i = 0; i < c; i++)
			{
				if (i % 2 == 0) small.AddFirst(x[i]);
				else small.AddLast(x[i]);
			}
			Array.Reverse(x);
			LinkedList<int> big = new LinkedList<int>();
			for (int i = 0; i < n - c; i++)
			{
				if (i % 2 == 0) big.AddLast(x[i]);
				else big.AddFirst(x[i]);
			}
			int[] sarr = small.ToArray(); int[] barr = big.ToArray();
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
			{
				if (z == 0)
				{
					if (i % 2 == 0) arr[i] = barr[i / 2];
					else arr[i] = sarr[i / 2];
				}
				else
				{
					if (i % 2 == 0) arr[i] = sarr[i / 2];
					else arr[i] = barr[i / 2];
				}
			}
			long sum = 0;
			for (int i = 1; i < n; i++) sum += Math.Abs(arr[i] - arr[i - 1]);
			ret = Math.Max(ret, sum);
		}
		Console.WriteLine(ret);
	}
}