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;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class C
{
	public static void Main()
	{
		int N = GetInt();
		var A = new List<long>(N);
		for(int i = 0; i < N; i++)
			A.Add(GetLong());
		A.Sort();

		long ans = A[N - 1] - A[0];
		int usedLeft = 0;
		int usedRight = N - 1;
		int nextLeft = 1;
		int nextRight = N - 2;
		while(nextRight >= nextLeft)
		{
			bool useLeft = false;
			bool addLeft = false;
			long tmp = long.MinValue;

			if(Math.Abs(A[usedLeft] - A[nextLeft]) > tmp)
			{
				tmp = Math.Abs(A[usedLeft] - A[nextLeft]);
				useLeft = true;
				addLeft = true;
			}

			if(Math.Abs(A[usedLeft] - A[nextRight]) > tmp)
			{
				tmp = Math.Abs(A[usedLeft] - A[nextRight]);
				useLeft = false;
				addLeft = true;
			}

			if(Math.Abs(A[usedRight] - A[nextLeft]) > tmp)
			{
				tmp = Math.Abs(A[usedRight] - A[nextLeft]);
				useLeft = true;
				addLeft = false;
			}

			if(Math.Abs(A[usedRight] - A[nextRight]) > tmp)
			{
				tmp = Math.Abs(A[usedRight] - A[nextRight]);
				useLeft = false;
				addLeft = false;
			}

			ans += tmp;

			if(addLeft)
				usedLeft = useLeft ? nextLeft : nextRight;
			else
				usedRight = useLeft ? nextLeft : nextRight;

			if(useLeft)
				nextLeft++;
			else
				nextRight--;				
		}

		Console.WriteLine(ans);
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}