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.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
using static System.Math;
class Z { static void Main() => new K(); }
class K
{
	int F => int.Parse(Str);
	long FL => long.Parse(Str);
	int[] G => Strs.Select(int.Parse).ToArray();
	long[] GL => Strs.Select(long.Parse).ToArray();
	string Str => ReadLine();
	string[] Strs => Str.Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries);
	const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	void Solve()
	{
		var N = F;
		var A = new int[N];
		for (var i = 0; i < N; i++) A[i] = F;
		Array.Sort(A);
		var coeff = new List<int>();
		if (N % 2 == 0)
		{
			for (var i = 0; i < N / 2 - 1; i++) coeff.Add(-2);
			coeff.Add(-1);
			coeff.Add(1);
			for (var i = 0; i < N / 2 - 1; i++) coeff.Add(2);
		}
		else
		{
			for (var i = 0; i < (N - 1) / 2; i++) coeff.Add(-2);
			coeff.Add(1);
			coeff.Add(1);
			for (var i = 0; i < (N - 3) / 2; i++) coeff.Add(2);
		}
		var ans = 0L;
		for (var i = 0; i < N; i++) ans += coeff[i] * A[i];
		var ans2 = 0L;
		for (var i = 0; i < N; i++) ans2 -= coeff[N - i - 1] * A[i];
		WriteLine(Max(ans, ans2));
	}
}