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;

class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        List<int> a = new List<int>();
        for (int i = 0; i < n; i++)
        {
            a.Add(int.Parse(Console.ReadLine()));
        }
        a.Sort();

        List<int> ans = new List<int>();
        int cnt = 0;
        ans.Add(a[0]);
        for (int i = 1; i < a.Count; i++)
        {
            switch (i % 4)
            {
                case 1:
                    ans.Add(a[a.Count - 1 - cnt]);
                    break;
                case 2:
                    ans.Insert(0, a[a.Count - 2 - cnt]);
                    break;
                case 3:
                    ans.Add(a[cnt + 1]);
                    break;
                case 0:
                    ans.Insert(0, a[cnt + 2]);
                    cnt += 2;
                    break;
            }
        }

        List<int> ans2 = new List<int>();
        cnt = 0;
        ans2.Add(a[a.Count - 1]);
        for (int i = 1; i < a.Count; i++)
        {
            switch (i % 4)
            {
                case 1:
                    ans2.Add(a[cnt]);
                    break;
                case 2:
                    ans2.Insert(0, a[cnt + 1]);
                    break;
                case 3:
                    ans2.Add(a[a.Count - 2 - cnt]);
                    break;
                case 0:
                    ans2.Insert(0, a[a.Count - 3 - cnt]);
                    cnt += 2;
                    break;
            }
        }

        long sum = 0;
        for (int i = 1; i < ans.Count; i++)
        {
            sum += Math.Abs(ans[i] - ans[i - 1]);
        }

        long sum2 = 0;
        for (int i = 1; i < ans2.Count; i++)
        {
            sum2 += Math.Abs(ans2[i] - ans2[i - 1]);
        }
        Console.WriteLine(Math.Max(sum, sum2));
    }
}