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 static System.Math;
using System;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        var a = new int[n];
        for (int i = 0; i < n; i++) a[i] = int.Parse(Console.ReadLine().Trim());
        Array.Sort(a);
        Console.WriteLine(n % 2 == 0 ? getAnsEven(a, n) :getAnsOdd(a, n));
    }
    public static long getAnsOdd(int[] a, int n)
    {
        var n2 = n / 2;
        var ans = 0L;
        for (int i = 0; i < n2; i++)
            ans += (a[i + n2 + 1] - a[i]) * 2;
        ans += a[n2 - 1] - a[n2 + 1];
        var ans1 = ans + a[n2 + 1] - a[n2];
        var ans2 = ans + a[n2] - a[n2 - 1];
        return Max(ans1, ans2);
    }
    public static long getAnsEven(int[] a, int n)
    {
        var n2 = n / 2;
        var ans = 0L;
        for (int i = 0; i < n2; i++)
            ans += (a[i + n2] - a[i]) * 2;
        ans += a[n2 - 1] - a[n2];
        return ans;
    }
}