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: Wrong Answer)

using System;
class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = int.Parse(Console.ReadLine());
        Array.Sort(a);
        if (n % 2 == 0)
        {
            long ans = 0;
            int m = (n - 1) / 2;
            for (int i = 0; i < m; i++)
            {
                ans += (a[i + 1] - a[i]) * 2 * (i + 1);
                ans += (a[n - i - 1] - a[n - i - 2]) * 2 * (i + 1);
            }
            ans += (a[m + 1] - a[m]) * (2 * m + 1);
            Console.WriteLine(ans);
        }
        else
        {
            long ans = 0;
            int m = n / 2 - 1;
            for (int i = 0; i < m; i++)
            {
                ans += (a[i + 1] - a[i]) * 2 * (i + 1);
                ans += (a[n - i - 1] - a[n - i - 2]) * 2 * (i + 1);
            }
            ans += Math.Max((a[n / 2] - a[n / 2 - 1]) * (2 * m + 1) + (a[n / 2 + 1] - a[n / 2]) * 2 * (m + 1),
                (a[n / 2] - a[n / 2 - 1]) * 2 * (m + 1) + (a[n / 2 + 1] - a[n / 2]) * (2 * m + 1));
            Console.WriteLine(ans);
        }
    }
}