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.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());//long.Parseはstringをlongに変換。
		long answer = 0;
    long[] nums = new long[n];
    long[] differences = new long[n-1];
    long l = 0;

    for(long i = 0; i < n; i++)
    {
      nums[i] = long.Parse(Console.ReadLine());
    }
    Array.Sort(nums);//ソート
    
    for(long i = 0; i < n-1; i++)
    {
      differences[i] = nums[i+1] - nums[i];
    }

    l = differences.Length;
    if(l % 2 == 1)
    {
      for(long i = 0; i <= l/2 - 1; i++)
      {
        answer += differences[i] * 2 * (i+1);
      }
      answer += differences[l/2] * l;
      for(long i = (l+1)/2; i < l; i++)
      {
        answer += differences[i] * 2 * (l-i);
      }
    }else
    {
      for(long i = 0; i <= l/2 - 1; i++)
      {
        answer += differences[i] * 2 * (i+1);
      }
      answer -= Math.Min(differences[l/2 - 1], differences[l/2]);
      
      for(long i = l/2; i < l; i++)
      {
        answer += differences[i] * 2 * (l-i);
      }
    }
    
		Console.WriteLine(answer);//WriteLineをWriteとすると、改行なしで出力。
	}
}