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;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = new int[N];
            for (var i = 0; i < N; i++)
                A[i] = int.Parse(Console.ReadLine());

            Array.Sort(A);

            var mid = N / 2;
            var one = CalcA(mid, 0, A);
            var two = 0L;
            if (N % 2 == 1) 
                two = CalcB(mid, N - 1, A);

            Console.WriteLine(Math.Max(one, two));
        }

        static long CalcA(int mid, int cur, int[] A)
        {
            var ret = 0L;
            var bef = mid;
            while (cur < mid)
            {
                ret += Math.Abs(A[bef] - A[cur]);
                bef = cur;
                var minusIndex = A.Length - cur - 1;
                if (minusIndex == mid) break;
                ret += Math.Abs(A[bef] - A[minusIndex]);
                bef = minusIndex;
                cur++;
            }

            return ret;
        }

        static long CalcB(int mid, int cur, int[] A)
        {
            var ret = 0L;
            var bef = mid;
            while (mid < cur)
            {
                ret += Math.Abs(A[bef] - A[cur]);
                bef = cur;
                var minusIndex = A.Length - cur - 1;
                if (minusIndex == mid) break;
                ret += Math.Abs(A[bef] - A[minusIndex]);
                bef = minusIndex;
                cur--;
            }

            return ret;
        }
    }
}