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;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder {

    class Program {

        static List<int> Coef(List<int> list, bool reverse) {

            var ret = new List<int>();
            var N = list.Count;

            if(N % 2 == 0) {

                for (int i = 0; i < N; i++) {

                    if (i == 0) {

                        ret.Add(1);
                    } else if (i == N - 1) {

                        ret.Add(-1);
                    } else if (i % 2 != 0) {

                        ret.Add(-2);
                    } else {

                        ret.Add(2);
                    }
                }

            } else {

                for (int i = 0; i < N; i++) {

                    if (i == 0 || i == N - 1) {

                        ret.Add(1);
                    } else if (i % 2 != 0) {

                        ret.Add(-2);
                    } else {

                        ret.Add(2);
                    }
                }
            }

            if(!reverse) {

                return ret.Select(e => e - e * 2).ToList();
            }
            return ret;
        }

        static void Main(string[] args) {

            var N = int.Parse(Console.ReadLine());

            var A = new List<int>();
            for(int _i = 0; _i < N; _i++) {

                A.Add(int.Parse(Console.ReadLine()));
            }
            A.Sort();

            var test1 = Coef(A, false);
            var test2 = Coef(A, true);

            test1.Sort();
            test2.Sort();

            var res1 = 0;
            for (int i = 0; i < N; i++) {

                res1 += A[i] * test1[i];
            }
            var res2 = 0;
            for (int i = 0; i < N; i++) {

                res2 += A[i] * test2[i];
            }

            Console.WriteLine(Math.Max(res1, res2));
        }
    }
}