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 int Calc(List<int> list) {

            var result = 0;
            for (int i = 0; i < list.Count; i++) {

                if (list.Count == i + 1) {

                    break;
                }

                var left = list[i];
                var right = list[i + 1];

                if (left > right) {

                    result += left - right;
                } else {

                    result += right - left;
                }
            }
            return result;
        }

        static void Rotate(List<int> list) {

            list.Insert(0, list.Last());
            list.RemoveAt(list.Count - 1);
        }


        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 acend = new List<int>(A);
            A.Reverse();
            var dcend = new List<int>(A);

            var list = new List<int>();

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

                if(i % 2 == 0) {

                    list.Add(dcend[vd++]);
                } else {

                    list.Add(acend[va++]);
                }
            }

            var result = Calc(list);

            if(N > 3) {

                for(int i = 0; i < 5; i++) {

                    Rotate(list);
                    var re = Calc(list);
                    if (result < re) {

                        result = re;
                    }
                }
            }
            Console.WriteLine(result);
        }
    }
}