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;

namespace atcorder
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            atcorder.Align.NaiveRun();
        }
    }
   public class Align
    {
        public Align()
        {
        }
        public static void Run(){
            int N;
            System.Collections.Generic.List<int> A = new System.Collections.Generic.List<int>();
            string s = Console.ReadLine();
            N = int.Parse(s);
            for (int i = 0; i < N;i++){
                s = Console.ReadLine();
                A.Add(int.Parse(s));
            }
            A.Sort();
            int L, R;
            L = 0;R = A.Count - 1;
            System.Collections.Generic.List<int> B = new System.Collections.Generic.List<int>();
            B.Add(A[R--]);
            for (int i = 0; L <= R;i++){
                int RR,RL,LR,LL,Rm,Lm;
                RR = Math.Abs(B[B.Count - 1] - A[R]);
                RL = Math.Abs(B[0] - A[R]);
                Rm = Math.Max(RR, RL);
                LR = Math.Abs(B[B.Count - 1] - A[L]);
                LL = Math.Abs(B[0] - A[L]);
                Lm = Math.Max(LR, LL);
                if (Lm < Rm)
                {//A[R]をつける
                    if(RR<RL){
                        B.Insert(0, A[R--]);
                    }else if(RR>RL){
                        B.Add(A[R--]);
                    }else{
                        if(B[0]<B[B.Count-1]){
                            B.Insert(0, A[R--]);
                        }else{
                            B.Add(A[R--]);
                        }
                    }
                }
                else if (Lm >= Rm)
                {//A[L]をつける
                    if (LR < LL)
                    {
                        B.Insert(0, A[L++]);
                    }
                    else if (LR > LL)
                    {
                        B.Add(A[L++]);
                    }
                    else
                    {
                        if (B[0] > B[B.Count - 1])
                        {
                            B.Insert(0, A[L++]);
                        }
                        else
                        {
                            B.Add(A[L++]);
                        }
                    }
                }
            }
            int sum = 0;
            for (int i = 0; i < B.Count-1;i++){
                sum += Math.Abs(B[i] - B[i + 1]);
            }
            Console.WriteLine(sum);
        }
        public static void NaiveRun(){
            int N;
            System.Collections.Generic.List<int> A = new System.Collections.Generic.List<int>();
            string s = Console.ReadLine();
            N = int.Parse(s);
            for (int i = 0; i < N; i++)
            {
                s = Console.ReadLine();
                A.Add(int.Parse(s));

            }
            System.Collections.Generic.List<int> B = new System.Collections.Generic.List<int>();
            A.Sort();
            A.Reverse();
            int min = A[A.Count - 1];
            B.Add(A[0]);
            for (int i = 1; i < A.Count;i++){
                if(A[i]!=min){
                    Console.WriteLine("now inserting {0}", A[i]);
                    Console.WriteLine("L={0},R={1}", B[0], B[B.Count - 1]);
                    if(B[0]<B[B.Count-1]){
                        B.Add(A[i]);
                        Console.WriteLine("insert at R");
                    }else{
                        B.Insert(0, A[i]);
                        Console.WriteLine("insert at L");
                    }
                }else{
                    int m = -1, idx = 0;
                    for (int j = 0; j < B.Count - 1;j++){
                        if(Math.Abs(B[j]-A[i])+Math.Abs(B[j+1]-A[i])>m){
                            idx = j+1;
                            m = Math.Abs(B[j] - A[i]) + Math.Abs(B[j + 1] - A[i]);
                        }
                    }
                    B.Insert(idx, A[i]);
                }
            }
            int sum = 0;
            for (int i = 0; i < B.Count - 1; i++)
            {
                Console.Write(B[i]);
                sum += Math.Abs(B[i] - B[i + 1]);
            }
            Console.WriteLine(B[B.Count-1]);
            Console.WriteLine(sum);
        }
    }
}