Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;
//using System.Numerics;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";


    void Solve()
    {
        int N = cin.Nextint;
        var A = cin.Scanint;


        var F = new SortedSet<int>();
        var G = new SortedSet<int>();
        var H = new SortedSet<int>();
        long mae = 0;
        long ato = 0;
        for (int i = 0; i < N; i++)
        {
            F.Add(A[i]);
            mae += A[i];
        }
        for (int i = 2 * N; i < 3 * N; i++)
        {
            G.Add(A[i]);
            ato += A[i];
        }
        for (int i = N; i < 2 * N; i++)
        {
            H.Add(A[i]);
        }

        long ans = mae - ato;

        //int cnt = 0;
        while (H.Any())
        {
            int ff = H.First(); int ll = H.Last();

            int f = ll - F.First();
            int g = G.Last() - ff;

            if (f > 0 && g > 0)
            {
                if (f <= g)
                {
                    G.Remove(G.Last());
                    G.Add(ff);
                    H.Remove(ff);
                    ans += g;
                }
                else
                {
                    F.Remove(F.First());
                    F.Add(ll);
                    H.Remove(ll);
                    ans += f;
                }
            }
            else if (f > 0)
            {
                F.Remove(F.First());
                F.Add(ll);
                H.Remove(ll);
                ans += f;
            }
            else if (g > 0)
            {
                G.Remove(G.Last());
                G.Add(ff);
                H.Remove(ff);
                ans += g;
            }
            else
            {
                H.Remove(ff);
            }
        }
           
       

        WriteLine(ans);

    }

}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}