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: Time Limit Exceeded)

//#pragma warning disable

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

// キーの重複がOKなset
public class DuplicatedSet<T> : IEnumerable<T>
{
    SortedDictionary<T, int> dict = new SortedDictionary<T, int>();
    int count = 0;
    
    public void Add(T key)
    {
        if (!dict.ContainsKey(key))
        {
            dict[key] = 0;
        }

        dict[key]++;
        count++;
    }

    public IEnumerator<T> GetEnumerator()
    {
        foreach (var kvpair in dict)
        {
            for (int i = 0; i < kvpair.Value; i++)
            {
                yield return kvpair.Key;
            }
        }
    }

    IEnumerator IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }
}

public class Test
{
    public static void Main()
    {
        var N = long.Parse(Console.ReadLine());

        var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

        // Xの値の配列を作成
        long[] X = new long[N + 1];
        {
            var list = new DuplicatedSet<long>();  // 降順
            for (int i = 0; i < N - 1; i++)
            {
                list.Add(-a[i]);
            }

            for (int i = (int)N - 1; i < 2 * N; i++)
            {
                list.Add(-a[i]);

                // list の最初の(大きい方の) N 個の総和
                X[i - N + 1] = -list.Take((int)N).Sum();
            }
        }

        // Yの値の配列を作成
        long[] Y = new long[N + 1];
        {
            var list = new DuplicatedSet<long>();  // 昇順
            for (int i = 3 * (int)N - 1; i >= 2 * N + 1; i--)
            {
                list.Add(a[i]);
            }

            for (int i = 2 * (int)N; i >= N; i--)
            {
                list.Add(a[i]);

                // list の最初の(小さい方の) N 個の総和
                Y[i - N] = list.Take((int)N).Sum();
            }
        }

        //Console.WriteLine(String.Join(", ", X));
        //Console.WriteLine(String.Join(", ", Y));

        var result = X.Zip(Y, (x, y) => (x - y)).Max();

        Console.WriteLine(result);
    }
}