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: Accepted)

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

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var xs = Console.ReadLine().Split()
            .Select(x => long.Parse(x))
            .ToArray();
        
        var xss = new []
        {
            xs,
            xs.Reverse().Select(x => -x).ToArray()
        };
        var score = new long[2][];
        var m = 2 * n;
        for (int i = 0; i < 2; ++i)
        {
            score[i] = new long[n + 1];
            score[i][0] = xss[i].Take(n).Sum();
            var dic = xss[i].Take(n)
                .GroupBy(x => x)
                .ToDictionary(x => x.Key, x => x.Count());
            var pbag = new SortedDictionary<long, int>(dic);
            for (int j = n; j < m; ++j)
            {
                if (pbag.ContainsKey(xss[i][j]))
                {
                    ++pbag[xss[i][j]];
                }
                else
                {
                    pbag[xss[i][j]] = 1;
                }

                var min = pbag.Keys.First();
                if (pbag[min] == 1)
                {
                    pbag.Remove(min);
                }
                else
                {
                    --pbag[min];
                }
                score[i][j - n + 1] = score[i][j - n] + xss[i][j] - min;
            }
        }
        Array.Reverse(score[1]);
        
        Console.WriteLine(Enumerable.Zip(score[0], score[1], (i, j) => i + j).Max());
    }
}