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;
public class MainApp
{
    static public void Main(string[] args)
    {
        var read = Console.ReadLine();
        int N = int.Parse(read);
        int[] a = new int[3 * N];
        read = Console.ReadLine();
        var split = read.Split(' ');
        for(int c = 0; c < 3*N;c++)
        {
            a[c] = int.Parse(split[c]);
        }
        int[] leftscore = new int[N];
        int[] rightscore = new int[N];

        int[] leftnumbers = new int[N];
        int[] rightnumbers = new int[N];
        for (int c = 0; c < N; c++)
        {
            leftnumbers[c] = a[c];
            rightnumbers[c] = a[3*N - c-1];

        }
        long firstscore = sum(leftnumbers) - sum(rightnumbers);
        for (int c = 0; c < N; c++)
        {
            int minimum_soeji = minimum(leftnumbers);

            leftscore[c] = a[c + N]-leftnumbers[minimum_soeji];
            leftnumbers[minimum_soeji] = a[c + N];

        }
        for (int c = 0; c < N; c++)
        {
            int maximum_soeji = maximum(rightnumbers);
            rightscore[c] =  rightnumbers[maximum_soeji]- a[2 * N - c - 1] ;
            rightnumbers[maximum_soeji] = a[2 * N - c-1];
        }
        for (int c = 0; c < N-1; c++)
        {
            leftscore[c + 1] += leftscore[c];
            rightscore[c + 1] += rightscore[c];

        }
        long maxscore = Math.Max(leftscore[N - 1], rightscore[N - 1]);
        for (int c = 0; c < N - 1; c++)
        {
            if (leftscore[c] + rightscore[N - 2 - c] > maxscore)
                maxscore = leftscore[c] + rightscore[N - 2 - c];

        }
        Console.WriteLine(maxscore + firstscore);
    }

    static public long sum(int[] a)
    {
        long output = 0;
        for (int c = 0; c < a.Length; c++)
        {
            output += a[c];
        }
        return output;
    }

    static public int maximum(int[] a)
    {
        int output_number = 0;
        int max = a[0];

        for (int c = 0; c < a.Length; c++)
        {
            if (max< a[c])
            {
                output_number = c;
                max = a[c];
            }
        }
        return output_number;
    }

    static public int minimum(int[] a)
    {
        int output_number = 0;
        int min = a[0];
        for (int c = 0; c < a.Length; c++)
        {
            if (min > a[c])
            {
                output_number = c;
                min = a[c];
            }
        }
        return output_number;
    }

}