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.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";

    //プライオリティーキュー
    void Solve()
    {
        int N = cin.Nextint;
        var A = cin.Scanint;
        var P = new PriorityQueue<int>();
        var Q = new PriorityQueue<int>();
        var R = new long[2 * N + 1];
        var S = new long[2 * N + 1];
        for (int i = 0; i < N; i++)
        {
            R[N - 1] += A[i];
            P.Enqueue(-A[i]);
        }
        for (int i = N; i < 2 * N; i++)
        {
            R[i] = R[i - 1];
            R[i] += A[i];
            P.Enqueue(-A[i]);
            R[i] -= -P.Dequeue();
        }

        for (int i = 2 * N; i < 3 * N; i++)
        {
            S[2 * N] += A[i];
            Q.Enqueue(A[i]);
        }
        for (int i = 2 * N - 1; i >= N; i--)
        {
            S[i] = S[i + 1];
            S[i] += A[i];
            Q.Enqueue(A[i]);
            S[i] -= Q.Dequeue(); 
        }

        long ans = long.MinValue;
        for (int i = N - 1; i < 2 * N; i++)
        {
            ans = Math.Max(ans, R[i] - S[i + 1]);
        }
        WriteLine(ans);

    }

}


class PriorityQueue<T> where T : IComparable
{
    List<T> heap;
    int size;
    int Compare(T x, T y) { return y.CompareTo(x); }
    public PriorityQueue() { heap = new List<T>(); }

    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = size++;

        while (i > 0)
        {
            int p = (i - 1) >> 1;

            if (Compare(heap[p], x) <= 0) break;

            heap[i] = heap[p];
            i = p;
        }
        heap[i] = x;
    }

    public T Dequeue()
    {
        T ret = heap[0];
        T x = heap[--size];

        int i = 0;
        while ((i << 1) + 1 < size)
        {
            int a = (i << 1) + 1;
            int b = (i << 1) + 2;

            if (b < size && Compare(heap[b], heap[a]) < 0)
                a = b;
            if (Compare(heap[a], x) >= 0)
                break;

            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        heap.RemoveAt(size);
        return ret;
    }

    public int Count { get { return size; } }

    public bool Any() { return size > 0; }

    public T Peek() { return heap[0]; }
}
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); } }
}