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;

namespace ARC074_D___3N_Numbers
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var Ai = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);

            var front = new PriorityQueue<long>(true);
            for (int i = 0; i < N; i++) front.Push(Ai[i]);


            var center = new long[N];
            Array.Copy(Ai, N, center, 0, N);

            var back = new PriorityQueue<long>(false);
            for (int i = 0; i < N; i++) back.Push(Ai[i + 2 * N]);

            var sumFront = new long[N + 1];
            sumFront[0] = Ai.Take(N).Sum();
            for (int i = 1; i < N + 1; i++)
            {
                front.Push(center[i - 1]);
                sumFront[i] = sumFront[i - 1] - front.Pop() + center[i - 1];
            }

            var sumBack = new long[N + 1];
            sumBack[N] = Ai.Skip(2 * N).Sum();
            for (int i = N - 1; i >= 0; i--)
            {
                back.Push(center[i]);
                sumBack[i] = sumBack[i + 1] - back.Pop() + center[i];
            }

            var score = new long[N + 1];
            for (int i = 0; i < N + 1; i++) score[i] = sumFront[i] - sumBack[i];

            Console.WriteLine(score.Max());
        }
    }
    class PriorityQueue<T> where T : IComparable
    {
        private List<T> nodes;
        private Boolean isAsc;

        public PriorityQueue(Boolean _isAsc)
        {
            this.nodes = new List<T>();
            this.isAsc = _isAsc;
        }

        public int Count()
        {
            return this.nodes.Count;
        }
        public T Pop()
        {
            T returnNode = this.nodes[0];
            this.nodes[0] = this.nodes[nodes.Count - 1];
            this.nodes.RemoveAt(nodes.Count - 1);
            int root = 0;
            while (root * 2 + 1 < this.nodes.Count)
            {
                int child = root * 2 + 1;
                if (child + 1 < this.nodes.Count && compare(this.nodes[child + 1], this.nodes[child]) > 0) child += 1;
                if (compare(this.nodes[child], this.nodes[root]) > 0)
                {
                    swap(child, root);
                    root = child;
                }
                else
                {
                    break;
                }
            }
            return returnNode;
        }
        public T Top()
        {
            return this.nodes[0];
        }
        public void Push(T t)
        {
            this.nodes.Add(t);
            var addPosition = nodes.Count - 1;
            while (addPosition > 0)
            {
                var parent = (int)(addPosition - 1) / 2;
                if (compare(nodes[addPosition], nodes[parent]) > 0)
                {
                    swap(addPosition, parent);
                    addPosition = parent;
                }
                else
                {
                    break;
                }
            }
        }
        private int compare(T x, T y)
        {
            return this.isAsc ? y.CompareTo(x) : x.CompareTo(y);
        }
        private void swap(int x, int y)
        {
            T temp = nodes[x];
            nodes[x] = nodes[y];
            nodes[y] = temp;
        }
    }
}