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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.PriorityQueue;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
	// arc074 D
	private class SumedQueue {
		private int maxSize = 0;
		private long sum = 0;
		private PriorityQueue<Integer> queue = null;
		
		public SumedQueue(int maxSize, boolean isReversed) {
			this.maxSize = maxSize;
			if (isReversed) {
				queue = new PriorityQueue<Integer>(new Comparator<Integer>() {
					@Override
					public int compare(Integer o1, Integer o2) {
						return o2 - o1;
					}
				});
			} else {
				queue = new PriorityQueue<Integer>();
			}
		}
		
		public void add(int n) {
			queue.add(n);
			sum += n;
			if (queue.size() > maxSize) {
				int out = queue.poll();
				sum -= out;
			}
		}
		
		public long total() {
			return sum;
		}
	}
	
	public void solve() {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();

		SumedQueue left = new SumedQueue(N, false);
		SumedQueue right = new SumedQueue(N, true);
		
		int[] middle = new int[N];
		for (int i=0; i<N; i++) {
			left.add(in.nextInt());
		}
		for (int i=0; i<N; i++) {
			middle[i] = in.nextInt();
		}
		for (int i=0; i<N; i++) {
			right.add(in.nextInt());
		}
		in.close();

		// sums[i] : middle[i-1] is left(plus), middle[i] is right(minus)
		long sums[] = new long[N+1];
		sums[0] = left.total();
		for (int i=0; i<N; i++) {
			left.add(middle[i]);
			sums[i+1] = left.total();
		}

		sums[N] -= right.total();
		for (int i=N-1; i>=0; i--) {
			right.add(middle[i]);
			sums[i] -= right.total();
		}

		long max = Long.MIN_VALUE;
		for (int i=0; i<sums.length; i++) {
			if (sums[i] > max) {
				max = sums[i];
			}
		}
		
		System.out.println(max);
	}

	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}
}