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: Time Limit Exceeded)

import java.util.HashMap;
import java.util.Scanner;

public class Main {
	// arc074 D
	
	private class Status implements Comparable<Status> {
		public int left = 0;
		public int start = 0;
		
		public Status(int left, int start) {
			this.left = left;
			this.start = start;
		}

		@Override
		public int compareTo(Status o) {
			int diff = this.left - o.left;
			if (diff == 0) {
				return 0;
			}
			return this.start - o.start;
		}
		
		@Override
		public int hashCode() {
			return (this.left << 15) | this.start;
		}
	}
	
	int N = 0;
	HashMap<Status, Long> results = new HashMap<Status, Long>();
	int[] nums = null;

	public long solveSub(int left, int start, int picked) {
		Status status = new Status(left, start);
		Long ret = results.get(status);
		if (ret != null) {
			return ret;
		}

		if (N*3-start < left) {
			return Long.MIN_VALUE;
		}

		if (left <= 0) {
			long sum = 0;
			for (; start < 3*N; start++) {
				if (picked < N) {
					sum += nums[start];
				} else {
					sum -= nums[start];
				}
				picked++;
			}
			results.put(status, sum);
			return sum;
		}
		
		// non-remove, pick-up
		long nonRemoveResult = solveSub(left, start+1, picked+1);
		if (nonRemoveResult != Long.MIN_VALUE) {
			if (picked < N) {
				nonRemoveResult += nums[start];
			} else {
				nonRemoveResult -= nums[start];
			}
		}
		
		// removed, no pick-up
		long removedResult = solveSub(left-1, start+1, picked);
		
		long result = Math.max(nonRemoveResult, removedResult);
		results.put(status, result);
		
		return result;
	}
	
	public void solve() {
		Scanner in = new Scanner(System.in);
		N = in.nextInt();
		
		nums = new int[3*N];
		for (int i=0; i<3*N; i++) {
			nums[i] = in.nextInt();
		}
		in.close();

		long result = solveSub(N, 0, 0);

		System.out.println(result);
	}

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