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.*;

public class Main {
	
	/*
	 * default function
	 * */	
	int ni() {
		return cin.nextInt();
	}
	
	long nl() {
		return cin.nextLong();
	}
	
	String line() {
		return cin.nextLine();
	}
	
	void println(String str) {	
		System.out.println(str);
	}
	
	void print(String str) {
		System.out.print(str);
	}
	
	/*
	 * default variable
	 */
	
	static final int MOD = 1000000007;
	
	Scanner cin = new Scanner(System.in);	
	String  output;
	
	public static void main(String[] args) {			
		new Main().run();						
	}
	/* default above */
		
	public void run() {
			
		input();
		/* 
		 * start
		 */	
		
		dfs(0, 0, 0, 0);
		
		/*
		 * finish
		 */
		
		output = res +"";
		println(output);
			
	}
	/* 
	 * define variable
	 */
	
	int N;
	int[] nums;
	
	long res;
	
	
	void input() {
		
		res = Long.MIN_VALUE;		
		
		N = ni();
		nums = new int[N * 3];
		
		for (int i = 0; i < nums.length; i ++) {
			nums[i] = ni();
		}		
	}
	
	void dfs(int index, long sum1, long sum2, int cnt) {
		
		
		if (index == 3*N) {
			if (cnt != 2*N) {
				return;
			}
			
			res = Math.max(res, sum1 - sum2);
			return;
		}
		
		if (3*N - index < 2*N - cnt) {
			return;
		}
			
		
		if (cnt < N) {
			dfs(index + 1, sum1 + nums[index], sum2, cnt + 1);
		} else {
			dfs(index + 1, sum1, sum2 + nums[index], cnt + 1);
		}
		
		dfs(index + 1, sum1, sum2, cnt);
	}
	
}