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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	/**
	 * @param args
	 * @throws IOException
	 */

	static int[] zeroes;
	public static void main(String[] args) throws IOException {
		BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));

		String input = scan.readLine();
		int changes = Integer.parseInt(input);
		//conChanges = changes;
		input = scan.readLine();
		 String[] array = input.split(" ");
		 zeroes = new int[changes];
		 set(changes);
		 System.out.println(max(0, changes, array));

	}

	public static int max(int index, int changes, String[] array) {
		if (changes == 0) {
			return cal(array);
		}

		if (index >= array.length && changes != 0 || (changes < 0)) {
			return (int) -10e9;
		}
		int choice1 = (int) -10e9;
		int choice2 = (int) -10e9;

		choice1 = max(index+1, changes, array);
		if (changes > 0) {
			zeroes[changes - 1] = index;
			choice2 = max(index+1, changes - 1, array);

		}
		return Math.max(choice1, choice2);
	}

	public static int cal(String[] array) {
		int number = (((array.length)- zeroes.length)/2);
		int taken = 0;
		int sum1 = 0;
		int sum2 = 0;
		int i = 0;
		for (i = 0; taken < number; i++) {
			if (!include(i)) {
				sum1 += Integer.parseInt(array[i]);
				taken++;
			}

		}
		int start = i;
		for (i = start; i <array.length; i++) {
			if (!include(i)) {
				sum2 += Integer.parseInt(array[i]);
			}

		}


		return sum1 - sum2;
	}

	public static boolean include(int number) {
		for (int i = 0; i < zeroes.length; i++) {
			if (number == zeroes[i]) {
				return true;
			}
		}
		return false;
	}

	public static void set(int changes) {
		for (int i = 0; i <changes; i++) {
			zeroes[i] = -1;
		}
	}

}