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: Wrong Answer)


import java.io.IOException;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {
		Scanner scan = new Scanner(System.in);
		ArrayList<Character> numbers = new ArrayList<Character>();


		int changes = scan.nextInt();
		scan.nextLine();
		String temp = scan.nextLine();

		for (int i = 0; i < temp.length(); i+=2) {
			numbers.add(temp.charAt(i));
		}

		while (changes > 0) {
			removeMin(numbers, numbers.size()/2);
			changes--;
			if (changes != 0) {
				removeMax(numbers, numbers.size()/2);
				changes--;
			}

		}

		System.out.println(cal(numbers));
	}

	public static void removeMin(ArrayList<Character> numbers, int end) {
		int min = (int) 10e9;
		int index = 0;
		for (int i = 0; i <= end; i++) {
			if (numbers.get(i) < min) {
				min = numbers.get(i);
				index = i;
			}
		}
		numbers.remove(index);
	}

	public static void removeMax(ArrayList<Character> numbers, int start) {
		int max = (int) -10e9;
		int index = 0;
		for (int i = start; i < numbers.size(); i++) {
			if (numbers.get(i) > max) {
				max = numbers.get(i);
				index = i;
			}
		}
		numbers.remove(index);

	}

	public static int cal(ArrayList<Character> numbers) {
		int sum1 = 0;
		int sum2 = 0;
		for (int i = 0; i < numbers.size()/2; i++) {
			sum1 += numbers.get(i) - '0';
		}
		for (int i = numbers.size()/2; i < numbers.size(); i++) {
			sum2 += numbers.get(i) - '0';
		}

		return sum1 - sum2;
	}

}