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.math.BigInteger;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;
public class Main {
	public static void main(String[] args){
		Main main = new Main();
		main.solveD();
	}

	private void solveD() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		List<Long> list = new ArrayList<Long>();
		for (int i = 0; i < 3 * N; i++) {
			list.add(sc.nextLong());
		}
		List<BigInteger> scoreList = new ArrayList<>();
		for (int splitIndex = 0; splitIndex < N; splitIndex++) {
			List<Long> pre = list.subList(0, N + splitIndex);
			List<Long> suf = list.subList(N + splitIndex, 3 * N);

			BigInteger score = BigInteger.ZERO;
			for (long l : pre.stream().mapToLong(i -> i).sorted().skip(splitIndex).toArray()) {
				score = score.add(BigInteger.valueOf(l));
			}
			for (long l : suf.stream().mapToLong(i -> i).sorted().limit(N).toArray()) {
				score = score.subtract(BigInteger.valueOf(l));
			}
			scoreList.add(score);
		}
		System.out.println(scoreList.stream().max((o1, o2) -> o1.compareTo(o2)).get());
	}
}