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.util.*;
public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int a[] = new int[3 * N];
		for(int i = 0; i < 3 * N; i++) {
			a[i] = sc.nextInt();
		}
		
		int ans = Integer.MIN_VALUE;
		for(int k = N; k <= 2 * N; k++) {
			int max = 0;
			Queue<Integer> queue1 = new PriorityQueue<>(k, new MyComparator());
			for(int i = 0; i < k; i++) {
				queue1.add(a[i]);
			}
			int temp1 = 0;
			for(int i = 0; i < N; i++) {
				temp1 += queue1.poll();
			}
			max = Math.max(max, temp1);
			
			int min = Integer.MAX_VALUE;
			Queue<Integer> queue2 = new PriorityQueue<>();
			for(int i = k ; i < 3 * N; i++) {
				queue2.add(a[i]);
			}
			int temp2 = 0;
			for(int i = 0; i < N; i++) {
				temp2 += queue2.poll();
			}
			min = Math.min(min, temp2);
			ans = Math.max(ans, max - min);
		}
		System.out.println(ans);
	}
}

class MyComparator implements Comparator {
    public int compare(Object obj1, Object obj2) {
         
        int num1 = (int)obj1;
        int num2 = (int)obj2;
         
        if(num1 < num2) {
            return 1;
        } else if(num1 > num2) {
            return -1;
        } else{
            return 0;
        }
    }
}