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.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int[] a = new int[3*n];
        for(int i=0;i<3*n;i++){
            a[i] = Integer.parseInt(sc.next());
        }
        sc.close();
        long[] lsum = new long[3*n+1];
        PriorityQueue<Integer> right = new PriorityQueue<>(new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return o2-o1;
            }
        });
        PriorityQueue<Integer> left = new PriorityQueue<>();
        for(int i=0;i<n;i++){
            lsum[i+1] = lsum[i] + a[i];
            left.add(a[i]);
        }
        Integer tmp;
        for(int i=n;i<2*n;i++){
            tmp = left.peek();
            if(a[i] > tmp){
                lsum[i+1] = lsum[i] + a[i] - tmp;
                left.poll();
                left.add(tmp);
            }else{
                lsum[i+1] = lsum[i];
            }
        }
        long[] rsum = new long[3*n+1];
        for(int i=3*n;i>2*n;i--){
            rsum[i-1] = rsum[i] + a[i-1];
            right.add(a[i-1]);
        }

        for(int i=2*n;i>n;i--){
            tmp = right.peek();
            if(a[i-1] < tmp){
                rsum[i-1] = rsum[i] + a[i-1] - tmp;
                right.poll();
                right.add(a[i-1]);
            }else{
                rsum[i-1] = rsum[i];
            }
        }
        long max = Long.MIN_VALUE;
        for(int i=n;i<=2*n;i++){
            max = Math.max(max, lsum[i] - rsum[i]);
        }
        System.out.println(max);
        

    }

}