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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
public class Main
{
	public static void main(String args[])throws IOException {
		BufferedReader br  =new BufferedReader(new InputStreamReader(System.in));
		int n =Integer.parseInt(br.readLine());
	
		String a =br.readLine();
		StringTokenizer st =new StringTokenizer(a);
		int arr[] =new int[3*n];
		for(int i =0;i<3*n;i++)
			arr[i]=Integer.parseInt(st.nextToken());
		int k =n;int max=Integer.MIN_VALUE;
		//System.out.println("n is : "+ n/3);
		while(k<=2*n) {
			
			int m =getlarge(arr,k,n)-getsmall(arr,k,n);k++;
			if(max<m)max=m;
		}
		System.out.println(max);
		
	}
	static int getlarge(int arr[] ,int k ,int n) {
		PriorityQueue <Integer> que=new PriorityQueue<>(new Comparator<Integer>() {
			@Override
			public int compare(Integer o1, Integer o2) {
				// TODO Auto-generated method stub
				return o2-o1;
			}
		});
		int max=0;
		for(int i =0;i<k;i++) {
			que.add(arr[i]);
		}
		for(int i=0;i<n;i++) {
			max+=que.poll();
		}
		
		return max;
		
	}
	static int getsmall(int arr[] ,int k ,int n) {
		PriorityQueue <Integer> que=new PriorityQueue<>();
		int max=0;
		for(int i =k;i<arr.length;i++) {
			que.add(arr[i]);
		}
	
		for(int i=0;i<n;i++) {
			max+=que.poll();
		}
	
		return max;
		
	}
}