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.Arrays;
import java.util.Collections;
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 = sc.nextInt();
		long[] a=new long[3*n]; 
		for(int i=0;i<a.length;i++) a[i]=sc.nextLong();
		
		long score=0;
		PriorityQueue<Long> leftQueue=new PriorityQueue<>();
		PriorityQueue<Long> rightQueue=new PriorityQueue<>(Collections.reverseOrder());		
		for(int i=0;i<n;i++){
			leftQueue.add(a[i]);
			score+=a[i];
			rightQueue.add(a[2*n+i]);
			score-=a[2*n+i];
		}
		
		int l=n;
		int r=2*n-1;
		long[] ds=new long[n+1];
		long d=0;
		for(int i=1;i<=n;i++){
			leftQueue.add(a[n+i-1]);
			d+=a[n+i-1]-leftQueue.poll();
			ds[i]+=d;
			System.out.println(leftQueue);
		}
		d=0;
		for(int i=1;i<=n;i++){
			rightQueue.add(a[2*n-i]);
			d+=rightQueue.poll()-a[2*n-i];
			ds[n-i]+=d;
			System.out.println(rightQueue);
		}

		System.out.println(Arrays.toString(ds));
		long maxds=ds[0];
		for(int i=1;i<=n;i++) maxds=Math.max(maxds, ds[i]);
		
		System.out.println(score+maxds);
	}
}