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 {
	
	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			int n = sc.nextInt();
			int [] a = new int[n];
			int [] b = new int[n];
			int [] c = new int[n];
			long suma = 0, sumb = 0, sumc = 0;
			for(int i = 0; i < n;i++){
				a[i] = sc.nextInt();
				suma += a[i];
			}
			for(int i = 0; i < n;i++){
				b[i] = sc.nextInt();
				sumb += b[i];
			}
			for(int i = 0; i < n;i++){
				c[i] = sc.nextInt();
				sumc += c[i];
			}
			Arrays.sort(a);
			for(int i = 1; i < n;i++){
				a[i] = a[i] + a[i-1]; 
			}
			
			Arrays.sort(c);
			for(int i = 0; i < n / 2; i++){
				int temp = c[i];
				c[i] = c[n -1 -i];
				c[n - 1 - i] = temp;
			}
			for(int i = 1; i < n;i++){
				c[i] = c[i] + c[i-1]; 
			}
	
			
			long ans = Integer.MIN_VALUE;
			for(int i = 1; i < n;i++){
				long adda = 0;
				for(int j = 0; j < i;j++){
					adda += b[j];
				}
				long addc = sumb - adda;
				
				long resa = suma + adda - a[i-1];
				long resc = sumc + addc - c[n-i-1];
				
				ans = Math.max(ans, resa - resc);
			}
			ans = Math.max(ans, suma - sumb);
			ans = Math.max(ans, sumb - sumc);
			System.out.println(ans);

		}
	}

	private void debug(Object... o) {
		System.out.println("debug = " + Arrays.deepToString(o));
	}

	public static void main(String[] args) {
		new Main().doit();
	}

}