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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

$N=<>;
$/=$";
$_.=$".$%++for@a=<>;
@s=sort{$b-$a}@a;

$X=-inf;
for$m($N..2*$N){
	$x=0;
	$c=0;
	for($i=0;$c<$N;++$i){
		$s[$i]=~$";
		if($'<$m){
			$x+=$`;
			++$c;
		}
	}
	$c=0;
	for($i=3*$N-1;$c<$N;--$i){
		$s[$i]=~$";
		if($'>=$m){
			$x-=$`;
			++$c;
		}
	}
	if($x>$X){$X=$x;}
}
print$X,v10