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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
/*
    Problem URL : http://arc074.contest.atcoder.jp/tasks/arc074_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d", $N);
$a = explode(" ", trim(fgets(STDIN)));

$ans = -PHP_INT_MAX;

for ($i = $N; $i <= $N * 2; $i++) {
    $x = array_slice($a, 0, $i);
    $y = array_slice($a, $i);

    rsort($x);
    sort($y);

    $x2 = array_slice($x, 0, $N);
    $y2 = array_slice($y, 0, $N);

    $xs = array_sum($x2);
    $ys = array_sum($y2);

    $ans = max($ans, $xs - $ys);
}

echo $ans . PHP_EOL;