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 Ruby (2.3.3) (judge verdict: Runtime Error)

class PriorityQueue
  attr :s
  
  def initialize
    @q = [nil]
    @s = 0
  end

  def bubble_up(i)
    p = i / 2
    return if i <= 1 || @q[p] <= @q[i]
    @q[i], @q[p] = @q[p], @q[i]
    bubble_up(p)
  end

  def push(e)
    @q << e
    @s += e
    bubble_up(@q.size - 1)
  end

  def bubble_down(i)
    c = i * 2
    return if c >= @q.size
    c += 1 if c != @q.size - 1 && @q[c] > @q[c + 1]
    return if @q[i] <= @q[c]
    @q[i], @q[c] = @q[c], @q[i]
    bubble_down(c)
  end

  def pop
    @q[1], @q[-1] = @q[-1], @q[1]
    ret = @q.pop
    @s -= ret
    bubble_down(1)
    ret
  end
end

N = gets.to_i
As = gets.split.map(&:to_i)

def f(xs, ys)
  pq = PriorityQueue.new
  xs.each{|x| pq.add(x)}
  ys.each_with_object([pq.s]){|y, o| pq.push_pop(y); o << pq.s}
end

as1, as2, as3 = As.each_slice(N).to_a
s1 = f(as1, as2)
s2 = f(as3.map{|a| -a}, as2.map{|a| -a}.reverse).reverse
puts s1.zip(s2).map{|x, y| x + y}.max