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)

  n = gets.to_i
  a = gets.chomp.split(" ").map(&:to_i)
  b1 = []
  b2 = []
  p a
  p n+(n.to_f/2).ceil
  ((n+(n.to_f/2).ceil)).times do
    b1 << a[0]
    a.delete_at(0)
  end
  (3*n-(n+(n.to_f/2).ceil)).times do
    b2 << a[0]
    a.delete_at(0)
  end
  p a
  p b1
  p b2
  if n != 1 and b1.include?(b1.min)
    (n-1).times do
      b1.delete(b1.min)
      end
  else
    b1.delete(b1.min)
  end
  if n != 1 and b2.include?(b2.max)
    b2.delete(b2.max)
  end
  p b1
  p b2
  puts b1.inject(:+)-b2.inject(:+)