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: Time Limit Exceeded)

n=gets.to_i
a=gets.split.map &:to_i
b1=a[0..n-1].sort
b2=a[n..-1].sort
g1=b1.inject(:+)
g2=b2[0..n-1].inject(:+)
max=g1-g2
n.upto(n+n-1) do |i|
  if a[i]>b1[0]
    g1+=a[i]-b1[0]
    b1=b1[1..n-1]
    b1=b1+[a[i]]
    b1.sort!
  end
  if a[i]<=b2[n-1]
    g2+=b2[n]-a[i]
  end
  b2.delete_at(b2.index(a[i]))
  max=[max,g1-g2].max
end
p max