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: Accepted)

class PriorityQueue
  
  def initialize
    @heap = Array.new
    @sz = 0
  end
  
  def push x
    i = @sz
    @sz += 1
    while i > 0 do
      p = ( i - 1 ) / 2
      break if @heap[p] <= x
      @heap[i] = @heap[p]
      i = p
    end
    @heap[i] = x
  end
  
  def pop
    
    ret = @heap[0]
    x = @heap[@sz-=1]
    
    i = 0
    while i * 2 + 1 < @sz do
      a = i * 2 + 1
      b = i * 2 + 2
      a = b if b < @sz && @heap[b] < @heap[a]
      break if @heap[a] >= x
      @heap[i] = @heap[a]
      i = a
    end
    
    @heap[i] = x
    @heap.delete_at(-1)
    ret
  end
  
  def top
    @heap[0]
  end
  
  def empty?
    @sz == 0
  end
  
  def all
    @heap
  end
end

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

fpq = PriorityQueue.new
spq = PriorityQueue.new

f_sum = Array.new( N + 1 )
s_sum = Array.new( N + 1 )

fa = A[0, N]
sa = A[2 * N, N]

f_sum[0] = fa.inject(:+)
s_sum[0] = sa.inject(:+)

A[0, N].each do |a|
  fpq.push( a )
end

N.times do |i|
  a = A[N+i]
  fpq.push( a )
  m = fpq.pop
  f_sum[i+1] = f_sum[i] + a - m
end

# p f_sum

A[2 * N, N].each do |a|
  spq.push( -a )
end

N.times do |i|
  a = A[2*N-i-1]
  spq.push( -a )
  m = -spq.pop
  s_sum[i+1] = s_sum[i] + a - m
end

s_sum.reverse!

ans = nil
(N+1).times do |i|
  v = f_sum[i] - s_sum[i]
  ans = v if ans.nil?
  ans = v if ans < v
end

puts ans