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: Wrong Answer)


# https://atcoder.jp/contests/abc062/tasks/arc074_b
# in
# 3
# 8 2 2 7 4 6 5 3 8
# out
# 5

N = gets.to_i
a3n = gets.split.map(&:to_i).each_slice(N).to_a

a2_lower = 0
a2_upper = N - 1

u = []
N.times do
  p a3n
  a1_min = a3n[0].min
  a2_low = a3n[1][a2_lower]
  a2_upp = a3n[1][a2_upper]
  a3_max = a3n[2].max

  if (a3_max - a2_upp) > (a2_low - a1_min)
    if (a3_max - a2_upp) > 0
      u << a3_max
      a3n[2][a3n[2].index(a3_max)] = a2_upp
      a2_upper -= 1
    else
      u << a2_upp
      a2_upper -= 1
    end
  else
    if (a2_low - a1_min) > 0
      u << a1_min
      a3n[0][a3n[0].index(a1_min)] = a2_low
      a2_lower += 1
    else
      u << a2_low
      a2_lower += 1
    end
  end
end
p a3n[0].reduce(:+) - a3n[2].reduce(:+)