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 Python (3.4.3) (judge verdict: Wrong Answer)

import heapq
N = int(input())
a = list(map(int, input().split()))

max_result = 0

for k in range(N, 2*N+1):
  big_a = a[:k]
  heapq.heapify(big_a)
  small_a =[(-x, x) for x in a[k:]]
  heapq.heapify(small_a)

  for i in range(len(big_a) - N):
    heapq.heappop(big_a)

  for i in range(len(small_a) - N):
    heapq.heappop(small_a)

  big_sum = sum(big_a)
  small_sum = 0
  for i in small_a:
    small_sum += i[1]

  if (big_sum - small_sum) > max_result:
    max_result = big_sum - small_sum

print(max_result)