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: Time Limit Exceeded)

n = int(input())
as_ =  list(map(int, input().split()))

l = [0]*n
m = [0]*n
r = [0]*n
for i in range(n):
  l[i] = as_[i]
  m[i] = as_[n+i]
  r[i] = (-1)*as_[2*n+i]

import heapq
heapq.heapify(l)
heapq.heapify(r)

l_maxs = [0]*(n+1)
r_mins = [0]*(n+1)

for i in range(n+1):
  if i != 0:
    j = i-1
    heapq.heappush(l, m[j])
    heapq.heappop(l)
    l_max = sum(l)
    
    k = -i
    heapq.heappush(r, m[k]*(-1))
    heapq.heappop(r)
    r_min = sum(r)
    
  else:
    l_max = sum(l)
    r_min = sum(r)
    
  l_maxs[i] = l_max
  r_mins[i] = r_min

#print(l_maxs)
#print(r_mins)

print(max([l_maxs[i] + r_mins[n-i] for i in range(n+1)]))