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 PyPy3 (2.4.0) (judge verdict: Accepted)

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

C = A[0:N]
S = sum(C)
prefix = [S]
heapq.heapify(C)
for i in range(N, 2*N):
  heapq.heappush(C,A[i])
  popped = heapq.heappop(C)
  S = S + A[i] - popped
  prefix.append(S)

C = [-e for e in A[2*N:]]
S = -sum(C)
suffix = [S]
heapq.heapify(C)
for i in range(2*N-1, N-1, -1):
  heapq.heappush(C,-A[i])
  popped = heapq.heappop(C)
  S = S + A[i] - (-popped)
  suffix.append(S)

res = -10**15 
j = len(suffix)-1
for i in range(len(prefix)):
  res = max(res, prefix[i] - suffix[j])
  j -= 1

print(res)