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().strip())
a = list(map(int, input().split()))
pre = a[:n]
heapq.heapify(pre)
suf = list(map(lambda x: -x, a[(2 * n):]))
heapq.heapify(suf)
left = {}
right = {}
pre_sum = sum(pre)
suf_sum = -sum(suf)
left[n - 1] = pre_sum
right[2 * n] = suf_sum
for i in range(n, 2 * n):
    heapq.heappush(pre, a[i])
    pre_sum = pre_sum + a[i] - heapq.heappop(pre)
    left[i] = pre_sum
for i in range(2 * n - 1, n - 1, -1):
    heapq.heappush(suf, -a[i])
    suf_sum = suf_sum + a[i] + heapq.heappop(suf)
    right[i] = suf_sum
ans = -float('inf')
for i in range(n - 1, 2 * n):
    ans = max(ans, left[i] - right[i + 1])
print(ans)