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 PyPy2 (5.6.0) (judge verdict: Accepted)

from heapq import heappush, heappop
n = input()
A = map(int, raw_input().split())
left = [None]*(3*n+1)
right = [None]*(3*n+1)
lsum = rsum = 0
que = []
for i in xrange(3*n):
    lsum += A[i]
    heappush(que, A[i])
    if len(que) > n:
        v = heappop(que)
        lsum -= v
    if len(que) == n:
        left[i] = lsum
que = []
for i in xrange(3*n-1, -1, -1):
    rsum += A[i]
    heappush(que, -A[i])
    if len(que) > n:
        v = heappop(que)
        rsum += v
    if len(que) == n:
        right[i] = rsum
ans = -10**18
for i in xrange(3*n):
    if left[i] is not None and right[i+1] is not None:
        ans = max(ans, left[i] - right[i+1])
print ans