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)

from heapq import *
N, = map(int, input().split())
A = list(map(int, input().split()))
s = sum(A[:N])
rs = [s] + [0] * N
l = []
for i in range(N):
    heappush(l, A[i])
for i in range(N, 2*N):
    s += A[i]
    heappush(l, A[i])
    x = heappop(l)
    s -= x
    rs[i-N+1] = s
l2 = []
s2 = 0
for i in range(2*N, 3*N):
    heappush(l2, -A[i])
    s2+=A[i]

rs2 = [0] * N + [s2]
for i in range(2*N-1, N-1, -1):
    s2 += A[i]
    heappush(l2, -A[i])
    x = -heappop(l2)
#    print(A[i])
#    print(x)
    s2 -= x
    rs2[i-N] = s2
#print(rs2)
r = -10**18
for i in range(N+1):
    c = rs[i] - rs2[i]
    r = max(c, r)
print(r)