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 (7.3.0) (judge verdict: Accepted)

import heapq
N = int(input())
A = list(map(int,input().split()))
B1 = []
for i in range(N):
    heapq.heappush(B1,(A[i],i))
C = []
for i in range(N,3*N):
    heapq.heappush(C,(A[i],i))
B2 = []
for _ in range(N):
    a,i = heapq.heappop(C)
    heapq.heappush(B2,(i,a))
dmax = 0
for i in range(N):
    dmax += B1[i][0]-B2[i][1]
d = dmax
for i in range(N,2*N):
    a = A[i]
    if B1[0][0]<a:
        d += a-B1[0][0]
        heapq.heappop(B1)
        heapq.heappush(B1,(a,i))
    while C and B2[0][0]<=i:
        _,b = heapq.heappop(B2)
        d += b
        a,j = heapq.heappop(C)
        heapq.heappush(B2,(j,a))
        d -= a
    dmax = max(dmax,d)
print(dmax)