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)

n=int(input())
a_list=list(map(int,input().split()))
import heapq
pre=a_list[0:n]
heapq.heapify(pre)
pre_list=[sum(a_list[0:n])]
for i in range(n):
    heapq.heappush(pre,a_list[i+n])
    pre_list.append(pre_list[-1]+a_list[i+n]-heapq.heappop(pre))
b_list=[]
for i in range(2*n,3*n):
    b_list.append(-a_list[i])
post=b_list
heapq.heapify(post)
post_list=[sum(b_list)]
for i in range(n):
    heapq.heappush(post,-a_list[2*n-1-i])
    post_list.append(post_list[-1]-a_list[2*n-1-i]-heapq.heappop(post))
ans=-10**16
for i in range(n+1):
    Max=pre_list[i]+post_list[n-i]
    ans=max(ans,Max)
print(ans)