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 Python (3.4.3) (judge verdict: Accepted)

def main():
    import heapq
    n=int(input())
    a=list(map(int,input().split()))
    h=a[:n]
    dp1=[sum(h)]
    heapq.heapify(h)
    for i in range(n):
        j=heapq.heappop(h)
        if a[n+i]>j:
            dp1.append(dp1[-1]+a[n+i]-j)
            heapq.heappush(h,a[n+i])
        else:
            dp1.append(dp1[-1])
            heapq.heappush(h,j)
    h=[-i for i in a[2*n:]]
    dp2=[sum(h)]
    heapq.heapify(h)
    for i in range(n):
        j=heapq.heappop(h)
        if -a[2*n-i-1]>j:
            dp2.append(dp2[-1]-a[2*n-i-1]-j)
            heapq.heappush(h,-a[2*n-i-1])
        else:
            dp2.append(dp2[-1])
            heapq.heappush(h,j)
    dp2=dp2[::-1]
    print(max([dp1[i]+dp2[i] for i in range(n+1)]))
main()