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: Wrong Answer)

import heapq


def main():
    n = int(input())
    a = list(map(int, input().split()))

    sum_max, sum_min = [0] * (n+1), [0] * (n+1)
    mx_pq, mn_pq = [], []

    for i in range(n):
        heapq.heappush(mx_pq, a[i])
        heapq.heappush(mn_pq, -a[3*n-i-1])

    sum_max[0], sum_min[n] = sum(mx_pq), -sum(mn_pq)

    for i in range(1, n+1):
        if mx_pq[0] < a[n+i-1]:
            sum_max[i] = sum_max[i-1] + a[n+i-1] - heapq.heappop(mx_pq)
            heapq.heappush(mx_pq, a[n+i-1])
        else:
            sum_max[i] = sum_max[i-1]

        if mn_pq[0] < -a[2*n-i]:
            sum_min[n-i] = sum_min[n-i+1] + a[2*n-i] + heapq.heappop(mn_pq)
            heapq.heappush(mn_pq, -a[2*n-i])
        else:
            sum_min[n-i] = sum_min[n-i+1]

    ans = -10 ** 10
    for i in range(n+1):
        ans = max(ans, sum_max[i]-sum_min[i])

    print(ans)


if __name__ == '__main__':
    main()