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)

#!/usr/bin/env python3
import sys
import heapq
from collections import deque


inf = float("inf")

def solve(N: int, a: "List[int]"):
    L = a[:N]
    R = [-x for x in a[2*N:]]
    heapq.heapify(L)
    heapq.heapify(R)
    M = a[N:2*N]
    sumL = [0 for _ in range(N+1)] # sumL[i]: a[0]からa[N-1+i]までの大きい順にN個の和
    sumR = [0 for _ in range(N+1)] # sumR[i]: -(a[N-1+i]からa[3*N-1]までの小さい順にN個の和)

    sumL[0] = sum(L)
    sumR[N] = sum(R)

    for i in range(N):
        l = heapq.heappop(L)
        diff = M[i] - l
        if diff > 0:
            sumL[i+1] = sumL[i] + diff
            heapq.heappush(L, M[i])
        else:
            sumL[i+1] = sumL[i]
            heapq.heappush(L, l)
    
    for i in range(N-1, -1, -1):
        r = heapq.heappop(R)
        diff = -M[i] - r
        if diff > 0:
            sumR[i] = sumR[i+1] + diff
            heapq.heappush(R, -M[i])
        else:
            sumR[i] = sumR[i+1]
            heapq.heappush(R, r)
    
    res = -inf
    for suml, sumr in zip(sumL, sumR):
        res = max(res, suml + sumr)
    print(res)
    return


# Generated by 1.1.4 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    a = [ int(next(tokens)) for _ in range(3*N) ]  # type: "List[int]"
    solve(N, a)

if __name__ == '__main__':
    main()