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)

import sys
from heapq import heapify, heappop, heappush

def solve():
    input = sys.stdin.readline
    N = int(input())
    A = [int(a) for a in input().split()]
    Type = [False] * (3 * N)
    Front, Back = [], []
    heapify(Front)
    heapify(Back)
    sumA = 0
    sumB = 0
    for i in range(N):
        heappush(Front, A[i])
        sumA += A[i]
    for i in range(N, 3*N):
        heappush(Back, (A[i], i))
    for i in range(N):
        bV, bI = heappop(Back)
        Type[bI] = True
        sumB += bV
    ans = sumA - sumB
    for i in range(N, 2*N):
        heappush(Front, A[i]) #前半の処理
        sumA += A[i]
        sumA -= heappop(Front)
        #後半の処理、境界条件
        newBack, newBackI = heappop(Back)
        if Type[i]:
            sumB -= A[i]
            while newBackI <= i: newBack, newBackI = heappop(Back)
            sumB += newBack
            Type[newBackI] = True
        elif newBackI > i: heappush(Back, (newBack, newBackI))
        ans = max(ans, sumA - sumB)
    print(ans)
    return 0

if __name__ == "__main__":
    solve()