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)

# -*- coding: utf-8 -*-

import heapq


class MaxHeap:
    def __init__(self, li):
        self.heap = [-e for e in li]
        heapq.heapify(self.heap)

    def push(self, val):
        heapq.heappush(self.heap, -val)

    def pop(self):
        return -heapq.heappop(self.heap)


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

fh_sum = 0
fh = []
sh_sum = 0
sh = MaxHeap([])
for i in range(n):
    heapq.heappush(fh, a[i])
    fh_sum += a[i]
    sh.push(a[-(i+1)])
    sh_sum += a[-(i+1)]

fh_sums = [fh_sum]
sh_sums = [sh_sum]
for k in range(n, 2 * n):
    fh_sum += a[k]
    heapq.heappush(fh, a[k])
    fh_sum -= heapq.heappop(fh)
    fh_sums.append(fh_sum)
    sh_sum += a[-(k+1)]
    sh.push(a[-(k+1)])
    sh_sum -= sh.pop()
    sh_sums.append(sh_sum)

sh_sums = sh_sums[::-1]

ans = -float("inf")
for fh_sum, sh_sum in zip(fh_sums, sh_sums):
    score = fh_sum - sh_sum
    ans = max(ans, score)

print(ans)