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: Runtime Error)

import heapq
N=int(input())
A=list(map(int, input().split()))

class MaxHeap:
    def __init__(self, li):
        self.hp = []
        for e in li:
            heappush(self.hp, -e)

    def push(self, x):
        heappush(self.hp, -x)

    def pop(self):
        ret = heappop(self.hp)
        ret *= -1
        return ret

    def seak(self):
        return -self.hp[0]

    def sum(self):
        return -sum(self.hp)

A1=A[:N]
A2=A[N:2*N]
A3=A[2*N:]

heapq.heapify(A1)
A1_sum=sum(A1)
A1_li=[A1_sum]
for a in A2:
  p=heapq.heappushpop(A1,a)
  A1_sum+=a-p
  A1_li.append(A1_sum)
  
A3=MaxHeap(A3)
A3_sum=sum(A3)
A3_li=[A3_sum]
for a in A3[::-1]:
  A3.push(a)
  A3_sum+=a
  p=A3.pop()
  A3_sum-=p
  A3_li.append(A3_sum)
  
A3_li=A3_li[::-1]  
ans=False
for a1, a3 in zip(A1_li, A3_li):
  if not ans:
    ans=a1-a3
  else:
    ans=max(ans, a1-a3)
print(ans)