p03714 AtCoder Beginner Contest 062 - 3N Numbers
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

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'.

Examples

Input

2
3 1 4 1 5 9


Output

1


Input

1
1 2 3


Output

-1


Input

3
8 2 2 7 4 6 5 3 8


Output

5
```python
def f(x):
    y=x[:n];heapify(y);z=sum(y);s=[z]
    for i in x[n:n*2]:z+=i-heappushpop(y,i);s+=[z]
    return s
from heapq import*;n,*a=map(int,open(0).read().split());print(max(map(sum,zip(f([-i for i in a[n:][::-1]]),f(a)[::-1]))))
```