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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::BinaryHeap;

use std::cmp::Ordering;

#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

pub fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse::<usize>().unwrap();
    let a: Vec<u64> = iter.take(3*n).map(|x| x.parse().unwrap()).collect();
    
    use std::iter::FromIterator;
    let mut front_heap: BinaryHeap<Rev<u64>> = BinaryHeap::from_iter(a.iter().take(n).map(|x| Rev(*x)));
    let mut back_heap: BinaryHeap<u64> = BinaryHeap::from_iter(a.iter().skip(2*n).map(|x| *x));
    let mut front_sum = a.iter().take(n).fold(0, |acc,x| acc + x);
    let mut back_sum = a.iter().skip(2*n).fold(0, |acc,x| acc + x);
    let mut front = vec![0u64;n+1];
    let mut back = vec![0u64;n+1];
    for i in 0..n+1 {
        let p = i + n;
        let q = 2*n - 1 - i;
        front[i] = front_sum;
        back[n-i] = back_sum;
        if i != n {
            if front_heap.peek().unwrap().0 < a[p] {
                let min = front_heap.pop().unwrap().0;
                front_heap.push(Rev(a[p]));
                front_sum -= min;
                front_sum += a[p];
            }

            if *back_heap.peek().unwrap() > a[q] {
                let max = back_heap.pop().unwrap();
                back_heap.push(a[q]);
                back_sum -= max;
                back_sum += a[q];
            }
        }
    }

    // println!("{:?}", front);
    // println!("{:?}", back);
    println!("{}", front.iter().zip(back.iter()).map(|(&a, &b)| a as i64 - b as i64).max().unwrap());
}