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;

fn main() {
    let n = read::<usize>();
    let a = read_vec::<i64>();

    let mut s: Vec<i64> = vec![0; 2*n+1];
    let mut queue1: BinaryHeap<Rev<i64>> = BinaryHeap::new();
    for i in 0..n {
        s[i+1] = s[i] + a[i];
        queue1.push(Rev(a[i]));
    }
    for i in n..2*n {
        if queue1.peek().unwrap().0 < a[i] {
            let min = queue1.pop().unwrap();
            s[i+1] = s[i] - min.0 + a[i];
            queue1.push(Rev(a[i]));
        } else {
            s[i+1] = s[i];
        }
    }

    let mut t: Vec<i64> = vec![0; 2*n+1];
    let mut queue2: BinaryHeap<i64> = BinaryHeap::new();
    for i in 0..n {
        t[i+1] = t[i] + a[3*n-1-i];
        queue2.push(a[3*n-1-i]);
    }
    for i in n..2*n {
        if queue2.peek().unwrap() > &a[3*n-1-i] {
            let max = queue2.pop().unwrap();
            t[i+1] = t[i] - max + a[3*n-1-i];
            queue2.push(a[3*n-1-i]);
        } else {
            t[i+1] = t[i];
        }
    }

    let mut res = i64::min_value();
    for i in n..2*n+1 {
        res = std::cmp::max(res, s[i]-t[3*n-i]);
    }

    println!("{}", res);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

#[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)
    }
}