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::cmp::{max, min};
use std::collections::{BinaryHeap, VecDeque};
use std::io::{stdin, Read};
use std::rc::Rc;
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let aa = (0..3 * n).map(|_| read::<i64>()).collect::<Vec<_>>();

    let mut qa = BinaryHeap::new();
    let mut a = 0;
    for i in 0..n {
        a += aa[i];
        qa.push(-aa[i]);
    }

    let mut sum_a = vec![0; n + 1];
    sum_a[0] = a;
    for i in 0..n {
        let next = aa[n + i];
        qa.push(-next);
        let discard = -qa.pop().unwrap();
        a += (next - discard);
        sum_a[i + 1] = a;
    }

    let mut qb = BinaryHeap::new();
    let mut b = 0;
    for i in 2 * n..3 * n {
        b += aa[i];
        qb.push(aa[i])
    }

    let mut sum_b = vec![0; n + 1];
    sum_b[0] = b;
    for i in 0..n {
        let next = aa[n * 2 - 1 - i];
        qb.push(next);
        let discard = qb.pop().unwrap();
        b += (next - discard);
        sum_b[i + 1] = b;
    }

    let mut ans = i64::min_value();
    for i in 0..n + 1 {
        ans = max(sum_a[i] as i64 - sum_b[n - i] as i64, ans);
    }
    println!("{}", ans)
}