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)

#[allow(unused_macros)]
macro_rules! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        line.pop();
        line
    }};
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        let iter = line.split_whitespace();
        iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
    }};
}

fn solve_(aa: Vec<isize>) -> Vec<isize> {
    let nnn = aa.len();
    let mut heap = std::collections::BinaryHeap::new();
    let mut acc = 0;
    let mut ans = Vec::new();
    for &a in aa.iter().take(nnn / 3) {
        heap.push(a);
        acc += a;
    }

    ans.push(acc);

    for &a in aa.iter().skip(nnn / 3).take(nnn / 3) {
        heap.push(a);
        let b = heap.pop().unwrap();
        acc += a - b;
        ans.push(acc);
    }

    ans
}

fn solve(aa: Vec<isize>) -> isize {
    let front = solve_(aa.iter().map(|a| -a).collect());
    let front: Vec<isize> = front.iter().map(|a| -a).collect();
    let back: Vec<isize> = solve_(aa.iter().cloned().rev().collect());
    let back = back.iter().rev().collect::<Vec<_>>();

    front
        .iter()
        .zip(back.iter())
        .map(|(&a, &b)| a - b)
        .max()
        .unwrap()
}

fn main() {
    read_line!();
    let aa = parse_vec!(isize);
    println!("{}", solve(aa));
}

#[test]
fn solve_test() {
    assert_eq!(solve(vec![3, 1, 4, 1, 5, 9]), 1);
    assert_eq!(solve(vec![1, 2, 3]), -1);
    assert_eq!(solve(vec![8, 2, 2, 7, 4, 6, 5, 3, 8,]), 5);
}