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 (1.42.0) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused)]
use proconio::marker::*;
use proconio::{fastout, input};
#[allow(unused)]
use std::cmp::{max, min, Reverse};
#[allow(unused)]
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [i64; 3 * n],
    }

    let mut left_min_heap = {
        let mut h = BinaryHeap::new();
        for &v in a[..n].iter() {
            h.push(-v);
        }
        h
    };

    let mut right_max_heap = {
        let mut h = BinaryHeap::new();
        for &v in a[2 * n..].iter() {
            h.push(v);
        }
        h
    };

    let mut maxes = vec![0; n + 1];
    maxes[0] = -left_min_heap.iter().sum::<i64>();
    for i in n..2 * n {
        left_min_heap.push(-a[i]);
        let poped = -left_min_heap.pop().unwrap();
        maxes[i - n + 1] = maxes[i - n] + a[i] - poped;
    }

    let mut mins = vec![0; n + 1];
    mins[n] = right_max_heap.iter().sum::<i64>();
    for i in (n..2 * n).rev() {
        right_max_heap.push(a[i]);
        let poped = right_max_heap.pop().unwrap();
        mins[i - n] = mins[i - n + 1] + a[i] - poped;
    }

    let mut ans = std::i64::MIN;
    for i in 0..n + 1 {
        ans = max(ans, maxes[i] - mins[i]);
    }
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin4099BFD8";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";