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)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait StringExt {
    fn get_reverse(&self) -> String;
}
impl StringExt for String {
    fn get_reverse(&self) -> String {
        self.chars().rev().collect::<String>()
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

fn main() {
    input! {
       N: usize,
       mut a:[usize;N*3],
    }

    let mut r = VecDeque::new();
    let mut l = VecDeque::new();
    let mut sum_l = 0;
    let mut sum_r = 0;
    let mut q_l = BinaryHeap::new();
    let mut q_r = BinaryHeap::new();
    let mut m_l = 0;
    let mut m_r = INF_USIZE;
    let mut ans_r = vec![0; N * 3];
    let mut ans_l = vec![0; N * 3];
    mydbg!(a);
    for i in 0..3 * N {
        l.push_back(a[i]);
    }
    for i in 0..N {
        if let Some(x) = l.pop_front() {
            q_l.push(Reverse(x));
            sum_l += x;
        }
    }
    ans_l[N - 1] = sum_l;
    for i in N..2 * N {
        if i < N {
            ans_l[i] = 0;
        }
        let Reverse(b) = q_l.pop().unwrap();
        let c = l.pop_front().unwrap();
        let d = max(c, b);
        sum_l += d;
        sum_l -= b;
        ans_l[i] = sum_l;
        q_l.push(Reverse(d));
    }
    //a.reverse();
    for i in 0..3 * N {
        r.push_back(a[i]);
    }
    for i in 0..N {
        if let Some(x) = r.pop_back() {
            q_r.push(x);
            sum_r += x;
        }
    }
    ans_r[N] = sum_r;
    for i in N + 1..(2 * N + 1) {
        let b = q_r.pop().unwrap();
        let c = r.pop_back().unwrap();
        let d = min(c, b);
        sum_r += d;
        sum_r -= b;
        ans_r[i] = sum_r;
        q_r.push(d);
    }
    ans_r.reverse();
    mydbg!(ans_l, ans_r);
    let mut ans = INF_I64 * -1;
    for i in 0..3 * N {
        if ans_r[i] == 0 || ans_l[i] == 0 {
            continue;
        }
        ans = max(ans, ans_l[i] as i64 - ans_r[i] as i64);
    }

    echo!(ans);
}