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_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

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

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub trait BinarySearch<T> {
    fn lower_bound(&self, &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

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

    let mut former_heap = BinaryHeap::new();
    for i in 0..n {
        former_heap.push(-a[i]);
    }
    let mut former_sums = vec![0i64; n + 1];
    former_sums[0] = a.iter().take(n).sum::<i64>();
    for i in 0..n {
        let smallest_former = -former_heap.pop().unwrap();
        former_sums[i + 1] = former_sums[i];
        if a[i + n] > smallest_former {
            former_sums[i + 1] += a[i + n] - smallest_former;
        }
        former_heap.push(-max(smallest_former, a[i + n]));
    }

    let mut latter_heap = BinaryHeap::new();
    for i in n * 2..n * 3 {
        latter_heap.push(a[i]);
    }
    let mut latter_sums = vec![0i64; n + 1];
    latter_sums[0] = a.iter().skip(2 * n).sum::<i64>();
    for i in 0..n {
        let largest_latter = latter_heap.pop().unwrap();
        latter_sums[i + 1] = latter_sums[i];
        if a[2 * n - i - 1] < largest_latter {
            latter_sums[i + 1] += a[2 * n - i - 1] - largest_latter;
        }
        latter_heap.push(min(largest_latter, a[2 * n - i - 1]));
    }

    println!(
        "{}",
        (0..n + 1)
            .map(|i| former_sums[i] - latter_sums[n - i])
            .max()
            .unwrap()
    );
}