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(non_snake_case,unused_imports)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BinaryHeap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N:usize = iter.next().unwrap().parse().unwrap();
    let A = (0..3*N)  .map(|_| iter.next().unwrap().parse::<i64>().unwrap()).collect::<Vec<_>>();

    let mut hq = BinaryHeap::new();
    let mut l_sum = Vec::new();
    let mut r_sum = Vec::new();

    for i in 0..N{
        hq.push(-A[i]);
    }
    l_sum.push(-hq.iter().sum::<i64>());

    for i in N..2*N{
        hq.push(-A[i]);
        let p = -hq.pop().unwrap();
        let v = l_sum[i-N];
        l_sum.push(v - p + A[i]);
    }
    let mut hq = BinaryHeap::new();
    for i in 2*N..3*N{
        hq.push(A[i]);
    }
    r_sum.push(hq.iter().sum::<i64>());
    for j in 0..N{
        let i = 2*N-1-j;
        hq.push(A[i]);
        let p = hq.pop().unwrap();
        let v = r_sum[j];
        r_sum.push(v - p + A[i]);
    }

    let ans = (0..N+1).map(|i| l_sum[i]-r_sum[N-i]).max().unwrap();

    println!("{}",ans);
}