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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author yassin
 */

#include <fstream>

#include <iostream>
#include <vector>
#include <string>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
#include <cstdlib>
#include <tuple>
#include <queue>
#include <functional>
#include <stack>
#include <numeric>
#include <cassert>

using namespace std;

class TaskD {
public:
    void solve(istream& in, ostream& out) {
        int N;
        in >> N;
        vector<int> a(3*N);
        for (int i = 0; i < 3*N; ++i) {
            in >> a[i];
        }
        
        vector<long long> mx(3*N, -1), mn(3*N, -1);
        set<int> s;
        long long cur_sum = 0;
        for (int i = 0; i < 3*N; ++i) {
            if (i < N) {
                s.insert(a[i]);
                cur_sum += a[i];
            } else {
                if (a[i] > *s.begin()) {
                    cur_sum -= *s.begin();
                    cur_sum += a[i];
                    s.erase(s.begin());
                    s.insert(a[i]);
                }
            }
            mx[i] = cur_sum;
        }
        cur_sum = 0;
        s.clear();
        for (int i = 3*N-1; i >= 0; --i) {
            if (3*N-1 - i < N) {
                s.insert(a[i]);
                cur_sum += a[i];
            } else {
                if (a[i] < *s.rbegin()) {
                    cur_sum -= *s.rbegin();
                    cur_sum += a[i];
                    s.erase(--s.end());
                    s.insert(a[i]);
                }
            }
            mn[i] = cur_sum;
        }
        
        long long res = -1000LL * 1000 * 1000 * 1000 * 1000 * 1000;
        for (int i = N-1; i < 2*N; ++i) {
            //cout << "cut after " << i << endl;
            //cout << mx[i] << " " << mn[i + 1] << endl;
            res = max(res, mx[i] - mn[i + 1]);
        }
        
        out << res << "\n";
    }
};


int main() {
	std::ios::sync_with_stdio(false); cin.tie(nullptr);

	TaskD solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}