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)

#include <iostream>
#include <string>
#include <vector>
#include <math.h>
#include <algorithm>
#include <stdint.h>
#include <queue>
#include <bitset>
#include <iomanip>

using namespace std;

#define PI 3.14159265358979323846
#define INF 1e+9
#define DIV_NUM (1000000007)



int main() {

	int N;
	cin >> N;
	vector<long long> inputs;
	for (int i = 0; i < 3 * N; i++) {
		long long tmp;
		cin >> tmp;
		inputs.push_back(tmp);
	}

	priority_queue<long long, vector<long long>, greater<long long>> first_half;
	priority_queue<long long> last_half;
	for (int i = 0; i < N; i++) {
		first_half.push(inputs[i]);
	}
	for (int i = 0; i < N; i++) {
		last_half.push(inputs[3 * N - 1 - i]);
	}

	int first_plus = 0;
	int last_plus = 0;
	while (first_plus + last_plus < N) {
		long long first_point = inputs[N - 1 + first_plus + 1] - first_half.top();
		long long last_point = last_half.top() - inputs[2 * N - 1 - last_plus];
		if (first_point >= last_point) {
			first_half.pop();
			first_half.push(inputs[N - 1 + first_plus + 1]);
			first_plus++;
		}
		else {
			last_half.pop();
			last_half.push(inputs[2 * N - 1 - last_plus]);
			last_plus++;

		}
	}

	long long ans = 0;
	while (!first_half.empty()) {
		ans += first_half.top();
		first_half.pop();
	}
	while (!last_half.empty()) {
		ans -= last_half.top();
		last_half.pop();
	}

	cout << ans << endl;

	return 0;
}