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: Time Limit Exceeded)

#include <algorithm>
#include <iostream>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
typedef unsigned int uint;
using namespace std;

int main() {
    cin.sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    ll a[3*n];
    for (int i = 0; i < 3*n; i++) {
        cin >> a[i];
    }

    ll ret = 1LL << 60;
    ret = - ret;
    for (int k = n; k <= 2*n; k++) {
        vector<ll> pre;
        vector<ll> pos;
        for (int i = 0; i < k; i++) {
            pre.push_back(a[i]);
        }
        for (int i = k; i < 3*n; i++) {
            pos.push_back(a[i]);
        }

        sort(pre.begin(), pre.end(), greater<ll>());
        sort(pos.begin(), pos.end());

        ll ans = 0LL;
        for (int i = 0; i < n; i++) {
            ans += pre[i] - pos[i];
        }

        ret = max(ret, ans);
    }

    cout << ret << "\n";
    return 0;
}