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: Runtime Error)

#include <bits/stdc++.h>
#define loop(i, a, b) for(int i = a; i < b; i++)
using namespace std;
void O_o() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
 }
 int Max = INT_MIN, n;
void solve(int idx, int nums[], vector<int> v){
    if(v.size() == n * 2) {
        int sum = 0;
        for(int i = 0; i <  v.size() / 2; i++){
            sum = sum + v[i] - v[v.size() - 1 - i];
        }
        Max = (Max > sum) ? Max : sum;
        return;
    }
    if(idx == n * 3) return;

    v.push_back(nums[idx]);
    solve(idx + 1, nums, v);
    v.pop_back();
    solve(idx + 1, nums, v);

}
int main()
{
    O_o();
    cin >> n;
    int nums[n * 3];
    for(int i = 0; i < n * 3; i++)
        cin >> nums[i];
    vector<int> v;
    solve(0, nums, v);
    cout << Max;
    return 0;
}