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 <bits/stdc++.h>

using namespace std;

typedef long long ll;
int N;
ll a[300001];
ll ans = -10000000000000;

int main() {
  cin >> N;

  for(int i = 0; i < 3*N; i++) cin >> a[i];

  for(int i = N; i < 2 * N; i++) {
    ll sum_a = 0, sum_b = 0;
    vector<int>g1(i,0);
    vector<int>g2(3*N-i,0);
    for(int j = 0; j < i; j++) g1[j] = a[j];
    for(int j = 0; j < 3*N-i; j++)g2[j] = a[i+j];
    sort(g1.begin(),g1.end(),greater<ll> ());
    sort(g2.begin(),g2.end());
    for(int j = 0; j < N; j++) sum_a += g1[j];
    for(int j = 0; j < N; j++) sum_b += g2[j];
    ans = max(ans,sum_a-sum_b);
  }

  cout << ans <<endl;
}