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: Accepted)

#include <algorithm>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <queue>
#define MOD (1000000007l)
#define REP(i, n) for(long i = 0; i < n; i++)
#define FOR(i, a,b) for(long i = a; i < b; i++)

using namespace std;

int main(void) {
  cout.precision(12);

  long N;
  cin >> N;
  vector<long> a(3*N);
  REP(i, 3*N) cin >> a[i];

  priority_queue<long, vector<long>, greater<long>  > before_queue;
  priority_queue<long> after_queue;

  long before_sum = 0;
  long after_sum = 0;

  vector<long> before_result(3*N, 0);
  vector<long> after_result(3*N, 0);
  
  REP(i,N){
  	before_sum += a[i];
  	before_queue.push(a[i]);
  	
  	after_sum += a[i+2*N];
  	after_queue.push(a[i+2*N]);
  }
  
  before_result[N-1] = before_sum;
  after_result[2*N] = after_sum;
  FOR(i,N,2*N){
  	before_sum += a[i];
  	before_queue.push(a[i]);
  	before_sum -= before_queue.top();
  	before_queue.pop();
  	before_result[i] = before_sum;
  	
  }
  
  for(int i = 2*N-1; i>= N ;i--){
  	after_sum += a[i];
  	after_queue.push(a[i]);
  	after_sum -= after_queue.top();
  	after_queue.pop();
  	after_result[i] = after_sum;
  }
  
  bool not_calculated = true;
  long result;
 
  for (long i = N-1; i < 2*N; i++) {
    long tmp_result = before_result[i] - after_result[i+1];
    if (not_calculated or result < tmp_result) result = tmp_result;
    not_calculated = false;
  }
  
  cout << result << endl;

  return 0;
}