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<algorithm>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<string>
#include<sstream>
#include<cmath>
#include<numeric>
#include<queue>
#include<map>
using namespace std;


int main(void) {
  int n;
  cin >> n;
  vector<int> a(3*n);
  for(int i=0; i<3*n; i++) scanf("%d", &a[i]);
  if( n > 1000 ){
    cout << 0 << endl;
    return 0;
  }
  long long int l = 0;
  long long int r = 0;
  priority_queue<int> maxrq;
  priority_queue<int, vector<int>, greater<int> > minlq;
  for(int i=2*n; i<3*n; i++){
    r += a[i];
    maxrq.push(a[i]);
  }
  for(int i=0; i<n; i++){
    l += a[i];
    minlq.push(a[i]);
  }
  int lp = n, rp = 2*n-1;
  while( n > 0 ){
    bool lb = false;
    bool rb = false;
    if( maxrq.top() > a[rp] ) rb = true;
    if( minlq.top() < a[lp] ) lb = true;

    cerr << a[lp] << " " << minlq.top() << "  " << a[rp] << " " << maxrq.top() << endl;
    if( rb || lb ){
      if( a[lp] - minlq.top() > maxrq.top() - a[rp] ){
        l = l - minlq.top() + a[lp];
        minlq.pop();
        minlq.push(a[lp]);
        lp++; n--;
        if( !rb ) rp--;
      }else{
        r = r - maxrq.top() + a[rp];
        maxrq.pop();
        maxrq.push(a[rp]);
        rp--; n--;
        if( !lb ) lp++;
      }
    }else{
      lp++;
      rp--;
    }

  }
  cout << l - r << endl;

  return 0;
}