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;
long long a[333333],pref[333333],suf[333333];
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<3*n;i++)
		cin>>a[i];
	long long su=0;
	multiset<int> s;
	for(int i=0;i<3*n;i++){
		su+=a[i];
		s.insert(a[i]);
		if(s.size()>n){
			su-=*s.begin();
			s.erase(s.begin()); 
		}
		pref[i]=su; 
	}
	s.clear();
	su=0;
	for(int i=3*n;i>0;i--){
		su+=a[i];
		s.insert(a[i]);
		if(s.size()>n){
			su-=*s.rbegin();
			s.erase(--s.end());
		}
		suf[i]=su;
	}
	long long best=-1e18;
	for(int i=n-1;i<=2*n;i++)
		best=max(best,pref[i]-suf[i+1]);
	cout<<best<<endl;
	return 0;
}