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 <vector>
#include <algorithm>
#include <vector>
#include <queue>
#define int long long
using namespace std;
 
signed main(){
    int n;
    int max=0;
    int min=0;
    cin>> n;
    int N=3*n;
    int a[N];
 
    priority_queue<int> PQ1;
    priority_queue<int, vector<int>, greater<int> >PQ2;
 
    int max_arr[n+1]={0};
    int min_arr[n+1]={0};
    
    for(int i=0;i<3*n;i++){
        cin>>a[i];
        
    }
 
    for(int i=0;i<n;i++){
        max+=a[i];
        min+=a[i+2*n];
    }
 
    // cout<<max<<" "<<min<<endl;
 
    max_arr[0]=max;
    
    for(int i=0;i<n;i++){
        PQ2.push(a[i]);
    }
 
    for(int i=n;i<2*n;i++){
        PQ2.push(a[i]);
        max+=a[i];
        max-=PQ2.top();
        PQ2.pop();
        max_arr[i-n+1]=max;
 
    }
 
    // for(int i=0;i<n+1;i++){
    //     cout<<max_arr[i]<<" ";
    // }
 
    min_arr[n]=min;
    for(int i=2*n;i<3*n;i++){
        PQ1.push(a[i]);
    }
    for(int i=3*n;i>2*n;i--){
        // cout<<i-n-1<<endl;
        PQ1.push(a[i-n-1]);
        min+=a[i-n-1];
        min-=PQ1.top();
 
        // cout<<PQ1.top()<<endl;
        PQ1.pop();
        min_arr[(i-2*n)-1]=min;
    }
    // cout<<count<<endl;
 
 
    // for(int i=0;i<n+1;i++){
    //     cout<<min_arr[i]<<" ";
    // }
 
 
    // for(int i=0;i<n+1;i++){
    //     max[i]=
    // }
 
    int ans=-1e9;
    for(int i=0;i<n+1;i++){
        if(ans<max_arr[i]-min_arr[i]){
            ans=max_arr[i]-min_arr[i];
        }
        // ans=max(ans,);
    }
    cout<<ans<<endl;
 
}