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;
#define ll long long
#define forn(n) for(ll i=0;i<n;i++)
int main()
{
    int m;
    cin>>m;
    ll n=3*m;
    ll a[n];
    
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
    }
    
    ll n1=n/2;
    ll n2=n-n1;
    
    ll f[n1],e[n2];    
    
    ll k=0;
    for(ll i=0;i<n1;i++)
    {
        f[i]=a[k];
        k++;
    }
    
   
    
    for(ll j=0;j<n2;j++)
    {
        e[j]=a[k];
        k++;
    }
    
    
    
    sort(f,f+n1,greater<ll>());
    sort(e,e+n2);
    
    
    ll p=0,q=0;
    ll sum=0;
    
    
    for(ll i=0;i<2*m;i++)
    {
        if(i%2==0)
        {
        sum+=f[p];
        p++;

        }
        else
        {
        sum-=e[q];
        q++;

        }
    }
    
    cout<<sum;
    
  
    return 0;
}