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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
int a[3000005];
int main()
{
    ios::sync_with_stdio(0);
    int n;
    cin>>n;
    for(int i=0; i<3*n; i++)
        cin>>a[i];
    multiset<int > s1,s2,s3;
    multiset<int >::iterator it;
    for(int i=0; i<n; i++)
        s1.insert(a[i]);
    for(int i=n; i<3*n; i++)
        s2.insert(a[i]);
    for(int i=0; i<n; i++)
    {
        s3.insert(*(s2.begin()));
        s2.erase(s2.begin());
    }
    long long x=0,y=0,maxx=0;
    for(it=s1.begin(); it!=s1.end(); it++)
        x+=*it;
    for(it=s3.begin(); it!=s3.end(); it++)
        y+=*it;
    maxx=x-y;
    for(int i=n; i<2*n; i++)
    {
        if(a[i]>*(s1.begin()))
        {
            x-=*(s1.begin());
            x+=a[i];
            s1.erase(s1.begin());
            s1.insert(a[i]);
            if(s3.count(a[i]))
            {

                y-=a[i];
                s3.erase(s3.find(a[i]));
                s3.insert(*(s2.begin()));
                y+=*(s2.begin());
                s2.erase(s2.begin());
            }
            else s2.erase(s2.find(a[i]));
            maxx=max(maxx,x-y);
        }
        else
        {
            if(s3.count(a[i]))
            {
                y-=a[i];
                s3.erase(s3.find(a[i]));
                s3.insert(*(s2.begin()));
                y+=*(s2.begin());
                s2.erase(s2.begin());
            }
        }
    }
    cout<<maxx;
    return 0;
}