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: Accepted)

#include <iostream>
#include <queue>

using namespace std;

priority_queue<long long> Q , QQ;

long long a[(int)(3*(1e5+10))] , n , s1[(int)(3*(1e5+10))] , s2[(int)(3*(1e5+10))] , s3[(int)(3*(1e5+10))] , res;

int main()
{
    s1[0] = s2[0] = s3[0] = 0;
    cin >> n;
    for (int i=1 ; i<=3*n ; i++)
        cin >> a[i];
    for (int i=1 ; i<=3*n ; i++)
        s1[i] = s1[i-1] + a[i];
    for (int i=1 ; i<=n ; i++)
        Q.push(-a[i]);
    for (int i=n+1 ; i<=2*n ; i++)
    {
        Q.push(-a[i]);
        s2[i-n] = s2[i-n-1] - Q.top();
        Q.pop();
    }
    for (int i=3*n ; i>=2*n+1 ; i--)
        QQ.push(a[i]);
    for (int i=2*n ; i>=n ; i--)
    {
        QQ.push(a[i]);
        s3[2*n-i+1] = s3[2*n-i] + QQ.top();
        QQ.pop();
    }
    res = -1e18;
    for (int i=n ; i<=2*n ; i++)
    {
        long long ts1=s1[i],ts2=s1[3*n]-s1[i];
        int len1=i-n,len2=2*n-i;
        res=max(res,ts1-s2[len1]-ts2+s3[len2]);
    }
    cout << res;
}