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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <stdio.h>      /* printf, scanf, NULL */
#include <stdlib.h>
#include <math.h>
#include <iomanip>      // std::setprecision
#include <algorithm>
using namespace std;

void reverse_array( long array[], int arraylength )
{
    for (int i = 0; i < (arraylength / 2); i++) {
        float temporary = array[i];                 // temporary wasn't declared
        array[i] = array[(arraylength - 1) - i];
        array[(arraylength - 1) - i] = temporary;
    }
}

void insert1(long x,int N,long* a){
    int k;
    long store;
    for(k=N-1;k>-1;k--){
        if (k==N-1){
            if(x < a[k]) a[k] = x;
        }
        else{
            if (x < a[k]){
                store = a[k];
                a[k] = x;
                a[k+1] = store;
            }
            else
                break;
        }
    }
}

void insert2(long x,int N,long* a){
    int k;
    long store;
    for(k=0;k<N;k++){
        if (k==0){
            if(x > a[0]) a[k] = x;
        }
        else{
            if (x > a[k]){
                store = a[k];
                a[k] = x;
                a[k-1] = store;
            }
            else
                break;
        }
    }
    return;
}

int main(){
    int N;
    int i,j,k;
    cin >> N;
    long store1[N+1];
    long store2[N+1];
    long store[3*N];
    long fval[N];
    long sval[N];
    long sumf = 0, sums = 0;
    for(i = 0; i<3*N ; i++){
        cin >> store[i];
    }
    reverse_array(store,3*N);
    long long first=0,second=0;
    for(i = 0; i < N; i++){
        fval[i] = store[i];
        sval[i] = store[3*N-1-i];
        sumf += store[i];
        sums += store[3*N-1-i];
    }
    store1[0] = sumf;
    store2[0] = sums;
    sort(fval,fval+N);
    sort(sval,sval+N);
    for(i = N; i < 2*N; i++){
        if(fval[N-1] > store[i]){
            sumf -= fval[N-1] - store[i];
            store1[i-N+1] = sumf;
            insert1(store[i], N, fval);
        }
        if(sval[0] < store[3*N-i-1]){
            sums += store[3*N-i-1] - sval[0];
            store2[i-N+1] = sums;
            insert2(store[3*N-i-1], N, sval);
        }
    }
    long MAX = store2[N] - store1[0];
    for(i = 0; i < N+1; i++){
        if (-store1[i] + store2[N-i] > MAX) MAX = store2[N-i] - store1[i];
    }
    return 0;
}