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>
#define forinc(i,a,b) for (int i = a ; i <= b ; i ++)
#define fordec(i,a,b) for (int i = a ; i >= b ; i --)
#define forv(j,u) for (int j = 0 ; j < u.size() ; j++)
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define mk make_pair
#define pii pair<int,int>
#define ooll (long long) 1e15
#define ooit (int) 2e9
#define maxN 100005

using namespace std ;

int n , a[3 * maxN] ;

void enter() {
    cin >> n ;
    forinc(i,1,3*n) cin>> a[i] ;
}

long long f[3 * maxN] , g[3 * maxN] ;

void build_1() {
    priority_queue<int> q ;
    long long sum = 0 ;
    forinc(i,1,n) sum += a[i] , q.push(-a[i]) ;
    forinc(i,n+1,3*n) {
        int tmin = -q.top() ;
        if (tmin < a[i]) sum -= tmin , sum += a[i] , q.pop() , q.push(-a[i]) ;
        f[i] = sum ;
    }
    while (!q.empty()) q.pop() ;
    sum = 0 ; fordec(i,3*n,2*n+1) sum += a[i] , q.push(a[i]) ; g[2 * n + 1] = sum ;
    fordec(i,2*n,1) {
        int tmax = q.top() ;
        if (tmax > a[i]) sum -= tmax , sum += a[i] , q.pop() , q.push(a[i]) ;
        g[i] = sum ;
    }
}

void process() {
    build_1() ;
    long long res = 0 ;
    forinc(i,n,2*n) res = max(res,f[i] - g[i+1]) ;
    cout << res << endl ;
}

int main() {
    //freopen("arc074_b.inp" , "r" , stdin) ;
    //freopen("arc074_b.out" , "w" , stdout) ;
    enter() ;
    process() ;
    return 0 ;
}