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: Runtime Error)

#include <bits/stdc++.h>

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = (n)-1; i >= 0; i--)

#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define pii pair<int, int>
#define vi vector<int>

using namespace std;
template <class S, class T>
ostream& operator<<(ostream& o, const pair<S, T>& p)
{
    return o << "(" << p.first << "," << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& o, const vector<T>& vc)
{
    o << "sz = " << vc.size() << endl
      << "[";
    for (const T& v : vc)
        o << v << ",";
    o << "]";
    return o;
}
using ll = long long;
constexpr ll MOD = 1000000007;

ll N;
constexpr ll MAX = 100000;
ll a[MAX];

int main()
{
    cin >> N;
    ll sum1 = 0;
    ll sum2 = 0;
    rep(i, 3 * N)
    {
        cin >> a[i];
        if (i < N) {
            sum1 += a[i];
        } else if (i >= 2 * N) {
            sum2 += a[i];
        }
    }
    sort(a, a + N);
    sort(a + 2 * N, a + 3 * N);

    ll score = sum1 - sum2;
    rep1(i, N)
    {  // removal from formar
        ll sum11 = sum1;
        ll sum22 = sum2;
        rep(j, i)
        {
            sum11 += (a[N + j] - a[j]);
        }
        rep(j, N - i)
        {
            sum22 -= (a[3 * N - 1 - j] - a[2 * N - 1 - j]);
        }
        score = max(score, (sum11 - sum22));
    }

    cout << score << endl;
    return 0;
}