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<iostream>
#include<iomanip>
#include<math.h>
#include<algorithm>
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<set>
#include<map>
#define REP(i, N) for(ll i = 0; i < N; ++i)
#define FOR(i, a, b) for(ll i = a; i < b; ++i)
#define ALL(a) (a).begin(),(a).end()
#define pb push_back
#define INF (long long)1000000000
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

int main(void) {
	int N;
	cin>>N;
	vector<ll> a(3 * N);
	REP(i, 3 * N) cin>>a[i];
	multiset<ll> mae;
	multiset<ll> ushiro;
	ll maesum = 0, ushirosum = 0;
	ll ans = - (INF * INF);
	REP(i, N) {
		mae.insert(a[i]);
		maesum += a[i];
	}
	REP(i, 2 * N) ushiro.insert(a[N + i]);
	multiset<ll>::iterator ite = ushiro.begin();
	multiset<ll> hoge1;
	multiset<ll> hoge2;
	REP(i, N) {
		ushirosum += *ite;
		hoge1.insert(*ite);
		++ite;
	}
	ans = max(ans, (maesum - ushirosum));
	REP(i, N) {
		if(a[N + i] > *(mae.begin())) {
			maesum -= *(mae.begin());
			mae.erase(mae.begin());
			mae.insert(a[N + i]);
			maesum += a[N + i];
		}
		if(hoge1.count(a[N + i]) != 0) {
			ushirosum -= a[N + i];
			hoge1.erase(hoge1.find(a[N + i]));
			while(true) {
				if(hoge2.count(*ite) == 0) {
					ushirosum += *ite;
					hoge1.insert(*ite);
					++ite;
					break;
				} else {
					hoge2.erase(hoge2.find(*ite));
					++ite;
				}
			}
		} else {
			hoge2.insert(a[N + i]);
		}
		ans = max(ans, (maesum - ushirosum));
	}
	cout<<ans<<endl;
}