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>
using namespace std;

#define fastIO ios::sync_with_stdio(false);cout.tie(0);cin.tie(0);
#define endl '\n'
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define MP make_pair
#define inf INT_MAX
#define minf INT_MIN

typedef long long int lli;

ofstream outfile;
ifstream infile;

int main()
{
	infile.open("input.txt");
	outfile.open("output.txt");

	int n, t, i;
	int arr[300003];
	bool flags[300003];
	vector <pair <int, int>> temp, temp2;
	lli sum_max = 0, sum_min = 0, fmax = 0;

	cin >> n;

	for(i = 1; i <= n; ++i){
		cin >> arr[i];
		flags[i] = 1;
		sum_max += arr[i];
		temp2.pb(MP(arr[i], i));
	}


	for(i = n+1; i <= 3*n; ++i){
		cin >> arr[i];
		flags[i] = 0;
		temp.pb(MP(arr[i], i));
	}

	sort(temp2.begin(), temp2.end());
	sort(temp.begin(), temp.end());

	for(i = 0; i < n; ++i){
		sum_min += temp[i].fi;
		flags[temp[i].se] = 1;
	}
	int counter2 = n, counter1 = 0;

	fmax = sum_max - sum_min;

	for(int k = n+1; k <= 2*n; ++k){
		if(arr[k] > temp2[counter1].fi){
			sum_max += (arr[k]-temp2[counter1].fi);
			++counter1;
		}

		if(flags[k]){
			sum_min -= arr[k];
			sum_min += temp[counter2].fi;
			flags[k] = 0;
			flags[temp[counter2].se] = 1;
		}

		fmax = max(sum_max-sum_min, fmax);
	}
	cout << fmax << "\n";
}