There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.

Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.

In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.

Input

The input is given from Standard Input in the following format:


N
a_1
:
a_N
b_1
:
b_N


Output

Print the number of ways to minimize the total length of the cables, modulo 10^9+7.

Examples

Input

2
0
10
20
30


Output

2


Input

3
3
10
8
7
12
5


Output

1
#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <functional>
#include <cmath>
#include <set>
#include <queue>
#include <vector>
#include <climits>
#include <sstream>
#include <iomanip>
#include <map>
#include <stack>
using namespace std;

int main()
{
	int N;
	cin >> N;

	vector<long long> a(N);
	vector<long long> b(N);
	for (auto i = 0; i < N; ++i)
	{
		cin >> a[i];
	}
	for (auto i = 0; i < N; ++i)
	{
		cin >> b[i];
	}

	sort(a.begin(), a.end());
	sort(b.begin(), b.end());

	auto result = 1ll;
	auto ia = 0;
	auto ib = 0;
	auto count = 0;
	auto mod = (long long)1e9 + 7;
	while (ia < N || ib < N)
	{
		auto isPlus = false;
		if (ia < N && ib < N)
		{
			if (a[ia] < b[ib])
			{
				++ia;
				isPlus = true;
			}
			else
			{
				++ib;
				isPlus = false;
			}
		}
		else if (ia < N)
		{
			++ia;
			isPlus = true;
		}
		else
		{
			++ib;
			isPlus = false;
		}

		if (isPlus)
		{
			if (count < 0)
			{
				result = result * abs(count) % mod;
			}
			++count;
		}
		else
		{
			if (count > 0)
			{
				result = result * abs(count) % mod;
			}
			--count;
		}
	}

	cout << result << endl;

	return 0;
}