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 "bits/stdc++.h"
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;

const LL mod = 1000000007;
LL N, couA, couB, ans;
std::vector<std::pair<LL, LL>>p;

int main()
{
	in >> N;
	std::vector<LL>a(N), b(N);
	rep(i, N) in >> a[i];
	rep(i, N) in >> b[i];
	rep(i, N)
	{
		p.push_back(std::make_pair(a[i], 1));
		p.push_back(std::make_pair(b[i], 2));
	}
	std::sort(p.begin(), p.end());
	ans = 1;
	rep(i, 2 * N)
	{
		if (p[i].second == 1) ++couA;
		else ++couB;
		if (couA > 0 && couB > 0)
		{
			ans *= couA * couB;
			ans %= mod;
			--couA; --couB;
		}
	}
	out << ans << std::endl;
	return 0;
}
