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<vector>
#include<algorithm>

struct unit{
	int x;
	int type;
};

int main(){
	int n;
	long long ans=1;
	long long mod= 1000000007;
	std::vector<unit> list;

	std::cin>>n;
	list.resize(2*n);

	for(int i=0; i<n; i++){
		std::cin>>list[i].x;
		list[i].type= 1;
	}

	for(int i=0; i<n; i++){
		std::cin>>list[n+i].x;
		list[n+i].type= 2;
	}

	std::sort(list.begin(), list.end(), [](const unit &a, const unit &b){return a.x< b.x;});

	int stackSize= 0;
	int elmType= 0;

	for(int i=0; i< 2*n; i++){
		if(elmType==0){
			stackSize++;
			elmType= list[i].type;
			continue;
		}

		if(elmType==list[i].type)
			stackSize++;

		if(elmType!=list[i].type){
			ans= (ans*stackSize) %mod;
			stackSize--;

			if(stackSize<=0)
				elmType=0;
		}
	}


	std::cout<< ans <<std::endl;

	return 0;
}