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 "algorithm"
#include "string"
#include "vector"
#include "cmath"
#include "bitset"
#include "queue"
#include "functional"
#include "map"
#include "unordered_map"
#include "set"
#include "stack"
 
#define lp(n) for (int i = 0; i < n; i++)
#define LP(n,i) for (int i = 0; i < n; i++)
#define mod 1000000007
#define sp ' '
#define intmax 2147483647
#define llmax 9223372036854775807
#define nyan "(=^･ω･^=)"
typedef long long ll;
using namespace std;
int n,mem,cnt;
ll ans;
bool b;
map<int,bool>mp;
int main(){
	cin>>n;
	lp(n){
		cin>>mem;
		mp[mem]=true;
	}
	lp(n){
		cin>>mem;
		mp[mem]=false;
	}
	ans=1;
	cnt=0;
	for(auto it=mp.begin();it!=mp.end();it++){
		if(cnt==0)b=it->second;
		if(b==it->second)cnt++;
		else {
			ans*=cnt;
			cnt--;
		}
		ans%=mod;
	}
	cout<<ans<<endl;
	return 0;
}