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 <iomanip>
#include <ios> 
#include <vector>
#include <string>
#include <algorithm>
#include <functional>
#include <queue>
#include <stack>
#include <set>
#include <cmath>
#include <bitset>
#include <map>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define sz(c) ((int)(c).size())

using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair<int,int> P;
const ll MOD=1e9+7;

ll tim(ll a, ll b){
	return (a*b)%MOD;
}


int main(){
	int N;
	cin>>N;
	priority_queue<P> q;
	rep(i,N){
		int a;
      	cin>>a;
		q.push(make_pair(a,1));
	}
	rep(i,N){
		int a;
      	cin>>a;
		q.push(make_pair(a,-1));
	}
	
	ll dif=0;
	ll ans=1;
	while(!q.empty()){
		P p=q.top();
		q.pop();
		ll f=(ll)p.second;
		if(dif==0)dif+=f;
		else if(dif>0){
			if(f==1)dif++;
			else{
				ans=tim(ans, dif);
				dif--;
			}
		}
		else{
			if(f==-1)dif--;
			else{
				ans=tim(ans, -dif);
				dif++;
			}
		}
	}
	cout<<ans<<endl;
	
}