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
#define _USE_MATH_DEFINES
#include "bits/stdc++.h"
#define rep(i,a,b) for (int i = (a); i < (b); i++)
using namespace std;
typedef long long int ll;
typedef pair<ll,ll> P;
typedef complex<double> com;
const int mod = 1e9 + 7;
const int MOD = 998244353;
const int inf = 2e9;



int main() {
	int n; cin>>n;
	vector<P> a;
	rep(i,0,n){
		int p; cin>>p;
		a.push_back(make_pair(p,1));
	}
	rep(i,0,n){
		int p; cin>>p;
		a.push_back(make_pair(p,-1));
	}
	sort(a.begin(),a.end());
	int ans=1,val=0;
	rep(i,0,2*n){
		if(val>0&&a[i].second==-1) ans=(1LL*ans*val)%mod;
		if(val<0&&a[i].second==1) ans=(-1LL*ans*val+mod)%mod;
		val+=a[i].second;
	}
	printf("%d",ans);
  	return 0;
}
