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 be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n,a;
    cin>>n;
    vector<pair<int,int> > v;
    for(int i=0;i<n;i++){
    	cin>>a;
    	v.push_back({a,0});
    }
    for(int i=0;i<n;i++){
    	cin>>a;
    	v.push_back({a,1});
    }
    sort(be(v));
    ll num=0,ans=1;
    n<<=1;
    for(int i=0;i<n;i++){
    	if(v[i].second){
    		if(num<0)ans*=(-num);
    		num++;
    	}
    	else{
    		if(num>0)ans*=num;
    		num--;
    	}
    	ans%=mod;
    }
    cout <<ans<<endl;
    return 0;
}
