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>
using namespace std;

typedef pair<int, int> P;

int main() {
int n,r;
long long m=0,c=1,q=1e9+7;
P p[200000];
cin>>n;
for(int i=0;i<n*2;i++){
    cin>>p[i].first;
    p[i].second=i/n;
}
sort(p,p+n*2);
for(int i=0;i<n*2;i++){
    if(m==0){
        m++;
        r=p[i].second;
    }else if(p[i].second==r){
        m++;
    }else{
        c=(c*m)%q;
        m--;
    }
}
cout<<c<<endl;


	return 0;
}