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>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
int main(){
    int n,a,b;
    cin>>n;
    vector<pair<int,int>> A;
    rep(i,n) cin>>a,A.push_back(make_pair(a,1));
    rep(i,n) cin>>b,A.push_back(make_pair(b,2));
    sort(A.begin(),A.end());
    ll ans=1,mod=1e9+7,x=0,y=0;
    rep(i,2*n){
        if(x==0) y=A[i].second,x++;
        else{
            if(y==A[i].second) x++;
            else ans=ans*x%mod,x--;
        }
    }
    cout<<ans;
}