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;
typedef long long ll;
typedef pair<ll,int> P;
#define Mod 1000000007;

int main(){
    ll i,n;
    cin>>n;
    vector<P> v;
    ll x;

    for(i=0;i<n;i++){
        cin>>x;
        v.push_back(P(x,0));
    }
    for(i=0;i<n;i++){
        cin>>x;
        v.push_back(P(x,1));
    }
    sort(v.begin(),v.end());

    ll ans=1;
    int b=1;
    int cnt=1;
    int f=v[0].second;
    while(b<2*n){
        if(f==-1){
            f=v[b].second;
            cnt=1;
        }
        else if(f==v[b].second) {
            cnt++;
        }
        else  {
            ans*=cnt;
            ans%=Mod;
            cnt--;
            if(cnt==0) f=-1;
        }
        b++;
    
    }
    cout<<ans<<endl;
    
    return 0;
}
