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;



int main(){
    ios::sync_with_stdio(false);
	cin.tie(0);

    ll n;
    cin>>n;
    pair<ll,ll> p[2*n];
    for(int i=0;i<n;i++){
        int a;
        cin>>a;
        p[i]=make_pair(a,0);
    }
    for(int i=0;i<n;i++){   
        int b;
        cin>>b;
        p[n+i]=make_pair(b,1);
    }

    sort(p,p+2*n);
    

    ll ans=1;
    ll mod=1e9+7;

    ll cnt1=0,cnt0=0;
    for(int i=0;i<2*n;i++){
        if(p[i].second==0){
            if(cnt1>0){
                ans*=cnt1;
                ans%=mod;
                cnt1--;
            }
            else cnt0++;
        }
        else{
            if(cnt0>0){
                ans*=cnt0;
                ans%=mod;
                cnt0--;
            }
            else cnt1++;
        }
    }
    cout<<ans<<endl;
}