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 ll long long
#define rep2(i,a,b) for(int i=a;i<=b;++i)
#define rep(i,n) for(int i=0;i<n;i++)
#define pii pair<int,int>
#define tii tuple<int,int,int>
#define pq priority_queue<int>
#define pqg priority_queue<int,vector<int>,greater<int>>
#define pb push_back
ll int MOD=1e9+7;
#define INF 2*1e9
#define N 310000
 
using namespace std;
string alphabet("abcdefghijklmnopqrstuvwxyz");

int main(){
    int n;
    cin>>n;
    vector<pii> v;
    rep(i,n){
        int a;cin>>a;
        v.pb({a,0});
    }
    rep(i,n){
        int a;cin>>a;
        v.pb({a,1});
    }
    sort(v.begin(),v.end());
    int t=0,s;
    ll ans=1;
    rep(i,2*n){
        s=v[i].second;t=1;
        while(t){
            i++;
            if(v[i].second==s){
                t++;
            }
            else{
                ans=ans*t%MOD;
                t--;
            }
        }
    }
    cout<<ans;
}

