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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
ll n,s[100000],a,tmp,cnt,MOD=1000000007,ans=1LL;
vector<P>v;
ll f(ll n){
    if(n==1)return 1;
    return n*f(n-1)%MOD;
}
int main(void){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a;
        v.push_back({a,1});
    }
    for(int i=0;i<n;i++){
        cin>>a;
        v.push_back({a,-1});
    }
    sort(v.begin(),v.end());
    for(auto x:v){
        if(x.second==1){
            if(tmp<0){
                ans*=-tmp;
                ans%=MOD;
            }
            tmp++;
        }
        else{
            if(tmp>0){
                ans*=tmp;
                ans%=MOD;
            }
            tmp--;
        }
    }
    cout<<ans<<endl;
}
