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 FI first
#define SE second
#define PB push_back
#define ll long long
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define ROF(i,a,b) for(int i=b-1;i>=a;i--)
#define YES(i) cout<<(i?"YES":"NO")<<endl
#define Yes(i) cout<<(i?"Yes":"No")<<endl
#define co(i) cout<<(i)<<endl
#define fcout cout<<fixed<<setprecision(10)
#define uni(i) i.erase(unique(i.begin(), i.end()), i.end());
#define all(i) i.begin(),i.end()
using namespace std;

const int INF=1e9+7;
const int MOD=1e9+7;

#define PA pair<int,int>
int main(){
    int n; cin>>n;
    vector<PA> p;
    FOR(i,0,n){
        int a; cin>>a;
        p.PB(PA(a,1));
    }
    FOR(i,0,n){
        int a; cin>>a;
        p.PB(PA(a,-1));
    }
    sort(all(p));
    int b[200001]={};
    FOR(i,0,2*n){
        b[i+1]=b[i]+p[i].SE;
    }
    //FOR(i,0,2*n) printf("%d %d\n",p[i].SE,b[i+1]);
    ll dp[200001]={};
    dp[0]=1;
    FOR(i,1,2*n+1){
        if(b[i]==0){
            dp[i]=dp[i-1];
        }else if((b[i]>0)^(p[i-1].SE==-1)){
            dp[i]=(dp[i-1]*abs(b[i]))%MOD;
        }else{
            dp[i]=dp[i-1];
        }
    }
    co(dp[2*n]);
}
