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;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=100001,INF=1<<30;

int main(){
    int N;cin>>N;
    vector<int> A(N),B(N);
    for(int i=0;i<N;i++){
        cin>>A[i];
    }
    for(int i=0;i<N;i++){
        cin>>B[i];
    }
    sort(all(A));
    sort(all(B));

    A.push_back(INF);
    B.push_back(INF);

    vector<int> S(2*N,0);
    int anow=0,bnow=0;
    
    while(anow+bnow<2*N){
        if(A[anow]<B[bnow]){
            S[anow+bnow]=1;
            anow++;
        }else{
            S[anow+bnow]=0;
            bnow++;
        }
    }
    ll ans=1;

    int acnt=0,bcnt=0;
    for(int i=0;i<2*N;i++){
        if(S[i]==1){
            if(bcnt>0){
                ans=ans*bcnt%mod;
                bcnt--;
            }else{
                acnt++;
            }
        }
        else{
            if(acnt>0){
                ans=ans*acnt%mod;
                acnt--;
            }
            else{
                bcnt++;
            }
        }
    }

    cout<<ans<<endl;
}