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<cstdio>
#include<algorithm>
#include<vector>
#include<utility>
#define mod 1000000007
using namespace std;
int main(){
    int a[100000],b[100000];
    vector<pair<int,int> > p;
    long long ans=1LL,l=0LL,n,x=0,y=0;
    scanf("%lld",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&a[i]);
        p.push_back(make_pair(a[i],1));
    }
    for(int i=0;i<n;i++){
        scanf("%d",&b[i]);
        p.push_back(make_pair(b[i],-1));
    }
    sort(p.begin(),p.end());
    for(long long i=0;i<p.size();i++){
        if(p[i].second==1){
            if(y){
                ans*=y;
                ans%=mod;
                y--;
            }
            else{
                x++;
            }
        }
        else{
            if(x){
                ans*=x;
                ans%=mod;
                x--;
            }
            else{
                y++;
            }
        }
    }
    printf("%ld\n",ans);
}