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;
#define int long long
const int MOD = 1000000007;
signed main(){
    int n;
    cin>>n;
    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(a,a+n);
    sort(b,b+n);
    int p=0,q,x=0,y=0,ans=1;
    while(x<n&&y<n){
        if(a[x]<b[y]){
            q=p+1;
            x++;
        }else {
            q=p-1;
            y++;
        }
        if(abs(p)>abs(q))ans=(ans*abs(p))%MOD;
        p=q;
    }
    while(x<n){
        ans=(ans*abs(p))%MOD;
        p++;
        x++;
        
    }
     while(y<n){
         ans=(ans*abs(p))%MOD;
        p--;
        y++;
        
    }
    cout<<ans;



    return 0;
}
