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;

using ll=long long;
const ll MOD=1e9+7;
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(a.begin(),a.end());
    sort(b.begin(),b.end());
    int ai=0,bi=0;
    int an=0;
    int bn=0;
    ll res=1;
    while(ai+bi<2*n){
        if(ai<n && (bi>=n || a[ai]<b[bi])){
            if(bn>0){
                res=(res*bn)%MOD;
                bn--;
            }
            else{
                an++;
            }
            ai++;
        }else{
            if(an>0){
                res=(res*an)%MOD;
                an--;
            }
            else{
                bn++;
            }
            bi++;
        }
    }
    cout<<res<<endl;
    return 0;
}