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 ll long long
const ll pri = 1000000007;
typedef pair<int, int>P;
int main(){
    ll N, ans = 1;
    cin>>N;
    vector<P>vec;
    for(int i=0;i<N;i++){
        int tmp;
        cin>>tmp;
        vec.push_back(P(tmp, 0));
    }
    for(int i=0;i<N;i++){
        int tmp;
        cin>>tmp;
        vec.push_back(P(tmp, 1));
    }
    sort(vec.begin(), vec.end());
    int lst[2] = {0, 0};
    for(int i=0;i<vec.size();i++){
        if(vec[i].second){
            if(lst[0]>0){
                lst[0]--;
            }
            else{
                lst[1]++;
                ans = ans * lst[1] % pri;
            }
        }
        else{
            if(lst[1]>0){
                lst[1]--;
            }
            else{
                lst[0]++;
                ans = ans * lst[0]%pri;
            }
        }
    }
    cout<<ans<<endl;
    return 0;
}