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
// This file is a "Hello, world!" in C++ language by GCC for wandbox.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD=1000000007;
int main()
{
    int n;cin>>n;
    vector<pair<int,int> > v;
    for(int i=0;i<n;i++){
        int a;cin>>a;
        v.push_back(make_pair(a,0));
    }
    for(int i=0;i<n;i++){
        int b;cin>>b;
        v.push_back(make_pair(b,1));
    }
    sort(v.begin(),v.end());
    int ac=0;int bc=0;ll ans=1;
    for(int i=0;i<2*n;i++){
        if(v[i].second){
            bc++;
        }else{
            ac++;
        }
        if(bc&&ac){
            (ans*=ac*bc)%=MOD;
            ac--;bc--;
        }
    }
    cout<<ans<<endl;
}

