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 <iostream>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <fstream>
#include <sstream>
#include <iomanip>

using namespace std;

int MOD=1000000007;

vector<long long> factorial(int N){
    vector<long long> ret(N+1,1);
    for(int i=1; i<=N; i++){
        ret[i]=ret[i-1]*i%MOD;
    }
    return ret;
}

int main(){
    int N;
    cin >> N;
    vector<int> a(N,0);
    vector<int> b(N,0);
    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());
    a.push_back(MOD);
    b.push_back(MOD);

    vector<long long> fact=factorial(100000);

    int j=0;
    int k=0;
    int diff=0;
    long long ans=1;
    for(int i=0; i<N*2; i++){
        if(a[j]<b[k]){
            if(diff<0){
                ans*=-diff;
            }
            diff++;
            j++;
        }
        else{
            if(diff>0){
                ans*=diff;
            }
            diff--;
            k++;
        }
        ans%=MOD;
    }
    cout << ans << endl;
}