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>
typedef long long ll;
using namespace std;
const int N = 1e5 + 5;


vector< pair < int , int > > v ;
ll mod = 1e9 + 7 ;

int main()
{
    int n ;
    cin >> n ;
    for(int i =0 ; i < n ; i ++){
        int x;
        scanf("%d",&x);
        v.push_back({x,1});
    }
    for(int i =0 ; i < n ; i ++){
        int y ;
        scanf("%d",&y);
        v.push_back({y,0});
    }
    ll res = 1;
    int x = 0 ;

    sort(v.begin() , v.end());

    // x x y
    for(int i =0 ; i < v.size() ; i ++){

        if(v[i].second == 1){

            if(x < 0 )
                res = ( res * -x ) % mod ;
            x ++ ;
        }else{

            if(x > 0 )
                res = (res * x ) %mod ;
            x -- ;
        }
    }
    cout << res << endl ;


    return 0;
}
