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
import java.util.*;
class Main{
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
PriorityQueue<Integer> a = new PriorityQueue<>();
PriorityQueue<Integer> b = new PriorityQueue<>();
for(int i=0;i<n;++i)a.add(sc.nextInt());
for(int i=0;i<n;++i)b.add(sc.nextInt());
long mod = (long)1e9+7;
int ac=0, bc=0;
long ans =1;
a.add(Integer.MAX_VALUE);b.add(Integer.MAX_VALUE);
while(a.size()>1 || b.size()>1){
if(a.peek() < b.peek()){
a.poll();
if(bc==0)++ac;
else ans = ans * (long)(bc--)%mod;
}else{
b.poll();
if(ac==0)++bc;
else ans = ans * (long)(ac--)%mod;
}
}
System.out.println(ans);
}
}
