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.Arrays;
import java.util.Scanner;
 
class event implements Comparable<event>{
		public int a;
		public int b;
		public event(int a , int b){
			this.a = a;
			this.b = b;
		}
		
		public int compareTo(event other){
			// return b - other.b;
			return Integer.compare(b , other.b);
		}
		
}
 
public class Main{
 
 
	
	public static void main(String[] args) {
			
		       Scanner in = new Scanner(System.in);
                       int N = in.nextInt();
                       int[] size = new int[2];
                       event[] vs = new event[2*N];
                       for (int x=0; x<2; x++)
                            for (int i=0; i<N; i++)
                                         vs[i+x*N] = new event(x, in.nextInt());
 
                      Arrays.sort(vs);
 
                  long mod = 1_000_000_007;
                  long res = 1L;
                  for (event e : vs)
                  {
                     if (size[1 - e.a] > 0){
                       res *= size[1 - e.a];
                       res %= mod;
 
                       size[1 - e.a]--;
                  }
                   else
                   {
                        size[e.a]++;
                    }
               }
			
			System.out.println(res);
 
	}
 
}