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
N=int(input())
A=sorted(int(input())for _ in'_'*N)
A+=10**10,
B=sorted(int(input())for _ in'_'*N)
B+=10**10,
z=1
a=b=i=j=0
M=10**9+7
while i<N or j<N:
	if A[i]<B[j]:
		if b:
			z=z*b%M
			b-=1
		else:
			a+=1
		i+=1
	else:
		if a:
			z=z*a%M
			a-=1
		else:
			b+=1
		j+=1
print(z)
