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
mod = 1000000007
N = int(input())
A = []
B = []
for i in range(N):
	A.append(int(input()))
for i in range(N):
	B.append(int(input()))

A.sort()
B.sort()
A.append(mod)
B.append(mod)

ans = 1
a = 0
b = 0

while a != N or b != N:
	if A[a] < B[b]:
		a += 1
		if a > b:
			ans = ans * (a - b) % mod
	else:
		b += 1
		if b > a:
			ans = ans * (b - a) % mod
print(ans)
		