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 bisect

N = int(input())
a = []
b = []
bb = []

for i in range(N):
	a.append(int(input()))

for i in range(N):
	b.append(int(input()))

a = sorted(a)
b = sorted(b)

for i in range(N):
	bb.append(bisect.bisect_left(a, b[i]))

ans = 1
for i in range(N):
	if bb[i] - i != 0:
		if bb[i] > i:
			ans = ans * (bb[i] - i)
		else:
			ans = ans * (i - bb[i] + 1)
		ans = ans % 1000000007

print(ans)