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 = 10**9 + 7
n = int(input())
a = []
for _ in range(n):
	x = int(input())
	a.append([x, 1])
for _ in range(n):
	x = int(input())
	a.append([x, -1])
a.sort()
ans = 1
tmp = 0
for i in range(2*n):
	x = a[i][1]
	if x == 1 and tmp < 0:
		ans *= -tmp
	elif x == -1 and tmp > 0:
		ans *= tmp
	tmp += x
	ans %= MOD
print(ans)