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, = [(int(input()),1) for _ in [0]*N]
*B, = [(int(input()),-1) for _ in [0]*N]

mod = 10**9+7
fact = [1]*(N+1)
for i in range(N):
    fact[i+1] = fact[i]*(i+1)%mod

AB = A+B
AB.sort()
ans = 1
c = 0
d = 0
for l,ab in AB:
    if d*ab<0:
        ans *= abs(d)
        ans %= mod
    d += ab
    c += 1
print(ans)