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()), 0) for i in range(N)]
B = [(int(input()), 1) for i in range(N)]
Object = sorted(A + B)
mod = 10 ** 9 + 7

ans = 1
memo = [0, 0]
for n, x in Object:
    if memo[1 - x] > 0:
        ans = (ans * memo[1 - x]) % mod
        memo[1 - x] -= 1
    else:
        memo[x] += 1

print(ans)
