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 range(N)]
b = [(int(input()), 0) for _ in range(N)]
X = sorted(a + b)

mod = 10 ** 9 + 7
ls = 0
stack = []
ans = 1
for v, f in X:
    if stack and stack[-1] != f:
        ans = ans * ls % mod
        stack.pop()
        ls -= 1
    else:
        stack.append(f)
        ls += 1

print(ans)