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())
M = 10**9+7
L = []
for _ in range(n):
  a = int(input())
  L.append((a, 1))
for _ in range(n):
  b = int(input())
  L.append((b, 0))
L.sort()
C = [0, 0]
ans = 1
for d, f in L:
  if C[f^1]:
    ans *= C[f^1]
    ans %= M
    C[f^1] -= 1
  else:
    C[f] += 1
print(ans)