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())
AB = []
for _ in range(N):
  AB.append([int(input()),True])
for _ in range(N):
  AB.append([int(input()),False])
AB.sort(key = lambda x:x[0])

ans = 1
c = 0
for _,f in AB:
  if f:
    c += 1
  else:
    if c>0:
      ans *= c
      c -= 1
      ans %= 10**9+7
    else:
      c -= 1
      ans *= -1*c
      ans %= 10**9+7
print(ans)