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())
pat = 1
mod = 10**9+7
l = []
for _ in range(n):
  a = int(input())
  l.append((a,0))
for _ in range(n):
  a = int(input())
  l.append((a,1))
l.sort()
cur = {0:0, 1:0}
for x in l:
  if cur[1-x[1]]:
    pat = pat*cur[1-x[1]]%mod
    cur[1-x[1]] -= 1
  else:
    cur[x[1]] += 1
print(pat)