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())
L = []
for i in range(N):
  L.append((int(input()),'a'))
for i in range(N):
  L.append((int(input()),'b'))
L.sort()
res = 1
cc = 0
nowcol = None
mo = 1000000007
for i in range(2*N):
  if cc == 0:
    nowcol=L[i][1]
  if nowcol == L[i][1]:
    cc += 1
  else:
    res *= cc
    res %= mo
    cc -= 1
print(res)
