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())

mod = int(1e9+7)

A = []
for _ in range(N):
  A.append([int(input()),1])
for _ in range(N):
  A.append([int(input()),2])
A.sort()

ans = 1
ca,cb = 0,0
for a in A:
  if a[1] == 1:
    if cb == 0:
      ca += 1
    else:
      ans = ans * cb % mod
      cb -= 1      
  else:
    if ca == 0:
      cb += 1
    else:
      ans = ans * ca % mod
      ca -= 1
    
print(ans)