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())
C=[]
for i in range(N):
  C.append((int(input()),"a")) 
for i in range(N):
  C.append((int(input()),"b")) 
C.sort()
mod=10**9+7
a,b=0,0
ans=1
for c in C:
  if c[1]=="a":
    if b>0:
      ans=(ans*b)%mod
      b-=1
    else:
      a+=1
  if c[1]=="b":
    if a>0:
      ans=(ans*a)%mod
      a-=1
    else:
      b+=1
print(ans)      
    