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())
ans=1
mod=10**9+7
A=[0,0]
AB=[]
for i in range(n):
  a=int(input())
  AB.append((a,0))
for i in range(n):
  b=int(input())
  AB.append((b,1))
AB.sort(key=lambda x:x[0])
for i in range(2*n):
  a,b=AB[i]
  if b==0:
    if A[1]>0:
      ans=(ans*A[1])%mod
      A[1]-=1
    else:
      A[0]+=1
  else:
    if A[0]>0:
      ans=(ans*A[0])%mod
      A[0]-=1
    else:
      A[1]+=1
print(ans)