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())
arr=[(int(input()),i//n) for i in range(2*n)]
arr=sorted(arr,key=lambda x:x[0])
mod=10**9+7
ans=1
cnta=0
cntb=0
for pos,flag in arr:
  if flag==0:
    if cntb==0:
      cnta+=1
    else:
      ans*=cntb
      ans%=mod
      cntb-=1
  else:
    if cnta==0:
      cntb+=1
    else:
      ans*=cnta
      ans%=mod
      cnta-=1
print(ans)