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())
a=[int(input())for _ in range(n)]+[10**9]
b=[int(input())for _ in range(n)]+[10**9]
a.sort(reverse=1)
b.sort(reverse=1)
aa=0
bb=0
if a[-1]>b[-1]:
  bb=1
  b.pop()
else:
  aa=1
  a.pop()
ans=1
while len(a)!=1 or len(b)!=1:
  if a[-1]>b[-1]:
    bb+=1
    b.pop()
  else:
    aa+=1
    a.pop()
  if aa*bb:
    ans*=max(aa,bb)
    ans%=10**9+7
    aa-=1
    bb-=1
print(ans)