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=[]
mod=10**9+7
for i in range(N):
    a=int(input())
    A.append((a,-1))
for i in range(N):
    a=int(input())
    A.append((a,1))
A.sort()
a=0
s=A[0][1]
ans=1
for i in range(2*N):
    if A[i][1]==s:
        a+=1
    else:
        ans*=a
        ans%=mod
        a-=1
    if a==0 and i<2*N-1:
        s=A[i+1][1]
    #print(a,s,ans)
print(ans)