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
import sys
input=sys.stdin.readline
N=int(input())
data=[]
ans=1
mod=10**9+7
for i in range(N):
    data.append(('a',int(input())))
for i in range(N):
    data.append(('b',int(input())))
cnt=0
bef=data[0][0]
data.sort(key=lambda x:x[1])
for d in data:
    if cnt==0:
        bef=d[0]
        cnt+=1
    elif bef==d[0]:
        cnt+=1
    elif bef!=d[0]:
        ans=(ans*cnt)%mod
        cnt-=1
print(ans)