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
from math import factorial
from collections import deque
mod=10**9+7
n=int(raw_input())
a=[int(raw_input()) for _ in xrange(n)]
b=[int(raw_input()) for _ in xrange(n)]
d={}
a.sort()
b.sort()
ab=sorted(a+b)
for i in xrange(n):
    d[a[i]]="a"
    d[b[i]]="b"

stack=deque()
ans=1
for i in xrange(2*n):
    if len(stack)==0:
        stack.append(d[ab[i]])
        continue
    if d[ab[i]]=="a":
        if stack[-1]=="a":
            stack.append("a")
        else:
            ans=ans*len(stack)%mod
            stack.popleft()
    if d[ab[i]]=="b":
        if stack[-1]=="b":
            stack.append("b")
        else:
            ans=ans*len(stack)%mod
            stack.popleft()
print ans