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 bisect import *

n = int(input())
a = [0]*n
b = [0]*n
for i in range(n):
    a[i] = int(input())
for i in range(n):
    b[i] = int(input())

a.sort()
b.sort()

ans = 1
mod = 1000000007

for x,y in zip(a,b):
    if x > y:
        x, y = y, x
    ans *= (bisect_right(a, y)-bisect_left(a, x))
    ans %= mod

print(ans)
