Mirko has received a homework assignment to compute the greatest common divisor of the two positive integers $A$ and $B$. Since the numbers are quite large, the teacher provided him with $N$ smaller integers whose product is $A$, and $M$ integers with product $B$.

Mirko would like to verify his result, so he has asked you to write a program to solve his problem. If the result is more than $9$ digits long, output only the last $9$ digits.

-----Input-----
The first line of input contains the positive integer $N$ ($1 \le N \le 1000$).

The second line of input contains $N$ space-separated positive integers less than $1000000000$, whose product is the number $A$.

The third line of input contains the positive integer $M$ ($1 \le M \le 1000$).

The fourth line of input contains $M$ space-separated positive integers less than $1000000000$, whose product is the number $B$.

-----Output-----
The first and only line of output must contain the greatest common divisor of numbers $A$ and $B$. If the result is more than $9$ digits long, output only the last (least significant) $9$ digits.

-----Examples-----
Sample Input 1:
3
2 3 5
2
4 5
Sample Output 1:
10

Sample Input 2:
4
6 2 3 4
1
1
Sample Output 2:
1

Source: kattis | Difficulty: MEDIUM


Solutions: