OpenKattis
Baylor University

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 $1\, 000\, 000\, 000$, 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 $1\, 000\, 000\, 000$, 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.

Sample Input 1 Sample Output 1
3
2 3 5
2
4 5

10

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

1

Sample Input 3 Sample Output 3
3
358572 83391967 82
3
50229961 1091444 8863

000012028