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 Specification

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 Specification

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

3
2 3 5
2
4 5

Sample Output 1

10

Explanation for Sample Output 1

The greatest common divisor of numbers $A=30$ and $B=20$ equals $10$.

Sample Input 2

4
6 2 3 4
1
1

Sample Output 2

1

Sample Input 3

3
358572 83391967 82
3
50229961 1091444 8863

Sample Output 3

000012028