Score : $200$ points

Problem Statement

Given is an integer sequence $A$: $A_1, A_2, A_3, \dots, A_N$. Let the GCD-ness of a positive integer $k$ be the number of elements among $A_1, A_2, A_3, \dots, A_N$ that are divisible by $k$. Among the integers greater than or equal to $2$, find the integer with the greatest GCD-ness. If there are multiple such integers, you may print any of them.

Constraints

• $1 \le N \le 100$
• $2 \le A_i \le 1000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1 \hspace{7pt} A_2 \hspace{7pt} A_3 \hspace{5pt} \dots \hspace{5pt} A_N$

Output

Print an integer with the greatest GCD-ness among the integers greater than or equal to $2$. If there are multiple such integers, any of them will be accepted.

3
3 12 7

3

Among $3$, $12$, and $7$, two of them - $3$ and $12$ - are divisible by $3$, so the GCD-ness of $3$ is $2$. No integer greater than or equal to $2$ has greater GCD-ness, so $3$ is a correct answer.

5
8 9 18 90 72

9

In this case, the GCD-ness of $9$ is $4$. $2$ and $3$ also have the GCD-ness of $4$, so you may also print $2$ or $3$.

5
1000 1000 1000 1000 1000

1000