Problem Statement

There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move.

Constraints

• All values in input are integers.
• $2 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move.