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C - GCD on Blackboard

Score : $300$ points

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.

3
7 6 8

2

If we replace $7$ with $4$, the greatest common divisor of the three integers on the blackboard will be $2$, which is the maximum possible value.

3
12 15 18

6

2
1000000000 1000000000

1000000000

We can replace an integer with itself.