Problem:
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.

Sample Input 1

3
7 6 8

Sample Output 1

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.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
    fscanf(STDIN,"%d", $n);
    $input = explode(' ',trim(fgets(STDIN)));
 
    $min = min($input);
 
    for ($m = $min; $m > 1; $m--) {
        $f = 0;
        for ($i = 0; $i < $n; $i++) {
            if ($input[$i] % $m) {
                $f++;
            }
        }
        if ($f <= 1) {
            echo $m;
            return;
        }
    }
    echo 1;