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: Accepted)

<?php
fscanf(STDIN, "%d", $n);
$a = explode(' ', trim(fgets(STDIN)));
$g = gcd($a[0], $a[1]);
$q[$a[0]] = $q[$a[1]] = 1;
for ($i = 2; $i < $n; $i++) {
	$t = [];
	foreach ($q as $r => $v) {
		$b = gcd($a[$i], $r);
		$t[$b] = 1;
	}
	$q = $t;
	$q[$g] = 1;
	$g = gcd($g, $a[$i]);
}
echo max(array_keys($q));

function gcd($n, $m) {
	return $n % $m ? gcd($m, $n % $m) : $m;
}