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
$n = trim(fgets(STDIN));
$vArray = explode(" ", trim(fgets(STDIN)));

$divmax = $vArray[0];
foreach($vArray as $i => $v){
    $dArray = divisor($v, $divmax);
    foreach($dArray as $d){
        @$map[$d]++;
    }
    $tmpmax = 0;
    foreach($map as $k => $c){
        if($c > $i - 1){
            $tmpmax = max($tmpmax, $k);
        }
    }
    $divmax = $tmpmax;
}
$max = 1;
foreach($map as $value => $count){
    if($count >= $n - 1){
        $max = max($max, $value);
    }
}
echo $max;

function divisor($n, $divmax){
    if(!isset($GLOBALS["cache"][$n])){
        for($i = min(ceil(sqrt($n)), $divmax); $i >= 1; $i--){
            if($n % $i == 0){
                $f[] = $i;
                $f[] = $n / $i;
            }
        }
        sort($f);
        $GLOBALS["cache"][$n] = array_unique($f);
    }
    return $GLOBALS["cache"][$n];
}