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: Runtime Error)

<?php
function gcd(array $list)
{
    $c = count($list);
    if ($c === 0) {
        return 0;
    } elseif ($c === 1) {
        return $list[0];
    }

    return calcGCD($list);
}
function calcGCD(array &$list)
{
    $c = count($list);

    $v = $list[$c - 1] % $list[$c - 2];
    if ($v === 0) {
        if ($c === 2) {
            return $list[$c - 2];
        }

        array_pop($list);

        return calcGCD($list);
    }
    $list[$c - 1] = $list[$c - 2];
    $list[$c - 2] = $v;

    return calcGCD($list);
}

fscanf(STDIN, '%d', $n);

$arr = explode(' ', fgets(STDIN));
$intArr = [];
foreach ($arr as $a) {
    $intArr[] = (int) $a;
}
sort($intArr);
$min = min($intArr);
$max = max($intArr);
if ($min === $max) {
    echo $max . PHP_EOL;
    exit;
}
if ($intArr[0] === 1) {
    $intArr[0] = $max;
}
$gcdOnlyMinMax = gmp_gcd($min, $max);
$gcdAll = gcd($intArr);
echo max($gcdAll, $gcdOnlyMinMax) . PHP_EOL;