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);

$arr = explode(' ', trim(fgets(STDIN)));

$ans = [];
$ans[0] = 1;
$ans[1] = $arr[1];

for ($i = 2;$i < $n;$i++) {
    $ans[$i] = gcd(array_merge($ans, [$arr[$i - 1]]));
}
$lastGcd = 1;
for ($i = $n; $i - 2 > -1; $i--) {
    $lastGcd = gcd([$lastGcd, $arr[$i + 1] ?? 1]);
    $ans[$i] = gcd([$lastGcd, $ans[$i] ?? 1]);
}

echo max($ans) . PHP_EOL;

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);
}