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: Time Limit Exceeded)

<?php

$n = trim(fgets(STDIN));
$a_arr = explode(' ', trim(fgets(STDIN)));

$gcd_max = 1;
$memo = [];

if ($n == 2) {
    echo max($a_arr), "\n";
    exit();
}

for ($i = 0; $i < $n; $i++) {
    $reduced_a_arr = $a_arr;
    unset($reduced_a_arr[$i]);
    $gcd = array_reduce($reduced_a_arr, 'gcd');
    if ($gcd > $gcd_max) {
        $gcd_max = $gcd;
    }
}

echo $gcd_max, "\n";

function gcd($a, $b) {
    if (isset($memo[$a][$b])) {
        return $memo[$a][$b];
    }
    $gcd =  $b ? gcd($b, $a % $b) : $a;
    $memo[$a][$b] = $gcd;
    return $gcd;
}