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 = array_map('intval', explode(' ', trim(fgets(STDIN))));

$gcd[0] = $a[0];
for($i = 1; $i < $n; $i++) {
    $gcd[$i] = gcd($gcd[$i - 1], $a[$i]);
}
$gcd_rev[$n - 1] = $a[$n - 1];
for($i = $n - 2; $i >= 0; $i--) {
    $gcd_rev[$i] = gcd($gcd_rev[$i + 1], $a[$i]);
}
$max = 0;
for($i = 0; $i < $n; $i++) {
    $val = gcd($gcd[$i - 1] ?? $gcd_rev[$i + 1], $gcd_rev[$i + 1] ?? $gcd[$i - 1]);
    $max = max($max, $val);
}
echo $max . PHP_EOL;

// 最大公約数
function gcd($m, $n){
    if($n > $m) list($m, $n) = [$n, $m];

    if ($m % $n === 0) return $n;
    else return gcd($n, $m % $n);
}