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
/**
 * ABC125 
 * C - GCD on Blackboard
 */

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

// 累積GCDを計算
$gcd_list_left = [(int) $a[0]];
$gcd_list_right = [(int) $a[$n - 1]];
$gcd_memo = [];
for ($i = 1; $i < $n - 1; $i++) {
    $gcd_list_left[$i] = gcd($gcd_list_left[$i - 1], $a[$i]);
    $gcd_list_right[$i] = gcd($gcd_list_right[$i - 1], $a[$n - 1 - $i]);
}

// gcd((左累積GCD), (右累積GCD))
$gcd[0] = $gcd_list_right[$n - 2];
$gcd[$n - 1] = $gcd_list_left[$n - 2];
for ($i = 1; $i < $n - 1; $i++) {
    $gcd[$i] = gcd($gcd_list_left[$i - 1], $gcd_list_right[$n - 1 - $i - 1]);
}

echo max($gcd), "\n";

function gcd($a, $b): int {
    return $gcd_memo[$a][$b] ?? ($b == 0 ? $a : gcd($b, $a % $b));
}