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 Perl (v5.18.2) (judge verdict: Accepted)

#!/usr/bin/perl

use strict;
use warnings;

my $n = <STDIN>;
chomp $n;

my @a;
{
    my $in = <STDIN>;
    @a = split(" ", $in);
}
my $gcd = sub
{
    my ($x, $y) = @_;
    
    while ($x>0 && $y>0)
    {
        if ($y > $x)
        {
            $y %= $x;
        }
        else
        {
            $x %= $y;
        }
    }
    return $x if $x>0;
    return $y if $y>0;
};
my (@l, @r);
$l[0] = $a[0];
$r[$n-1] = $a[$n-1];
for (my $i=1; $i<$n; $i++)
{
    $l[$i] = $gcd->($l[$i-1], $a[$i]);
    $r[$n-$i-1] = $gcd->($r[$n-$i], $a[$n-$i-1]);
}
my $ans = 0;
for (my $i=0; $i<$n; $i++)
{
    my $c = 0;
    $c = $gcd->($c, $l[$i-1]) if $i>0;
    $c = $gcd->($c, $r[$i+1]);
    $ans = $c if $ans<$c;
}
print "$ans\n";