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: Wrong Answer)

$n=<>;@A=glob<>;
$max = 0;

for(my $i=0;$i<$n;$i++){
    $mm = gcd(L($i),R($i+1));
    $max = $mm if ($mm > $max);
}
print "$max";
sub L{
    my$j=$_[0];
    return 0 if($j==-1);
    return $l{$i} if($l{$i}!=undef);
    my $ret=gcd(L($j-1),$A[$j-1]);
    $l{$j}=$ret;
    return $ret;
}
sub R{
    my$j=$_[0];
    return 0 if($j==$n);
    return $r{$i} if($r{$i}!=undef);
    my $ret=gcd(R($j+1),$A[$j]);
    $r{$j}=$ret;
    return $ret;
}

sub gcd{
    my ($a, $b) = @_;
    ($a, $b) = ($b, $a) if ($a > $b);
    until ($a == 0){
        ($a, $b) = ($b%$a, $a)
    }
    return $b;
}