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: Time Limit Exceeded)

$n = <stdin>;
chomp($n);
@A = split (/ /,<stdin>,-1);
chomp(@A);


for(my $i=0;$i<$n;$i++){
    $L = 0;
    $G = 0;
    for ($ll=0;$ll<$i;$ll++){
        $L = gcd($L,$A[$ll]);
        # print ("ll:$ll,L:$L,A[ll]:$A[$ll] // ");
    }
    for (my $gg=$i+1;$gg<$n;$gg++){
        $G = gcd($G,$A[$gg]);
        # print ("gg:$gg,G:$G,A[gg]:$A[$gg] // ");
    }
    $mm = gcd($L,$G);
    # print "$i:$mm $L $G\n";
    push (@M,$mm);  
}

$max = 0;
foreach (@M){
    $max = $_ if ($_ > $max);
}

print "$max";

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