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)

use v5.18;
use warnings;
use List::Util qw( reduce max );

<>;
my @nums = glob <>;

say max map {
  my $r = reduce_gcb(\@nums, 0, $_ - 1);
  my $l = reduce_gcb(\@nums, $_ + 1, $#nums);
  my @defined = grep { defined $_ } ($r, $l);
  if (@defined == 2) {
    gcb($r, $l);
  } elsif (@defined == 1) {
    $defined[0];
  } else {
    ();
  }
} 0 .. $#nums;

sub reduce_gcb {
  my ($nums, $begin, $end) = @_;
  if ($begin > $end) {
    undef;
  }
  elsif ($begin == $end) {
    $nums->[$begin];
  } else {
    my $gcb = gcb($nums->[$begin], $nums->[$begin + 1]);
    for (my $i = $begin + 2; $i <= $end; $i++) {
      $gcb = gcb($gcb, $nums->[$i]);
    }
    $gcb;
  }
}

sub gcb {
  my ($x, $y) = @_;
  return $x if $y == 0;
  state $dp = +{};
  return $dp->{$x}{$y} if defined $dp->{$x}{$y};
  my $mod = $x % $y;
  $dp->{$x}{$y} = $mod;
  $mod == 0 ? $y : gcb($y, $mod);
}