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)

use v5.18;
use warnings;
use List::Util qw( reduce max );
 
<>;
my @nums = glob <>;
say max map { gcb(right($_ - 1), left($_ + 1)) } 0 .. $#nums;

sub right {
  my $n = shift;
  return 0 if $n < 0;
  state @dp;
  return $dp[$n] if defined $dp[$n];
  if ($n > 0) {
    $dp[$n] = gcb($nums[$n], right($n - 1));
  } else {
    $nums[$n];
  }
}

sub left {
  my $n = shift;
  return 0 if $n > $#nums;
  state @dp;
  return $dp[$n] if defined $dp[$n];
  if ($n < $#nums) {
    $dp[$n] = gcb($nums[$n], left($n + 1));
  } else {
    $nums[$n];
  }
}
 
sub gcb {
  my ($x, $y) = @_;
  return $x if $y == 0;
  my $mod = $x % $y;
  $mod == 0 ? $y : gcb($y, $mod);
}