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)

$_ = <>;
$_ = <>;
chmop;
@x = split(" ");

$ans = 0;
for($i = 0; $i <= $#x; $i++){
  @a = @x;
  splice(@a, $i, 1);
  $ans1 = commax();
  $ans = max($ans, $ans1);
}

print "$ans\n";

sub max(){
  my($a) = $_[0];
  my($b) = $_[1];
  if($a > $b){
    $a;
  }else{
    $b;
  }
}

sub min(){
  my($a) = $_[0];
  my($b) = $_[1];
  if($a > $b){
    $b;
  }else{
    $a;
  }
}

sub commax(){
  $min = 1000000000;

  while(){
    # print (join(" ", @a),"\n");
    if($#a == 0){
      return $a[0];
    }
    foreach $a1(@a){
      if($a1 < $min){
	$min = $a1;
	if($min < $ans){
	  return 0;
	}
      }
    }

    @b = ();
    foreach $a1(@a){
      if($a1 % $min != 0){
	push @b, $a1 % $min;
      }
    }
    push @b, $min;
    @a = @b;
  }
}