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)

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

$ans = 1;

$commax_left[0] = $a[0];
for($i = 1; $i <= $#a -1; $i++){
  $commax_left[$i] = commax($commax_left[$i -1], $a[$i]);
}
$commax_right[$#a] = $a[$#a];
for($i = $#a -1; $i >= 1; $i--){
  $commax_right[$i] = commax($commax_right[$i +1], $a[$i]);
}

if($#a >= 2){
  $ans = max($commax_left[$#a -1], $commax_right[1]);
  for($i = 2; $i <= $#a -1; $i++){
    $ans = max($ans, commax($commax_left[$i -1], $commax_right[$i +1]));
  }
}else{
  $ans = commax($a[0], $a[1]);
}

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(){
  my($x) = $_[0];
  my($y) = $_[1];

  # print "commax $x $y\n";
  while(){
    $x = $x % $y;
    if($x == 0){
      return $y;
    }
    $z = $x;
    $x = $y;
    $y = $z;
  }
}