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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php

class Scanner
{
  private $arr = [];
  private $count = 0;
  private $pointer = 0;

  public function next()
  {
    if ($this->pointer >= $this->count) {
      $str = trim(fgets(STDIN));
      $this->arr = explode(' ', $str);
      $this->count = count($this->arr);
      $this->pointer = 0;
    }
    $result = $this->arr[$this->pointer];
    ++$this->pointer;

    return $result;
  }

  public function hasNext()
  {
    return $this->pointer < $this->count;
  }

  public function nextInt()
  {
    return (int) $this->next();
  }

  public function nextDouble()
  {
    return (float) $this->next();
  }
}

$sc = new Scanner();
$n = $sc->nextInt();
$array=[];
$sum = 0;
$answer = 0;

for($i=0;$i<$n;$i++){
  $array[] = $sc->nextInt();
}

sort($array);

if($array[0] == $array[$n-1]){
  $answer = $array[0];
} else {
  for($i=$array[1];$i>0;$i--){
    $sum = 0;
    foreach($array as $key=>$value){
      if($value%$i > 0){
        $sum++;
      }
    }
    if($sum == 1){
      $answer = $i;
      break;
    }
  }
}

echo $answer . PHP_EOL;