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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php

$N = trim(fgets(STDIN));
$A = explode(" ",trim(fgets(STDIN)));

$gcd1[0] = $A[0];
$gcd2[0] = $A[$N-1];

for ( $i = 1; $i < $N-1; $i++) {
    $gcd1[$i] = gmp_gcd( $gcd1[$i-1], $A[$i] );
    $gcd2[$i] = gmp_gcd( $gcd2[$i-1], $A[$N-$i] );
    $gcd[$i] = gmp_gcd($gcd1[$i],$gcd2[$i]);
}

echo max($gcd);