Y has no one to talk but he has an array $a_1, a_2, ..., a_n$. Y wants to remove one element of array, so the gcd value of the remaining array ($gcd(a_1, a_2, ..., a_{j-1}, a_{j+1}, ..., a_n)$, $j$ is removed) is maximum.

What is the maximum value Y can get by removing exactly one element of the array?

Input

First line contains only $n$, legnth of array.

Second line contains the array elements $a_1, a_2, ..., a_n$separated by space.

$2 \leq n \leq 2 \times 10^5$

$1 \leq a_i \leq 10^9$

Output

The only line of output contains an integer, maximum value value that Y can get.