The missing GCD (hard version)

Given an array $arr_1,arr_2,...arr_n$, consisting of n positive integers. Find the smallest positive integer $g$ such that, there exists **no** pair of integers $i, j$ where $1\leq i$ < $j\leq n$ for which [gcd](https://en.wikipedia.org/wiki/Greatest_common_divisor) of $arr_i$ and $arr_j$ is **equal** to $g$. ### Input - The first line contains a single integer $n$, denoting the size of $arr$. -