GCD Equals Mex

You are given an array $A$ containing $N$ positive integers. Count the number of ordered pairs of **disjoint** non-empty subsequences $(S_1, S_2)$ such that $\gcd(S_1) = \text{mex}(S_2)$. Here, the mex of a sequence of integers is the smallest **positive** integer that doesn't appear in it. Print the answer modulo $998244353$. --- Note that: - A subsequence of $A$ is a sequence obtained by t