GCD Add Size

You’re given a sequence $A$ of size $N$. Your task is to choose a non-empty subsequence $B$ of $A$ to maximize $f(B)$. Here, $f(B)$ is defined as $|B|+gcd(B_1,B_2,\ldots,B_{|B|})$, where $|B|$ is the size of $B$ and $gcd(B_1,B_2,\ldots,B_{|B|})$ is the greatest common divisor of all numbers in $B$. ### Input - The first line of input will contain a single integer $T$, denoting the number of test