Total Components

You are given all $N - 1$ integers in the range $[2, N]$. In each step, you choose $2$ distinct integers and if they share a common factor greater than $1$, you combine them into the same group. You keep doing it until no further merging is possible. Belonging to a group is an equivalence relation. So if integers $a$ and $b$ are in the same group and integers $b$ and $c$ are in the same group,