We define the weight $W$ of a positive integer as follows: 
1. $W(1) = 0$
2. $W(2) = 1$
3. $W(p) = 1 + W(p + 1)$ for every odd prime $p$
4. $W(c) = 1 + W(d)$ for every composite $c$, where $d$ is the greatest proper factor of $c$.

Compute the greatest possible weight of a positive integer less than 100.

Let's think step by step and output the final answer within \boxed{}.
user