Let \( f(n) = \begin{cases} n^2+1 & \text{if }n\text{ is odd} \\ \dfrac{n}{2} & \text{if }n\text{ is even} \end{cases}. \)
For how many integers \(n\) from 1 to 100, inclusive, does \(f ( f (\dotsb f (n) \dotsb )) = 1\) for some number of applications of \(f\)?
