You can try to prove the following:

$f$ is an integer; $f$ is even; $f$ is positive.  So $f\geq 2$.  Then find a pair of values $m$ and $n$ so that $f=2$.  This is the minimum.

The maximum part is more tedious.  Show that $n$ is a factor of $2(a+1)$, and $n\leq 64$, thus $n\leq 52$.   And this gives a maximum of $f$.   I will give more details in class. 

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