Let $f(n) = \sum_{d=1}^{n} \left\lfloor \frac{n}{d} \right\rfloor$ and $g(n) = f(n) - f(n - 1)$. For how many $n$ from $1$ to $100$ inclusive is $g(n)$ even?

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