Let $f(n)$ be a sequence of integers defined by $f(1) = 1$, $f(2) = 1$, and $f(n) = f(n-1) + (-1)^n f(n-2)$ for all integers $n \geq 3$. What is the value of $f(20) + f(21)$?

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