For a bijective function $g : R \to R$, we say that a function $f : R \to R$ is its superinverse if it satisfies the following identity $(f \circ g)(x) = g^{-1}(x)$, where $g^{-1}$ is the inverse of $g$. Given $g(x) = x^3 + 9x^2 + 27x + 81$ and $f$ is its superinverse, find $|f(-289)|$.

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