Let $Q$ be a quadratic polynomial. If the sum of the roots of $Q^{100}(x)$ (where $Q^i(x)$ is defined by $Q^1(x)=Q(x)$, $Q^i(x)=Q(Q^{i-1}(x))$ for integers $i \geq 2$) is $8$ and the sum of the roots of $Q$ is $S$, compute $|\log_2(S)|$.

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