Let $Q(x) = a_0 + a_1x + \dots + a_nx^n$ be a polynomial with integer coefficients, and $0 \le a_i < 3$ for all $0 \le i \le n$.

Given that $Q(\sqrt{3}) = 20 + 17\sqrt{3}$, compute $Q(2)$.

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