Evaluate the sum $\left\lfloor\log_2 1\right\rfloor + \left\lfloor\log_2 2\right\rfloor + \left\lfloor\log_2 3\right\rfloor + \ldots + \left\lfloor\log_2 256\right\rfloor$.

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