Evaluate the following product and apply the ceiling function to the result: $$\left\lceil \frac{1}{2} \times 4 \times \frac{1}{8} \times 16 \times \frac{1}{32} \times 64 \times \frac{1}{128} \times 256 \times \frac{1}{512} \times 1024 \right\rceil.$$ Let's think step by step and output the final answer within \boxed{}.
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