Three builders are scheduled to build a house in 60 days. However, they procrastinate and do nothing for the first 50 days. To complete the house on time, they decide to hire more workers and work at twice their original speed. If the new workers also work at this doubled rate, how many new workers are needed? Assume each builder works at the same rate and does not interfere with the others.

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