A factory produces a type of widget over a 10-day period. On days when the factory operates, it produces 100 widgets per day. However, if the factory does not operate on a given day, the production is zero for that day. The factory operated for some days and did not operate for others. At the end of the 10-day period, the factory had produced a total of 700 widgets. How many days did the factory not operate? Let's think step by step and output the final answer within \boxed{}.
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