Dima has written the numbers $\frac{1}{80!}, \frac{1}{81!}, \ldots, \frac{1}{99!}$ on 20 infinite pieces of paper as decimal fractions. For example, the following is written on the last piece: \( \frac{1}{99!} = 0.\underbrace{00\ldots00}_{155\text{ zeros}}10715\ldots \). Sasha wants to cut a fragment of $N$ consecutive digits from one of these pieces without the comma. What is the maximal $N$ for which Sasha can do this so that Dima cannot guess from which piece Sasha has cut his fragment?

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