For each of the $9$ positive integers $n, 2n, 3n, \ldots, 9n$, Alice takes the first decimal digit (from the left) and writes it onto a blackboard. She selected $n$ such that among the nine digits on the blackboard, there is the least possible number of different digits. What is this number of different digits equal to?

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