2022 AIME I Problem 13

Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form 0.\overline{abcd}, where at least one of the digits a, b, c, or d is nonzero. Let N be the number of distinct numerators obtained when numbers in S are written as fractions in lowest terms. For example, both 4 and 410 are counted among the distinct numerators for numbers in S because 0.\overline{3636} = \frac{4}{11} and 0.\overline{1230} = \frac{410}{3333}. Find the remainder when N is divided by 1000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.