Farey sequence

Select a positive integer n. Find the simplest fraction of all denominators that do not exceed n and sort them from small to large. This score sequence is called the Farey sequence.
Theorem: In a Farey sequence, for any two adjacent fractions, first multiply the denominator of the former by the numerator of the latter, and then multiply the numerator of the former by the denominator of the latter, then these two products must be exactly 1 different.

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