Let $a_n$ be the number of unordered sets of three distinct bijections $f, g, h : \{1, 2, ..., n\} \to \{1, 2, ..., n\}$ such that the composition of any two of the bijections equals the third. What is the largest value in the sequence $a_1, a_2, ...$ which is less than $2021$?

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