BALTIC-WAY 2022 Problem 2

We define a sequence of natural numbers by the initial values $a_0 = a_1 = a_2 = 1$ and the recursion $$a_n = \bigg \lfloor \frac{n}{a_{n-1}a_{n-2}a_{n-3}} \bigg \rfloor$$ for all $n \ge 3$ . Find the value of $a_{2022}$ .