MathNet 2019-part-07 — 184 problems (EN–VI) Question 43

Let $S$ be a set having $2019$ elements and $A_1, A_2, \dots, A_n$ be subsets of $S$ such that the union of any three of them is equal to $S$ and the union of any two of them is not equal to $S$. Find the maximal possible value of $n$.