CGMO 2015 Problem 8

Let $n\geq 2$ be a given integer. Initially, we write $n$ sets on the blackboard and do a sequence of moves as follows: choose two sets $A$ and $B$ on the blackboard such that none of them is a subset of the other, and replace $A$ and $B$ by $A\cap B$ and $A\cup B$ . This is called a $\textit{move}$ . Find the maximum number of moves in a sequence for all possible initial sets.