Let the set $S = \{2, 4, 8, 16, \dots, 512\}$ be partitioned into $3$ sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \varnothing$. The maximum number of such possible partitions of $S$ is equal to: