Permutations And Combinations

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