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 \( A\cup B\cup C=S \) and \( A\cap B=B\cap C=A\cap C=\phi. \). The maximum number of such possible partitions of \( S \) is equal to:
