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 …

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

[JEE Main 2024, 5 Apr (Shift 2)]