Sly Subsets of S

Let \( S = \{ 1, 2, 3, \ldots 12\} \) and \( T_1, T_2, \ldots T_a\) be subsets of \(S\) such that \( T_i \not \subset T_j \, \forall i \neq j \). What is the maximum possible value of \(a\)?

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