Sly Subsets of S

Let S={1,2,3,12} S = \{ 1, 2, 3, \ldots 12\} and T1,T2,Ta T_1, T_2, \ldots T_a be subsets of SS such that Ti⊄Tjij T_i \not \subset T_j \, \forall i \neq j . What is the maximum possible value of aa?

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