# 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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