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1. Minimum number of 7-subsets covering all triples ●●●●○ 100 ptsLet $S=\{1,2,\ldots,15\}$. Choose $n$ subsets $A_1,A_2,\ldots,A_n$ of $S$ such that: (i) $|A_i|=7$ for each $i$; (ii) $|A_i\cap A_j|\leq 3$ for all $1\leq i<j\leq n$; (iii) for every 3-element subset $M$ of $S$, there is some $k$ with $M\subset A_k$. Find the minimum possible value of $n$.