Let S=\{1,2,3,4,5,6,7\}. Compute the number of sets of subsets T=\{A, B, C\} with A, B, C \in S such that A \cup B \cup C=S,(A \cap C) \cup(B \cap C)=\emptyset, and no subset contains two consecutive integers.
Let S=\{1,2,3,4,5,6,7\}. Compute the number of sets of subsets T=\{A, B, C\} with A, B, C \in S such that A \cup B \cup C=S,(A \cap C) \cup(B \cap C)=\emptyset, and no subset contains two consecutive integers.