Question 87
Suppose set $S = \{1, 2, 3, \dots, 10\}$ and the subset $A$ of $S$ satisfies
$$
A \cap \{1, 2, 3\} \neq \emptyset, \quad A \cup \{4, 5, 6\} \neq S.
$$
The number of such subsets is ________.
$$
A \cap \{1, 2, 3\} \neq \emptyset, \quad A \cup \{4, 5, 6\} \neq S.
$$
The number of such subsets is ________.