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2370. 
$A$, $B$, and $C$ are sets such that $A \cup C = \{1,2,3,4,5,6\}$, $B \cup C = \{1,2,3,4\}$, $A \cap C = \emptyset$, $A \cap B = \{3\}$, and $B \cap C = \{1,2\}$. Find the product of the elements in $B$.

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