Sets $A$, $B$, and $C$ satisfy the following conditions:  
- $|A| = 92$  
- $|B| = 35$  
- $|C| = 63$  
- $|A \cap B| = 16$  
- $|A \cap C| = 51$  
- $|B \cap C| = 19$  

Compute the number of possible values of $|A \cap B \cap C|$.

Let's think step by step and output the final answer within \boxed{}.
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