Three sets, $\mathbb A$, $\mathbb B$ and $\mathbb C$, have 3, 12, and 13 elements respectively. The set $\mathbb D$ is defined as:

$\mathbb D = \{(x,y,z) \mid x \in\mathbb A, y \in\mathbb B, z \in\mathbb C\}$

How many elements does $\mathbb D$ have?

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