MathNet 2021 — Part 02 Question 64

Given set $A = \{1, 2, m\}$, $m$ is real. Let $B = \{a^2 \mid a \in A\}$, $C = A \cup B$. If the sum of all the elements of $C$ is $6$, then the product of all the elements of $C$ is ______.