A Boolean function $f: \{0, 1\}^n \to \{0, 1\}$ is monotone if for any $x, y \in \{0, 1\}^n$, $x \le y$ (component-wise) implies $f(x) \le f(y)$. The number of monotone Boolean functions of $n$ variables is known as the $n$-th Dedekind number. What is the number of monotone Boolean functions of $3$ variables?