Cardinality of partial orders on $\mathbb R \times \mathbb R$

Question

Let the set $A$ be defined: $A=\{X \subseteq \mathbb R \times \mathbb R: X$ is a partial order $\land \max X \in \mathbb Z \land min X \in \mathbb Z \}$

What's the cardinality of $A$?

Answer 1

HINT: Pick any partial order on $\Bbb R\setminus\{0,1\}$ and declare that $0$ is the new minimum and $1$ is the new maximum. How many ways do you have to define partial orders on $\Bbb R$?