Let $\displaystyle Y$ be the complement of the following subset of the plane $\displaystyle \mathbb{R}^2:$

$\displaystyle \{(x,0) \in \mathbb{R}^2: x \in \mathbb{Z} \}$

Prove that $\displaystyle \pi_1(Y)$ is a free group on a countable set of generators.

I don't know how to start this problem. Thanks in advance.