Fundamental group of $\mathbb{R}^2\setminus\{x_1, x_2\}$

Question

For $M = \mathbb{R}^2\setminus\{x\}$, you can calculate $\pi_1$ using the fact that you can retract $M$ onto a circle, s.t. $\pi_1(M)$ is $\mathbb{Z}$. But how can you calculate the fundamental group of $\mathbb{R}^2\setminus\{x_1, x_2\}$? And is there any rule for the $n$-punctured plane?

Answer 1

Hint: you can deformation retract the plane minus $n$ distinct points onto the wedge of $n$ circles.