Fair Coin from Biased Coin (Von Neumann)

You have a biased coin:

\mathbb{P}(H)=p,\qquad 0<p<1,

where $p$ is unknown.

You want to generate a fair coin flip (probability $1/2$ ) using only this coin, without knowing $p$ .

Question: What procedure do you use? Show that the output is fair.