analysis - Find all real and continuous functions that are a 3-involution.

Find all continuous functions $f: \mathbb R \rightarrow \mathbb R$such that $f(f(f(x)))=x$.

Obviously one solution to this functional equation is $f(x)=x$.

If the function is NOT continuous, there are also other solutions such as $f(x)=\frac{1}{1-x}$, but I'm not sure how to find all solutions that are continuous.