real analysis - About a function continuous on [0,1]

Let $f:[0,1]\to [0,1]$ be a continuous function. Given that $f(0)=0$, $f(1)=1$ and $f(f(x))=x$ prove that $f(x)=x$.
I've been thinking about this one for ages, but I can't figure out even where to begin. Give me some hints, please?