real analysis - Example of a continuous function that is monotone at no point

I have seen examples and proofs of functions that are everywhere continuous but nowhere monotone. However I have never seen a proof and example of a function that is everywhere continuous but monotonic at no point. Do you know of an example (preferably with a proof) or can you provide an accessible reference?

P.S Definition of monotonic at a point:

Let $x$ be a real number. We say that $f$ is non-decreasing at $x$ if there is a neighborhood of $x$, $N_x$, such that $\frac{f(y)-f(x)}{y-x} \ge 0$ if $y \in N_x-\{x\}$. We say that $f$ is monotone at $x$ if $f$ is non-decreasing at $x$ or non-increasing at $x$.