Partial Derivatives & the Gradient · Superchallenge problem

Let $f(x,y) = \sqrt{\lvert xy\rvert}$. For how many unit vectors $\mathbf{u}$ does the directional derivative $D_{\mathbf{u}}f(0,0) = \displaystyle\lim_{h\to 0}\frac{f(h\mathbf{u}) - f(0,0)}{h}$ (a two-sided limit) exist?