Let f : ℝ² → ℝ be the function defined as follows:

f(x, y) = \(\begin{cases}\rm \left(x^2-1\right)^2 \cos ^2\left(\frac{y^2}{\left(x^2-1\right)^2}\right) & \text { if }\rm x \neq \pm 1 \\ 0 & \text { if }\rm x= \pm 1 .\end{cases}\)

The number of points of discontinuity of f(x, y) is equal to ______.