The number of points where the function
$$f(x) = \begin{cases} |2x^2 - 3x - 7| & \text{if } x \leqslant -1 \\ [4x^2 - 1] & \text{if } -1 < x < 1 \\ |x+1| + |x-2| & \text{if } x \geqslant 1 \end{cases}$$
where $$[t]$$ denotes the greatest integer $$\leqslant t$$, is discontinuous is ______