Let $f(x) = \begin{cases} \left\lfloor 4x ^ { 2 } - 8x + 5 \right\rfloor, & \text{if } 8x ^ { 2 } - 6x + 1 \geq 0 \\ \left\lfloor 4x ^ { 2 } - 8x + 5 \right\rfloor, & \text{if } 8x ^ { 2 } - 6x + 1 < 0 \end{cases}$, where $\lfloor \alpha \rfloor$ denotes the greatest integer less than or equal to $\alpha$. Then the number of points in $R$ where $f$ is not differentiable is $\_\_\_\_$.