Let a function $\mathrm{g}:[0,4] \rightarrow R$ be defined as $\mathrm{g}(\mathrm{x})=\left\{\begin{array}{cl}\max _{0 \leq t \leq \mathrm{x}}\left\{\mathrm{t}^3-6 \mathrm{t}^2+9 \mathrm{t}-3\right\} & , 0 \leq \mathrm{x} \leq 3 \\ 4-\mathrm{x} & , 3<\mathrm{x} \leq 4\end{array}\right.$ then the number of points in the interval $(0,4)$ where $g(x)$ is NOT differentiable, is $\_\_\_\_$ .