Playing with Graphs - 8

Calculus Level 4

Given that

$\begin{cases} f (x) = x \\ g (x) = | 1 - f (x) | \\ h (x) = 2 - g (x) \\ L (x) = h (|x|) + | h (x) | \end{cases}$

What is the number of points where $L (x)$ is non-differentiable?

4 0 6 1 3 5 2 10