Let $g\left(x\right)=|x-2|$  and $h\left(x\right)=g\left(g\left(x\right)\right),$ the find the value of the expression
$h\text{'}(-1)+h\text{'}\left(1\right)+h\text{'}\left(3\right)+h\text{'}\left(5\right)$  
 

$$\begin{gathered} g\left(x\right)=\{\begin{array}{cc}x-2,& x>2\\ 2-x,& x<2\end{array} h\left(x\right)=\{\begin{array}{cc}g\left(x\right)-2,& g\left(x\right)>2\\ 2-g\left(x\right),& g\left(x\right)<2\end{array} \\ h\left(x\right)=\{\begin{array}{cc}x-4,& x\ge 4\\ -x,& x\le 0\\ 4-x,& x\in [2,4)\\ x,& x\in (0,2)\end{array} \Rightarrow h\text{'}\left(x\right)=\{\begin{array}{cc}1,& x\ge 4\\ -1,& x\le 0\\ -1,& x\in [2,4)\\ 1,& x\in (0,2)\end{array} \end{gathered}$$