The sum of all local minimum values of the function
$$f(x) = \left\{\begin{array}{l l}1-2x, & \quad {x<-1}\\ \frac{1}{3}(7+2|x|), & \quad {-1\leq x\leq 2}\\\frac{11}{18}(x-4)(x-5), & \quad {x>2}\\ \end{array}\right.$$ is

A

$$\frac{157}{72}$$

B

$$\frac{131}{72}$$

C

$$\frac{171}{72}$$

D

$$\frac{167}{72}$$