$\text{ Let }f\left(x\right)=\left|x-2\right|\text{ and }\underset{\left(n\text{ times }\right)}{\underbrace{g\left(x\right)=f\left(f\right(f\dots \dots \left(f\right(x\left)\right))\dots )}}.\text{ If equation }g\left(x\right)=k, k\in \left(0,2\right)\text{ has }8$ $\text{ distinct solutions than value of }n\text{ is equal to }$

• A

  3

• B

  4

• C

  5

• D

  8