Let $$[x]$$ denote the greatest integer function and $$f(x) = \max\{1 + x + [x], 2 + x, x + 2[x]\}$$, $$0 \leq x \leq 2$$, where $$f$$ is not continuous and $$n$$ be the number of points in $$(0, 2)$$, where $$f$$ is not differentiable. Then $$(m + n)^2 + 2$$ is equal to

A

$$2$$

B

$$11$$

C

$$6$$

D

$$3$$