Let $S$ be the $4 \times 4$ square grid $\{(x, y): x, y \in \{0, 1, 2, 3\} \}$. A $monotone \: \: path$ in this grid starts at $(0, 0)$ and at each step either moves one unit up or one unit right. For example, from the point $(x, y)$ one can in one step either move to $(x+1, y) \in S$ or $(x, y+1) \in S$, but never leave $S$. Let the number of distinct monotone paths to reach point $(2, 2)$ starting from $(0, 0)$ bt $z$. How many distinct monotone paths are there to reach point $(3, 3)$ starting from $(0, 0)$?

- $2z+6$
- $3z+6$
- $2z+8$
- $3z+8$
- $3z+4$