AMC 10 2018a Problem 1

What is the value of $$\bigg(\Big((2+1)^{-1}+1\Big)^{-1}+1\bigg)^{-1}+1?$$ $\textbf{(A) } \frac{5}{8} \textbf{(B) } \frac{11}{7} \textbf{(C) } \frac{8}{5} \textbf{(D) } \frac{18}{11} \textbf{(E) } \frac{15}{8}$