Let $f(x)=10^{10x}$, $g(x)={\log }_{10}\left(\frac{x}{10}\right)$, $h_1(x)=g(f(x))$, and $h_n(x)=h_1(h_{n-1}(x))$ for integers $n\ge 2$. What is the sum of the digits of $h_{2011}(2)$?