Consider a sequence x1,x2,x3,..., defined by
\begin{align*}x_1 &= \sqrt [3]{3}\\
x_2 &= \sqrt [3]{3} ^ {\sqrt [3]{3}},\end{align*}and in general
x_n \equal{} (x_{n \minus{} 1}) ^ {\sqrt [3]{3}}\,\,\text{ for }\,\,n > 1.
What is the smallest value of n for which xn is an integer?<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>27