AMC 10 2014a Problem 19

Four cubes with edge lengths $1$, $2$, $3$, and $4$ are stacked as shown. What is the length of the portion of $\overline{XY}$ contained in the cube with edge length $3$?

$\textbf{(A)}\ \dfrac{3\sqrt{33}}5 \textbf{(B)}\ 2\sqrt3 \textbf{(C)}\ \dfrac{2\sqrt{33}}3 \textbf{(D)}\ 4 \textbf{(E)}\ 3\sqrt2$