Q49

Let $G=(V, \Sigma, S, P)$ be a context-free grammar in Chomsky Normal Form with $\Sigma=\{a, b, c\}$ and $V$ containing $10$ variable symbols including the start symbol $S$. The string $w=a^{30} b^{30} c^{30}$ is derivable from $S$. The number of steps (application of rules) in the derivation $S \rightarrow^* w$ is __________.