How do I use curly braces to typeset the definition of Graham Number?

Question

This is the definition of Graham's Number.

How do I subdivide the text in the bracket, as shown?

Answer 1

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\[g_n =
  \begin{cases}
    3\uparrow\uparrow\uparrow\uparrow3 & n=1\\
    3\uparrow^{g_{n-1}}3 & n\geq2, n\in\mathbb{N}
  \end{cases}
\]
\end{document}