Q$4\mathrm{.}9$: Define an AVL$-2$ tree to be a BST where each node $v$ satisfies balance $(v)in\{-2,-1,0,1,2\}.$ Let

$N(h)$ be the minimum number of nodes in an AVL$-2$ tree of height $h.$ Prove that $h=O(lgn)$

for the case where $h$ is a multiple of $3$ plus $1.$