22SP - 11 Tropical Vacation

To escape his responsibilities, Christian has decided to travel to the Amazon Rainforest. Being an avid botanist, he decides that the beauty of a tree rooted at $t$ (represented as $t!$) is given by:   $t! = |s| \prod_{i = 1}^{n} t_i!$   Where $t$ is the root of the tree, $|s|$ is the number of leaves in $t$ and $t_i!$ is the beauty of the $i^{th}$ subtree. The beauty of a single verte