Naruto Run Extended

Naruto is done visiting all the villages. It turns out that this was a secret mission to collect data that might be useful. Naruto found out that each village belongs to a group $G$. Let's define $G_i$ as the group to which the $i^{th}$ village belongs. As we already know, The whole network of villages is in the form of a rooted tree, where each village represents a vertex, with village $1$ being