MEX Tree

You are given a tree $T$ consisting of $N$ nodes, numbered $1$ to $N$, and the tree is rooted at node $1$. The parent of the $i$-th node is $P_i$ ($1$ has no parent because it is the root). Define $subtree(x)$ as the set of nodes $y$ such that the unique path from node $1$ to node $y$ passes through $x$. Note that this means $x \in subtree(x)$. A vertex $x$ is called a **leaf** if $|subtree(x)| =