Max-digit Tree

You have a tree with $N$ vertices (numbered $1$ through $N$) rooted at vertex $1$. Each vertex contains a decimal digit; let's denote the digit in vertex $i$ by $d_i$. A subtree is a non-empty subgraph satisfying the following condition: for any vertex $v$, if $v$ belongs to subtree $S$, then the parent of $v$ also belongs to $S$. Note that each subtree contains the root. The vertices in any subt