Node Codon

You are given an undirected graph with $N$ nodes (numbered $1$ through $N$) and $M$ edges. Each edge connects two distinct nodes. However, there may be multiple edges connecting the same pairs of nodes, and they are considered to be distinct edges. A lowercase English letter is written in each node. You are also given a string $S$ with length $L$. A *beautiful path* is a sequence of $L-1$ edges