Q55

In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality-score of $v$ is defined to be the maximum among the quality-scores of all the paths from $\textsf{s}$ to $v$. The quality-score of $\textsf{s}$ is assumed to be $1$.

The sum of the quality-scores of all vertices on the graph shown above is _______