In a directed acyclic graph with a source vertex $\mathbf{s}$, the *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 $\mathbf{s}$, the quality-score of $v$ is defined to be the maximum among the quality-scores of all the paths from $\mathbf{s}$ to $v$. The quality-score of $\mathbf{s}$ is assumed to be 1. The sum of the quality-scores of all the vertices in the graph shown above is ________.

In a directed acyclic graph with a source vertex s, the *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 s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1. The sum of the quality-scores of all the vertices in the graph shown above is …

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