In a directed acyclic graph with source vertex \( s \), the quality-score of a directed path is the product of the weights of the edges on the path.
For a vertex \( v \neq s \), the quality-score of \( v \) is the maximum among the quality-scores of all 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 is \(\underline{\hspace{2cm}}\).
