Consider a weighted graph G$=($V$,$E$)$ representing highways. To promote safety, any path

with more than $10$ edges is classified as high$-$risk, and the effective weight of such paths

is doubled. Explain how to reduce the problem of finding the shortest path weight

between every pair of vertices $($under this classification$)$ to a standard all$-$pairs shortest

paths problem, as solved by the Floyd$-$Warshall algorithm.