Statement

Marco was recently hired by the Italian road-safety authority to oversee the rain storm forecasting operations. He was provided with a map of M bidirectional roads that connect N cities. We know that, if there is no rain, we can traverse every road and it is always possible to reach any city starting from any other city. However, as the expected rain flooding (in millimeters) becomes higher, some of the roads become impossible to traverse and have to be closed to traffic. For each road, Marco knows exactly how many millimeters of rain flooding it can withstand at most. As long as there is at least one way to reach every city starting from any other city (even if it means taking a longer-than-usual route), life can go on pretty much as usual. However, if the flooding causes any two cities to be disconnected, a state of emergency must be declared! Help Marco calculate what is the maximum amount of rain flooding (in millimeters) that the whole network can withstand...