Tours on Tree

There are $N$ cities in your country numbered $1,2,3....,N$ with population $A_1, A_2, A_3,..., A_N$. There are $N-1$ bidirectional roads connecting these cities such that every city is reachable from every other city. A tour between two cities $x$ and $y$ is considered beautiful if the population of all the cities on the path from $x$ to $y$ ($x$ and $y$ are distinct.) is in one of the followin