Traverse it!

*The story in this one is omitted due to lack of time. Just solve the problem. :P* You have been given a tree of $N$ vertices, where each vertex $i$ has a number $a_i$ associated with it. Lets call a path cool if the labels of the vertices along the path is non-decreasing. Your task is to find the longest cool path and also the number of such paths. The length of a path is defined to be the num