Hong has a tree, whose vertices are conveniently labeled by 1, 2, ..., n. Each node has a weight wi.
A set with m nodes v1, v2, ..., vm is a Hong Set if:
- The tree induced by this set is connected.
- After we sort these nodes in set by their weights in ascending order, we get u1, u2, ..., um, (that is, w_ui < w_ui+1 for i from 1 to m-1). For any node x in the path from ui to ui+1(excluding ui and ui+1), should satisfy w_x < w_ui.
Your task is to find the maximum size of Hong Set in a given tree.