Hong has a tree, whose vertices are conveniently labeled by 1, 2, ..., n. Each node has a weight w_{i}.
A set with m nodes v_{1}, v_{2}, ..., v_{m} 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 u_{1}, u_{2}, ..., u_{m}, (that is, w_u_{i} < w_u_{i+1} for i from 1 to m-1). For any node x in the path from u_{i} to u_{i+1}(excluding u_{i} and u_{i+1}), should satisfy w_x < w_u_{i}.
Your task is to find the maximum size of Hong Set in a given tree.