Candies on a Tree

There’s a tree with $N$ vertices where each of the vertices have some candies. Chandra is a greedy boy and wants to get as many candies as possible on his walk. However, he will only take candies from a node if the current node has strictly more candies than the previous node he emptied. Help him choose two nodes so that he collects the maximum number of candies. Chandra defines a walk as follow