Valentine Break-Up

Jack and Rose are in a very deep Relationship. But this Valentine's Day they had a break-up and now they hate each other. You are given a tree of $N$ nodes and edges. Each Node represents location of a house and cost of that house is equal to the value of the node. Now both of them wants to live away from each other as much as possible . You need to select two Nodes $X$ and $Y$ in the tree suc