You are given a tree. Your task is to identify the node that, when used as the root, maximizes the depth of the tree. If there are multiple nodes that achieve this, provide the sum of the values of all correct nodes. Please input a number in the provided box below.
Tip: To solve this problem effectively, avoid breaking or altering the tree's structure. A helpful approach is to draw the given tree on paper and experiment with different nodes as the root while keeping the tree intact. This visual method can aid in finding the optimal root node.