CF980F Cactus to Tree

You are given a special connected undirected graph where each vertex belongs to at most one simple cycle. Your task is to remove as many edges as needed to convert this graph into a tree (connected graph with no cycles). For each node, independently, output the maximum distance between it and a leaf in the resulting tree, assuming you were to remove the edges in a way that minimizes this distance.

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In the first sample, a possible way to minimize the maximum distance from vertex $ 1 $ is by removing the marked edges in the following image: Note that to minimize the answer for different nodes, you can remove different edges.