We define a windmill graph as a graph G centered on node $$c$$ with at least $$5$$ adjacent paths. One of these paths has to have length at least $$3$$ and it is interpreted as the base of the windmill. The remaining paths have length exactly $$1$$ and are interpreted as the sails of the windmill.
For example, the graph given below is a windmill with $$8$$ nodes centered on node $$1$$ with $$5$$ adjacent paths and the base of length $$3$$.
2 3 \ / 5 ---- 1 -----4 | 6 | 7 | 8
For a given tree $$T$$ with $$N$$ nodes, the goal is to find the size of its largest subgraph (in terms of the number of nodes) which is a windmill graph and it’s center vertex. If there are many such largest subgraphs, take the one with the smallest center vertex. If no windmill graph is a subgraph of $$T$$, then the answer is $$-1$$.
$$1 \leq N \leq 10^5$$
On the first line, there is a single integer $$N$$ denoting the number of nodes in the tree $$T$$. Then, $$N-1$$ lines follow. Each of them contains two space-separated integers $$u$$ and $$v$$ and denotes that there is an edge between nodes $$u$$ and $$u$$ in the tree.
If there is no subgraph of $$T$$ which is a windmill graph output $$-1$$ in a single line. Otherwise, output two space-separated integers $$result$$ and $$c$$, where $$result$$ is the size of the largest windmill subgraph of $$T$$ and $$c$$ is the smallest center node among all the largest windmill subgraphs of $$T$$.
The graph is the same as the example windmill graph described in the statement.