CF1761G Centroid Guess

This in an interactive problem. There is an unknown tree consisting of $ n $ nodes, which has exactly one centroid. You only know $ n $ at first, and your task is to find the centroid of the tree. You can ask the distance between any two vertices for at most $ 2\cdot10^5 $ times. Note that the interactor is not adaptive. That is, the tree is fixed in each test beforehand and does not depend on your queries. A vertex is called a centroid if its removal splits the tree into subtrees with at most $ \lfloor\frac{n}{2}\rfloor $ vertices each.

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Here is an image of the tree from the sample.