Description:
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.
Input Format:
The only line of the input contains an integer $$$n$$$ ($$$3\le n\le 7.5\cdot10^4$$$) — the number of nodes in the tree.
Output Format:
None
Note:
Here is an image of the tree from the sample.