Description: This is an interactive problem. You're given a tree consisting of $$$n$$$ nodes, rooted at node $$$1$$$. A tree is a connected graph with no cycles. We chose a hidden node $$$x$$$. In order to find this node, you can ask queries of two types: - d $$$u$$$ ($$$1 \le u \le n$$$). We will answer with the distance between nodes $$$u$$$ and $$$x$$$. The distance between two nodes is the number of edges in the shortest path between them. - s $$$u$$$ ($$$1 \le u \le n$$$). We will answer with the second node on the path from $$$u$$$ to $$$x$$$. However, there's a plot twist. If $$$u$$$ is not an ancestor of $$$x$$$, you'll receive "Wrong answer" verdict! Node $$$a$$$ is called an ancestor of node $$$b$$$ if $$$a \ne b$$$ and the shortest path from node $$$1$$$ to node $$$b$$$ passes through node $$$a$$$. Note that in this problem a node is not an ancestor of itself. Can you find $$$x$$$ in no more than $$$36$$$ queries? The hidden node is fixed in each test beforehand and does not depend on your queries. Input Format: The first line contains the integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of nodes in the tree. Each of the next $$$n-1$$$ lines contains two space-separated integers $$$u$$$ and $$$v$$$ ($$$1 \le u,v \le n$$$) that mean there's an edge between nodes $$$u$$$ and $$$v$$$. It's guaranteed that the given graph is a tree. Output Format: To print the answer, print "! x" (without quotes). Note: In the first example, the hidden node is node $$$5$$$. We first ask about the distance between node $$$x$$$ and node $$$2$$$. The answer is $$$3$$$, so node $$$x$$$ is either $$$4$$$ or $$$5$$$. We then ask about the second node in the path from node $$$3$$$ to node $$$x$$$. Note here that node $$$3$$$ is an ancestor of node $$$5$$$. We receive node $$$5$$$ as the answer. Finally, we report that the hidden node is node $$$5$$$.