F. Ehab and the Big Finaletime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis 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.InputThe 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.OutputTo print the answer, print "! x" (without quotes).InteractionTo ask a question, print it in one of the formats above:   d u (1 \le u \le n), or  s u (1 \le u \le n). After each question, you should read the answer: either the distance or the second vertex on the path, as mentioned in the legend. If we answer with -1 instead of a valid answer, that means you exceeded the number of queries, made an invalid query, or violated the condition in the second type of queries. Exit immediately after receiving -1 and you will see Wrong answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use: fflush(stdout) or cout.flush() in C++; System.out.flush() in Java; flush(output) in Pascal; stdout.flush() in Python; See the documentation for other languages.Hacks:The first line should contain two integers n and x (2 \le n \le 2 \cdot 10^5, 1 \le x \le n).Each of the next n-1 lines should contain two integers u and v (1 \le u,v \le n) that mean there is an edge between nodes u and v. The edges must form a tree.ExampleInput
5
1 2
1 3
3 4
3 5
3
5Output
d 2
s 3
! 5NoteIn 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.
5
1 2
1 3
3 4
3 5
3
5
d 2 s 3 ! 5
['constructive algorithms', 'divide and conquer', 'graphs', 'implementation', 'interactive', 'trees', '*2400']