Processing math: 100%

F. Ehab and the Big Finale
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 (1un). 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 (1un). 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 ab 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

The first line contains the integer n (2n2105) — the number of nodes in the tree.

Each of the next n1 lines contains two space-separated integers u and v (1u,vn) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

To print the answer, print "! x" (without quotes).

Interaction

To ask a question, print it in one of the formats above:

  • d u (1un), or
  • s u (1un).

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 (2n2105, 1xn).

Each of the next n1 lines should contain two integers u and v (1u,vn) that mean there is an edge between nodes u and v. The edges must form a tree.

Example
Input
5
1 2
1 3
3 4
3 5
3
5
Output
d 2
s 3
! 5
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.