Pinely Round 1 (Div. 1 + Div. 2) |
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Finished |

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interactive

probabilities

trees

*3500

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G. Centroid Guess

time limit per test

4 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputThis 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

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.

Interaction

Start interaction by reading $$$n$$$.

To ask a query about the distance between two nodes $$$u, v$$$ ($$$1 \le u, v \le n$$$), output "? u v".

If you determine that the centroid of the tree is $$$x$$$, use "! x" to report.

After printing a query, do not forget to output the end of a 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 documentation for other languages.

Hacks are disabled in this problem.

It's guaranteed that there are at most $$$500$$$ tests in this problem.

Example

Input

5 2 1 2 3 1 1 1

Output

? 1 2 ? 1 3 ? 1 4 ? 1 5 ? 2 3 ? 3 4 ? 4 5 ! 3

Note

Here is an image of the tree from the sample.

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