G. Centroid Guess
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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

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.