G. Centroid Guesstime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard 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.InputThe only line of the input contains an integer n (3\le n\le 7.5\cdot10^4) — the number of nodes in the tree.InteractionStart 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.ExampleInput
5

2

1

2

3

1

1

1
Output

? 1 2

? 1 3

? 1 4

? 1 5

? 2 3

? 3 4

? 4 5

! 3
NoteHere is an image of the tree from the sample.  
5

2

1

2

3

1

1

1

 ? 1 2  ? 1 3  ? 1 4  ? 1 5  ? 2 3  ? 3 4  ? 4 5  ! 3 
['interactive', 'probabilities', 'trees', '*3500']