Deleting Numbers

This is an interactive problem.

There is an unknown integer $$$x$$$ ($$$1\le x\le n$$$). You want to find $$$x$$$.

At first, you have a set of integers $$$\{1, 2, \ldots, n\}$$$. You can perform the following operations no more than $$$10000$$$ times:

• A $$$a$$$: find how many numbers are multiples of $$$a$$$ in the current set.
• B $$$a$$$: find how many numbers are multiples of $$$a$$$ in this set, and then delete all multiples of $$$a$$$, but $$$x$$$ will never be deleted (even if it is a multiple of $$$a$$$). In this operation, $$$a$$$ must be greater than $$$1$$$.
• C $$$a$$$: it means that you know that $$$x=a$$$. This operation can be only performed once.

Remember that in the operation of type B $$$a>1$$$ must hold.

Write a program, that will find the value of $$$x$$$.

In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer $$$a$$$ ($$$1\le a\le n$$$ for operations A and C, $$$2\le a\le n$$$ for operation B). This line desribes operation you make.

If your operation has type C your program should terminate immediately.

Else your program should read one line containing a single integer, which is the answer to your operation.

After outputting each line, don't forget to flush the output. To do it use:

• fflush(stdout) in C/C++;
• System.out.flush() in Java;
• sys.stdout.flush() in Python;
• flush(output) in Pascal;
• See the documentation for other languages.

It is guaranteed, that the number $$$x$$$ is fixed and won't change during the interaction process.

Hacks:

To make a hack, use such input format:

The only line should contain two integers $$$n$$$, $$$x$$$ ($$$1 \leq x \leq n \leq 10^5$$$).