In order to visit the center of the galaxy and see a quasar from a close distance, it is necessary to go through a fairly long and dangerous path. During the journey to the center of the galaxy, you encounter a space patrol. You are warned that in order to continue moving, you need to provide the password — a positive integer $$$x$$$, otherwise you will be destroyed. You have the opportunity to ask no more than $$$32$$$ questions of the following type: how many prime numbers $$$p$$$ exist such that there is an integer $$$i$$$ such that $$$p \cdot i = \lfloor \frac{n}{q} \rfloor$$$, where $$$q$$$ is the number you ask in the question. In response, you will receive the number of such prime numbers, or $$$-1$$$ if there are infinitely many.

To ask a question, you need to output the string: "? q", where $$$q$$$ is some positive integer. In response, you will receive a single number — the number of prime numbers satisfying the condition of your request.

Once you have determined the password, output in a separate line "! x". After that, your program should immediately terminate.

$$$$$$1 \le x, q \le 10^9$$$$$$

If your program asks more than $$$32$$$ questions, it will receive the verdict "Wrong Answer".