This problem is the December 22 problem of yukicoder Advent Calendar Contest 2021.

Problem Statement

This is an interactive problem.
In this problem, each input contains $T$ test cases.

A loves a certain real number $x$ between $0$ and $12.22\times 10^{74}$, inclusive.
Guess A's favorite real number $x$ by asking the following question.

• Is the real number $y$ less than or equal to $x$?

However, A is busy and will answer at most $24$ questions.
But A is kind, and will accept your answer as correct if its absolute error or relative error is at most $10^{-5}$.

Input and Output

First, the number of test cases $T$ is given.

$T$

$T$ is an integer satisfying $1\le T \le 100$.

Then, $T$ test cases follow.

Print each question to standard output in the following format.

? $y$

Here, $0\le y\le 12.22\times 10^{74}$ must be satisfied.

The response to a question is given from standard input in the following format.

$S$

Here, $S$ is one of the following strings.

• Yes: the real number $y$ is less than or equal to $x$.
• No: the real number $y$ is not less than or equal to $x$.
• -1: the number of questions exceeded $24$, or you produced invalid output. In this case, terminate your program immediately.

When answering with the real number $x$, print it to standard output in the following format.

! $x$

Here, $0\le x\le 12.22\times 10^{74}$ must be satisfied.
Your answer is treated as correct if its absolute error or relative error is at most $10^{-5}$.

After that, continue with the next test case if there is one; otherwise, terminate your program immediately.

End each output with a newline and flush standard output.

Constraints

$1\le T\le 100$
$0\le x\le 12.22\times 10^{74}$

Sample

For $T=2$, the following interaction is possible.