This is an interactive problem.

Kevin is dissatisfied with his MBTI, so he asked Doraemon for a magical machine: the MBTI converter.

The MBTI converter can convert the MBTI attributes of $$$8$$$ people at a time. It will generate a "random" new MBTI for all individuals based on their initial MBTIs and a $$$32$$$-bit key $$$k$$$.

Kevin carefully studied this machine and found that the "random" MBTI it generates actually follows a certain pattern. The machine mainly includes three basic structures that shuffle the MBTI: "xor", "perm", and "mix". Each of these structures takes the MBTIs of $$$8$$$ individuals as input and outputs $$$8$$$ MBTIs as a result. In each structure, the input $$$8$$$ MBTIs are denoted as $$$in_0, in_1, in_2, \cdots, in_7$$$ and the output $$$8$$$ MBTIs are denoted as $$$out_0, out_1, out_2, \cdots, out_7$$$. For convenience, Kevin replaces each MBTI with a hexadecimal number according to the following table.

"xor" Structure:

The xor structure flips certain attributes of the MBTI based on the key $$$k$$$.

Let $$$k_j$$$ be the $$$j$$$-th binary bit of the key $$$k$$$ ($$$0 \leq j \lt 32$$$). The functionality of the xor structure can be expressed as: $$$$$$ out_i = in_i \oplus (\overline{k_{4i+3}k_{4i+2}k_{4i+1}k_{4i}})_2 $$$$$$ where $$$\oplus$$$ denotes the bitwise XOR$$$^{1}$$$.

"perm" Structure:

The perm structure replaces the MBTI, where each MBTI is replaced by another fixed MBTI.

The functionality of the perm structure can be expressed as: $$$$$$ out_i = p_{in_i} $$$$$$ where $$$p$$$ is a fixed array of length $$$16$$$ with the following values:

"mix" Structure:

The mix structure is used to mix the MBTIs of different people, with each output determined by two inputs.

The mix structure requires an intermediate array $$$t$$$ of length $$$8$$$, defined as: $$$$$$ t_i = \begin{cases} in_i \ll 1 & 0 \leq in_i \lt 8 \\ ((in_i \oplus 8) \ll 1) \oplus 3 & 8 \leq in_i \lt 16 \\ \end{cases} $$$$$$ where $$$\oplus$$$ denotes the bitwise XOR$$$^{1}$$$ and $$$\ll$$$ denotes logical left shift of four binary digits$$$^{2}$$$.

The functionality of the mix structure can be expressed as: $$$$$$ out_i = in_{i \ggg 1} \oplus (t_{(i \ggg 1) \oplus 1}) $$$$$$ where $$$\oplus$$$ denotes the bitwise XOR$$$^{1}$$$, and $$$\ggg$$$ denotes circular right shift of three binary digits$$$^{3}$$$.

The initial $$$8$$$ MBTIs will sequentially go through $$$19$$$ structures to produce the final output of $$$8$$$ MBTIs. These structures are: xor, perm, mix, xor, perm, mix, xor, perm, mix, xor, perm, mix, xor, perm, mix, xor, perm, mix, xor, which is six consecutive rounds of "xor, perm, mix" followed by an "xor".

Users of this machine typically hope to obtain a specific MBTI. Unfortunately, when Doraemon built this machine, he encapsulated the key $$$k$$$ inside the machine and refused to tell Kevin the value of the key. Thus, Kevin turned to you, the clever one. Kevin hopes you can construct some inputs (not exceeding $$$4096$$$, or the machine may be damaged), test run to obtain the corresponding outputs, and then analyze the value of the key. This way, he can write a program to predict the output for each input, allowing everyone to get their desired MBTI.

Can you accomplish this task?

$$$^{1}$$$ Bitwise XOR refers to performing the modulo $$$2$$$ addition operation on each corresponding bit of two binary numbers. For example: $$$(0011)_2$$$ $$$\oplus$$$ $$$(0101)_2$$$ $$$=$$$ $$$(0110)_2$$$.

$$$^{2}$$$ $$$x \ll y$$$ means to logically left shift the binary number $$$x$$$ by $$$y$$$ bits, discarding the overflow and filling the vacated parts with 0. For example: $$$(1100)_2$$$ $$$\ll$$$ $$$1$$$ $$$=$$$ $$$(1000)_2$$$, $$$(1001)_2$$$ $$$\ll$$$ $$$1$$$ $$$=$$$ $$$(0010)_2$$$.

$$$^{3}$$$ $$$x \ggg y$$$ means to circularly right shift the binary number $$$x$$$ by $$$y$$$ bits. For example: $$$(101)_2$$$ $$$\ggg$$$ $$$1$$$ $$$=$$$ $$$(110)_2$$$, $$$(110)_2$$$ $$$\ggg$$$ $$$1$$$ $$$=$$$ $$$(011)_2$$$.

To run the MBTI converter, please output "? $$$in_7in_6in_5in_4in_3in_2in_1in_0$$$" ($$$in_i \in \{0-9,a-f\}$$$), where $$$in_i$$$ is the hexadecimal value corresponding to the $$$i$$$-th input MBTI. You may perform this operation at most $$$4096$$$ times. After flushing your output, please read the output of the MBTI converter in the format "$$$out_7out_6out_5out_4out_3out_2out_1out_0$$$" ($$$out_i \in \{0-9,a-f\}$$$).

To answer for the value of $$$k$$$, please output "! $$$k$$$" ($$$0 \leq k \lt 2^{32}$$$), where $$$k$$$ is the decimal representation of the value you believe the key $$$k$$$ to be. You may perform this operation at most once. After performing the operation, you should exit your program immediately.

If you run the MBTI converter more than $$$4096$$$ times, or if your output contains invalid characters, the interactor will output "-1". Upon receiving such a response, you should immediately exit your program, and you will receive a "Wrong Answer" result. Otherwise, the result is uncertain, as you will attempt to read data from a closed output stream.

To flush your output, you can use:

• fflush(stdout) (if you use printf) or cout.flush() (if you use cout) in C and C++.
• System.out.flush() in Java and Kotlin.
• stdout.flush() in Python.