CF1167B.Lost Numbers

This is an interactive problem. Remember to flush your output while communicating with the testing program. You may use fflush(stdout) in C++, system.out.flush() in Java, stdout.flush() in Python or flush(output) in Pascal to flush the output. If you use some other programming language, consult its documentation. You may also refer to the guide on interactive problems: https://codeforces.com/blog/entry/45307.

The jury guessed some array $a$ consisting of $6$ integers. There are $6$ special numbers — $4$, $8$, $15$, $16$, $23$, $42$ — and each of these numbers occurs in $a$ exactly once (so, $a$ is some permutation of these numbers).

You don't know anything about their order, but you are allowed to ask up to $4$ queries. In each query, you may choose two indices $i$ and $j$ ($1 \le i, j \le 6$, $i$ and $j$ are not necessarily distinct), and you will get the value of $a_i \cdot a_j$ in return.

Can you guess the array $a$?

The array $a$ is fixed beforehand in each test, the interaction program doesn't try to adapt to your queries.

Interaction

Before submitting the answer, you may ask up to $4$ queries. To ask a query, print one line in the following format: $?$ $i$ $j$, where $i$ and $j$ should be two integers such that $1 \le i, j \le 6$. The line should be ended with a line break character. After submitting a query, flush the output and read the answer to your query — one line containing one integer $a_i \cdot a_j$. If you submit an incorrect query (or ask more than $4$ queries), the answer to it will be one string 0. After receiving such an answer, your program should terminate immediately — otherwise you may receive verdict "Runtime error", "Time limit exceeded" or some other verdict instead of "Wrong answer".

To give the answer, your program should print one line $!$ $a_1$ $a_2$ $a_3$ $a_4$ $a_5$ $a_6$ with a line break in the end. After that, it should flush the output and terminate gracefully.

这是一个交互式问题。在与评测程序通信时，请务必刷新输出。你可以使用 C++ 中的 fflush(stdout)、Java 中的 system.out.flush()、Python 中的 stdout.flush() 或 Pascal 中的 flush(output) 来刷新输出。若使用其他编程语言，请查阅其文档。你也可以参考交互式问题指南：https://codeforces.com/blog/entry/45307。

出题人预先选定一个由 $6$ 个整数组成的数组 $a$。存在 $6$ 个特殊数字：$4$、$8$、$15$、$16$、$23$、$42$，且每个数字在 $a$ 中恰好出现一次（即 $a$ 是这六个数的一个排列）。

你对它们的顺序一无所知，但最多可以提出 $4$ 次询问。每次询问中，你可以选择两个下标 $i$ 和 $j$（$1 \le i, j \le 6$，$i$ 与 $j$ 可以相同），系统将返回 $a_i \cdot a_j$ 的值。

你能推断出数组 $a$ 吗？

在每个测试用例中，数组 $a$ 是预先固定好的；交互程序不会根据你的询问动态调整。

交互流程

在提交最终答案前，你最多可进行 $4$ 次询问。要提出一次询问，请输出一行，格式为：? $i$ $j$，其中 $i$ 和 $j$ 是满足 $1 \le i, j \le 6$ 的整数。该行末尾需换行。提交一次询问后，请刷新输出，并读取询问结果——即一行包含单个整数 $a_i \cdot a_j$ 的输入。若你提交了非法询问（例如下标越界），或询问次数超过 $4$ 次，则返回结果为字符串 0。一旦收到该结果，你的程序应立即终止；否则，你可能收到 “运行错误”、“时间超限” 或其他判定结果，而非 “答案错误”。

要提交最终答案，你的程序应输出一行：! $a_1$ $a_2$ $a_3$ $a_4$ $a_5$ $a_6$，末尾换行。之后请刷新输出并正常终止。

If you want to submit a hack for this problem, your test should contain exactly six space-separated integers $a_1$, $a_2$, ..., $a_6$. Each of $6$ special numbers should occur exactly once in the test. The test should be ended with a line break character.

如果你想为此题提交一个 Hack 数据，你的测试用例应恰好包含六个以空格分隔的整数 $a_1$, $a_2$, ..., $a_6$。这六个特殊数字在测试用例中必须各自恰好出现一次。测试用例末尾应以换行符结尾。