E. XOR Guessing
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 picked an integer $x$ not less than $0$ and not greater than $2^{14} - 1$. You have to guess this integer.

To do so, you may ask no more than $2$ queries. Each query should consist of $100$ integer numbers $a_1$, $a_2$, ..., $a_{100}$ (each integer should be not less than $0$ and not greater than $2^{14} - 1$). In response to your query, the jury will pick one integer $i$ ($1 \le i \le 100$) and tell you the value of $a_i \oplus x$ (the bitwise XOR of $a_i$ and $x$). There is an additional constraint on the queries: all $200$ integers you use in the queries should be distinct.

It is guaranteed that the value of $x$ is fixed beforehand in each test, but the choice of $i$ in every query may depend on the integers you send.

Output

To give the answer, your program should print one line $!$ $x$ with a line break in the end. After that, it should flush the output and terminate gracefully.

Interaction

Before giving the answer, you may submit no more than $2$ queries. To ask a query, print one line in the following format: $?$ $a_1$ $a_2$ ... $a_{100}$, where every $a_j$ should be an integer from the range $[0, 2^{14} - 1]$. The line should be ended with a line break character. After submitting a query, flush the output and read the answer to your query — the value of $a_i \oplus x$ for some $i \in [1, 100]$. No integer can be used in queries more than once.

If you submit an incorrect query (or ask more than $2$ queries), the answer to it will be one integer $-1$. 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".

Example
Input
0
32
Output
? 3 5 6
? 32 24 37
! 5
Note

The example of interaction is not correct — you should sumbit exactly $100$ integers in each query. Everything else is correct.

Hacks are forbidden in this problem.