This is an interactive problem.

You are Professor Utonium, the brilliant scientist of Townsville. You were about to start your project of creating the 'perfect little girls'. Unfortunately, you discover that your lab assistant Jojo has removed all the labels from the chemical containers in the lab.

Now, you have $$$N$$$ unlabeled chemicals, numbered from $$$1$$$ to $$$N$$$. Among them are two very dangerous chemicals – Chemical X and Chemical Y. When these two are mixed in the same mixture, they react explosively.

To identify the exact indices of Chemical X and Chemical Y, you'll need to carry out a series of controlled experiments. In each experiment, you may mix a subset of the chemicals in a secure environment. If both Chemical X and Chemical Y are present in the mixture, it results in "Kaboom" – an explosion! If not, you'll simply observe a "Noboom", meaning the mixture is stable.

But there's a catch — you can perform at most $$$20$$$ experiments before the Mayor and Miss Bellum shut the lab down for safety violations!

The interaction begins by reading the value of $$$N$$$.

After that, the experiments begin.

For performing an experiment, output $$$(m + 1)$$$ integers $$$(1 \le m \le N)$$$ in a line in the following format (without the quotes):

• "? m $$$c_1 \ c_2 \ \dots \ c_m$$$" $$$(1 \le c_i \le N \text{, where } 1 \le i \le m)$$$

Here, $$$\{c_1, c_2, \dots, c_m\}$$$ are the indices of the $$$m$$$ selected chemicals for the mixture. After each experiment, the judge will respond with:

• "Kaboom", if the experiment causes an explosion, i.e., the indices of Chemical X and Chemical Y are present in $$$\{c_1, c_2, \dots, c_m\}$$$.
• "Noboom", if the experiment doesn't cause an explosion.

After performing at most $$$20$$$ experiments, you must output your final answer in a line in the following format (without the quotes):

• "! x y" $$$(1 \le x \lt y \le N)$$$

Here, $$$x$$$ and $$$y$$$ are the indices of the explosive chemicals.

After printing a line, do not forget to output the end of the line and flush the output. Otherwise, you will get Idleness Limit Exceeded. To flush the output, you can use:

• fflush(stdout) in C;
• fflush(stdout), std::cout.flush() or std::cout « std::flush in C++;
• System.out.flush() in Java;
• sys.stdout.flush() in Python;
• std::io::stdout().flush() in Rust;
• Appropriate flush operation in any language.