Score : $400$ points

Problem Statement

This is an interactive task, where your program and the judge interact via Standard Input and Output.

The judge has a string of length $N$ consisting of $0$ and $1$: $S = S_1S_2\ldots S_N$. Here, $S_1 = 0$ and $S_N = 1$.

You are given the length $N$ of $S$, but not the contents of $S$. Instead, you can ask the judge at most $20$ questions as follows.

• Choose an integer $i$ such that $1 \leq i \leq N$ and ask the value of $S_i$.

Print an integer $p$ such that $1 \leq p \leq N-1$ and $S_p \neq S_{p+1}$. It can be shown that such $p$ always exists under the settings of this problem.

Constraints

• $2 \leq N \leq 2 \times 10^5$

Input and Output

First, receive the length $N$ of the string $S$ from Standard Input:

N

Then, you get to ask the judge at most $20$ questions as described in the problem statement.

Print each question to Standard Output in the following format, where $i$ is an integer satisfying $1 \leq i \leq N$:

? i

In response to this, the value of $S_i$ will be given from Standard Input in the following format:

S_i

Here, $S_i$ is $0$ or $1$.

When you find an integer $p$ satisfying the condition in the problem statement, print it in the following format, and immediately quit the program:

! p

If multiple solutions exist, you may print any of them.

Notes

• Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.
• If there is malformed output during the interaction or your program quits prematurely, the verdict will be indeterminate.
• After printing the answer, immediately quit the program. Otherwise, the verdict will be indeterminate.
• The string $S$ will be fixed at the start of the interaction and will not be changed according to your questions or other factors.

Sample Input and Output

In the following interaction, $N = 7$ and $S = 0010011$.

For the presented $p = 5$, we have $1 \leq p \leq N-1$ and $S_p \neq S_{p+1}$. Thus, if the program immediately quits here, this case will be judged as correctly solved.