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D - Find by Query

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