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