B. Guess an array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

This is an interactive problem.

You are given a sorted array $$$a$$$ of length $$$n$$$ in non-decreasing order. Array elements do not exceed $$$n$$$. You only know the length of the array. Using no more than $$$2 \cdot n$$$ queries, you need to guess the entire array. Queries can be made of the following type: «? i x», where $$$1 \leq i \leq n$$$ and $$$x$$$ is an integer. The jury will respond as follows:

  • = if $$$a_i = x$$$,
  • > if $$$x \gt a_i$$$,
  • < if $$$x \lt a_i$$$.

After you determine the array, you must output it as follows: «! $$$a_1$$$ $$$a_2$$$ ... $$$a_n$$$», where $$$a_1, a_2, \ldots, a_n$$$ are the elements of the array that you guessed.

Input

The only line of input contains a single integer $$$n$$$ $$$(1 \leq n \leq 3000)$$$ - the size of the array.

Output

Output your answer in the format «! $$$a_1$$$ $$$a_2$$$ ... $$$a_n$$$».

Interaction
  1. Output your queries in the format «? i x».
  2. The jury will respond with one of three characters: «=» if $$$a_i = x$$$, «>» if $$$x \gt a_i$$$, or «<» if $$$x \lt a_i$$$.
  3. Output your answer in the format «! $$$a_1$$$ $$$a_2$$$ ... $$$a_n$$$».
Example
Input
3

=

> 

>

=

=
Output
? 1 1

? 1 2

? 2 3

? 2 2

? 3 3

! 1 2 3