Steven, the monkey, is baking banana bread today!

The recipe for banana bread calls for $N$ ingredients numbered from $1$ to $N$. The recipe can be modelled as an array $A$ of length $N$, where $A_i$ describes the amount for ingredient $i$. Moreover, Steven's special banana bread recipe is a permutation of the first $N$ positive integers!

Unfortunately, Steven lost the recipe and doesn't remember the ordering!

Fortunately, Steven had sent his recipe to his friend Tony for safekeeping. However, being a monkey, Tony obfuscated the recipe and tells Steven that he can only ask for the number of inversions present in some subarray of array $A$ from $l$ to $r$ inclusive satisfying $1\le l<r\le N$. Due to how impatient Tony is, he informs Steven that he can only ask up to $N$ questions. Help Steven recover the recipe so he can have dessert tonight!

A pair of indices $i$ and $j$ in the array $A$ is considered an inversion if $i<j$ and $A[i]>A[j]$.

Constraints

$1\le N\le 3000$

Array $A$ is a permutation of the first $N$ positive integers.

Interaction

This is an interactive problem.

You will start by reading in a single integer $N$, the number of ingredients in the bread.

Note: The grader is NOT adaptive.

After reading $N$, you can start interacting with the interactor.

To ask a query, you must output in the form ? l r to standard output. You will then read a single integer from standard input, which is the number of inversions in the contiguous subarray from $l$ to $r$.

To validate your final answer, you must output ! followed by a space, then $N$ space-separated numbers, which are the elements of the array $A$. Your program should then terminate immediately.

The output must be flushed after every line is printed, including the last line. In C/C++, you can use fflush(stdout) or cout << endl, in Java you can use System.out.flush(), and in Python you can use sys.stdout.flush().

At any time, if you ask an invalid query or exceed $N$ queries, the interactor will print -1. Once you read -1, terminate your program immediately and you will receive a Wrong Answer verdict. Failure to terminate your program may result in an undefined result.

Sample Interaction 1

Note: Do not actually print out <<< and >>>. >>> means that the interactor printed out the line, and <<< means that you printed out the line.

>>> 5
<<< ? 3 4
>>> 0
<<< ? 1 5
>>> 5
<<< ? 2 4
>>> 0
<<< ! 3 2 4 5 1

Explanation for Sample Interaction 1

Our array is $[3,2,4,5,1]$ and there are $5$ inversions. The pairs of indices that form inversions are $(1,2),(1,5),(2,5),(3,5),(4,5)$.

Sample Interaction 2

>>> 3
<<< ? 1 2
>>> 0
<<< ! 1 2 3