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 3\,000~

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