C. Chocolate Bunnytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an interactive problem.We hid from you a permutation p of length n, consisting of the elements from 1 to n. You want to guess it. To do that, you can give us 2 different indices i and j, and we will reply with p_{i} \bmod p_{j} (remainder of division p_{i} by p_{j}).We have enough patience to answer at most 2 \cdot n queries, so you should fit in this constraint. Can you do it?As a reminder, a permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).InputThe only line of the input contains a single integer n (1 \le n \le 10^4) — length of the permutation.InteractionThe interaction starts with reading n. Then you are allowed to make at most 2 \cdot n queries in the following way:   "? x y" (1 \le x, y \le n, x \ne y). After each one, you should read an integer k, that equals p_x \bmod p_y. When you have guessed the permutation, print a single line "! " (without quotes), followed by array p and quit.After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use: fflush(stdout) or cout.flush() in C++; System.out.flush() in Java; flush(output) in Pascal; stdout.flush() in Python; see documentation for other languages.Exit immediately after receiving "-1" and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.Hack formatIn the first line output n (1 \le n \le 10^4). In the second line print the permutation of n integers p_1, p_2, \ldots, p_n.ExampleInput
3

1

2

1

0Output
? 1 2

? 3 2

? 1 3

? 2 1

! 1 3 2
3

1

2

1

0
? 1 2  ? 3 2  ? 1 3  ? 2 1  ! 1 3 2
['constructive algorithms', 'interactive', 'math', 'two pointers', '*1600']