CF1407C Chocolate Bunny

This 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).

The only line of the input contains a single integer $ n $ ( $ 1 \le n \le 10^4 $ ) — length of the permutation.

The 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 format In 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 $ .