CF1621C Hidden Permutations

This is an interactive problem. The jury has a permutation $ p $ of length $ n $ and wants you to guess it. For this, the jury created another permutation $ q $ of length $ n $ . Initially, $ q $ is an identity permutation ( $ q_i = i $ for all $ i $ ). You can ask queries to get $ q_i $ for any $ i $ you want. After each query, the jury will change $ q $ in the following way: - At first, the jury will create a new permutation $ q' $ of length $ n $ such that $ q'_i = q_{p_i} $ for all $ i $ . - Then the jury will replace permutation $ q $ with pemutation $ q' $ . You can make no more than $ 2n $ queries in order to quess $ p $ .

The first line of input contains a single integer $ t $ ( $ 1 \leq t \leq 1000 $ ) — the number of test cases.

Interaction in each test case starts after reading the single integer $ n $ ( $ 1 \leq n \leq 10^4 $ ) — the length of permutations $ p $ and $ q $ . To get the value of $ q_i $ , output the query in the format $ ? $ $ i $ ( $ 1 \leq i \leq n $ ). After that you will receive the value of $ q_i $ . You can make at most $ 2n $ queries. After the incorrect query you will receive $ 0 $ and you should exit immediately to get Wrong answer verdict. When you will be ready to determine $ p $ , output $ p $ in format $ ! $ $ p_1 $ $ p_2 $ $ \ldots $ $ p_n $ . After this you should go to the next test case or exit if it was the last test case. Printing the permutation is not counted as one of $ 2n $ queries. 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. It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 10^4 $ . The interactor is not adaptive in this problem. Hacks: To hack, use the following format: The first line contains the single integer $ t $ — the number of test cases. The first line of each test case contains the single integer $ n $ — the length of the permutations $ p $ and $ q $ . The second line of each test case contains $ n $ integers $ p_1, p_2, \ldots, p_n $ — the hidden permutation for this test case.

In the first test case the hidden permutation $ p = [4, 2, 1, 3] $ . Before the first query $ q = [1, 2, 3, 4] $ so answer for the query will be $ q_3 = 3 $ . Before the second query $ q = [4, 2, 1, 3] $ so answer for the query will be $ q_2 = 2 $ . Before the third query $ q = [3, 2, 4, 1] $ so answer for the query will be $ q_4 = 1 $ . In the second test case the hidden permutation $ p = [1, 3, 4, 2] $ . Empty strings are given only for better readability. There will be no empty lines in the testing system.