Description: This is an interactive problem. There is a hidden permutation $$$p_1, p_2, \dots, p_n$$$. Consider an undirected graph with $$$n$$$ nodes only with no edges. You can make two types of queries: 1. Specify an integer $$$x$$$ satisfying $$$2 \le x \le 2n$$$. For all integers $$$i$$$ ($$$1 \le i \le n$$$) such that $$$1 \le x-i \le n$$$, an edge between node $$$i$$$ and node $$$x-i$$$ will be added. 2. Query the number of edges in the shortest path between node $$$p_i$$$ and node $$$p_j$$$. As the answer to this question you will get the number of edges in the shortest path if such a path exists, or $$$-1$$$ if there is no such path. Note that you can make both types of queries in any order. Within $$$2n$$$ queries (including type $$$1$$$ and type $$$2$$$), guess two possible permutations, at least one of which is $$$p_1, p_2, \dots, p_n$$$. You get accepted if at least one of the permutations is correct. You are allowed to guess the same permutation twice. 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). Input Format: Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^3$$$) — the length of the permutation. It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^3$$$. Output Format: None Note: In the first test case, $$$n=6$$$ and the hidden permutation $$$p = [1,4,2,5,3,6]$$$. Firstly, make a type $$$1$$$ query on $$$x=12, 2, 3$$$ respectively. This adds four edges to the graph in total: - An edge that connects node $$$6$$$ and node $$$6$$$. - An edge that connects node $$$1$$$ and node $$$1$$$. - An edge that connects node $$$1$$$ and node $$$2$$$. - An edge that connects node $$$2$$$ and node $$$1$$$. Since all of these queries are valid, the interactor returns $$$1$$$ after each of them. Then, query the number of edges in the shortest path between node $$$p_1 = 1$$$ and $$$p_3 = 2$$$, which is equal to $$$1$$$. Then, make a type $$$1$$$ query on $$$x=5$$$. This adds four edges to the graph in total: - An edge that connects node $$$1$$$ and node $$$4$$$. - An edge that connects node $$$2$$$ and node $$$3$$$. - An edge that connects node $$$3$$$ and node $$$2$$$. - An edge that connects node $$$4$$$ and node $$$1$$$. Since this query is valid, the interactor returns $$$1$$$. Then, query the number of edges in the shortest path between node $$$p_1 = 1$$$ and $$$p_5 = 3$$$, which is equal to $$$2$$$. Then, query the number of edges in the shortest path between node $$$p_4 = 5$$$ and $$$p_5 = 3$$$. Such a path doesn't exist, therefore the interactor returns $$$-1$$$. Afterwards, due to some magic, two possible permutations that can be $$$p$$$ are determined: the first permutation is $$$[1,4,2,5,3,6]$$$ and the second permutation is $$$[1,2,3,4,5,6]$$$. Since the first permutation is equal to the hidden permutation, this test case is solved correctly. In total, $$$7$$$ queries are used, which is within the limit of $$$2 \cdot 6 = 12$$$ queries. Since the answer is correct, the interactor returns $$$1$$$. In the second test case, $$$n=2$$$ and the hidden permutation is $$$p = [2,1]$$$. Since there are only $$$2! = 2$$$ possible permutations, no queries are needed. It is sufficient to just output the two permutations, $$$[1,2]$$$ and $$$[2,1]$$$. In total, $$$0$$$ queries are used, which is within the limit of $$$2 \cdot 2 = 4$$$ queries. Since the answer is correct, the interactor returns $$$1$$$.