CF1930B Permutation Printing

You are given a positive integer $ n $ . Find a permutation $ ^\dagger $ $ p $ of length $ n $ such that there do not exist two distinct indices $ i $ and $ j $ ( $ 1 \leq i, j < n $ ; $ i \neq j $ ) such that $ p_i $ divides $ p_j $ and $ p_{i+1} $ divides $ p_{j+1} $ . Refer to the Notes section for some examples. Under the constraints of this problem, it can be proven that at least one $ p $ exists. $ ^\dagger $ 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).

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^3 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 3 \leq n \leq 10^5 $ ) — the length of the permutation $ p $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, output $ p_1, p_2, \ldots, p_n $ . If there are multiple solutions, you may output any one of them.

In the first test case, $ p=[4,1,2,3] $ is a valid permutation. However, the permutation $ p=[1,2,3,4] $ is not a valid permutation as we can choose $ i=1 $ and $ j=3 $ . Then $ p_1=1 $ divides $ p_3=3 $ and $ p_2=2 $ divides $ p_4=4 $ . Note that the permutation $ p=[3, 4, 2, 1] $ is also not a valid permutation as we can choose $ i=3 $ and $ j=2 $ . Then $ p_3=2 $ divides $ p_2=4 $ and $ p_4=1 $ divides $ p_3=2 $ . In the second test case, $ p=[1,2,3] $ is a valid permutation. In fact, all $ 6 $ permutations of length $ 3 $ are valid.