B. Permutation Printingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputEach 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.OutputFor each test case, output p_1, p_2, \ldots, p_n.If there are multiple solutions, you may output any one of them.ExampleInput
243Output
4 1 2 3
1 2 3
NoteIn 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.
243
4 1 2 3 1 2 3 
['brute force', 'constructive algorithms', 'math', '*1000']