B. Kevin and Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputFor his birthday, Kevin received the set of pairwise distinct numbers 1, 2, 3, \ldots, n as a gift.He is going to arrange these numbers in a way such that the minimum absolute difference between two consecutive numbers be maximum possible. More formally, if he arranges numbers in order p_1, p_2, \ldots, p_n, he wants to maximize the value \min \limits_{i=1}^{n - 1} \lvert p_{i + 1} - p_i \rvert, where |x| denotes the absolute value of x.Help Kevin to do that.InputEach test consists of multiple test cases. The first line contains a single integer t (1 \le t \le 100) — the number of test cases. Description of the test cases follows.The only line of each test case contains an integer n (2 \le n \leq 1\,000) — the size of the set.OutputFor each test case print a single line containing n distinct integers p_1, p_2, \ldots, p_n (1 \le p_i \le n) describing the arrangement that maximizes the minimum absolute difference of consecutive elements. Formally, you have to print a permutation p which maximizes the value \min \limits_{i=1}^{n - 1} \lvert p_{i + 1} - p_i \rvert.If there are multiple optimal solutions, print any of them.ExampleInput
243Output
2 4 1 3
1 2 3
NoteIn the first test case the minimum absolute difference of consecutive elements equals \min \{\lvert 4 - 2 \rvert, \lvert 1 - 4 \rvert, \lvert 3 - 1 \rvert \} = \min \{2, 3, 2\} = 2. It's easy to prove that this answer is optimal.In the second test case each permutation of numbers 1, 2, 3 is an optimal answer. The minimum absolute difference of consecutive elements equals to 1.
243
2 4 1 3 1 2 3 
['constructive algorithms', 'greedy', 'math', '*800']