CF1754B Kevin and Permutation

For 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.

Each 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.

For 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.

In 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 $ .