B. Shrink
constructive algorithms
A shrink operation on an array \(a\) of size \(m\) is defined as follows: Choose an index \(i\) (\(2 \le i \le m - 1\)) such that \(a_i \gt a_{i - 1}\) and \(a_i \gt a_{i + 1}\). Remove \(a_i\) from the array. Define the score of a permutation\(^{\text{∗}}\) \(p\) as the maximum number of times that you can perform the shrink operation on \(p\).Yousef has given you a single integer \(n\). Construct a permutation \(p\) of length \(n\) with the maximum possible score. If there are multiple answers, you can output any of them.\(^{\text{∗}}\)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).
The first line of the input contains an integer \(t\) (\(1 \le t \le 10^3\)) — the number of test cases.Each test case contains an integer \(n\) (\(3 \le n \le 2 \cdot 10^5\)) — the size of the permutation.It is guaranteed that the sum of \(n\) over all test cases does not exceed \(2 \cdot 10^5\).
For each test case, output any permutation \(p_1, p_2, \dots, p_n\) that maximizes the number of shrink operations.
In the first test case: We choose \(p = [1, 3, 2]\). Choose index \(2\), and remove \(p_2\) from the array. The array becomes \(p = [1, 2]\). It can be shown that the maximum number of operations we can perform is \(1\). Another valid answer is \(p = [2, 3, 1]\).In the second test case: We choose \(p = [2, 3, 6, 4, 5, 1]\). Choose index \(5\), and remove \(p_5\) from the array. The array becomes \(p = [2, 3, 6, 4, 1]\). Choose index \(3\), and remove \(p_3\) from the array. The array becomes \(p = [2, 3, 4, 1]\). Choose index \(3\), and remove \(p_3\) from the array. The array becomes \(p = [2, 3, 1]\). Choose index \(2\), and remove \(p_2\) from the array. The array becomes \(p = [2, 1]\). The maximum number of operations we can perform is \(4\). Any permutation with a score of \(4\) is valid.