CF2189C1 XOR Convenience (Easy Version)
Description
This is the easy version of the problem. The difference between the versions is that in this version, $ 2 \le i \le n-1 $ . Note that a correct solution for the hard version is not necessarily a correct solution for the easy version.
Given a natural number $ n $ . Find a permutation $ ^{\text{∗}} $ $ p $ of length $ n $ , such that for each $ i $ ( $ \style{color:red}{2 \le i \le n-1} $ ) there exists a $ j $ ( $ \style{color:red}{i \le j \le n} $ ) such that $ p_i = p_j \oplus i $ $ ^{\text{†}} $ .
It can be proven that under the constraints of the problem, there exists at least one suitable permutation $ p $ .
$ ^{\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).
$ ^{\text{†}} $ $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
Input Format
Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows.
The only line of each test case contains a single integer $ n $ ( $ 3 \leq n \leq 2 \cdot 10^5 $ ) — the length of the permutation.
It is guaranteed that the sum of $ n $ across all test cases does not exceed $ 2\cdot 10^5 $ .
Output Format
For each test case, output $ n $ integers $ p_1,p_2,\ldots,p_n $ — the permutation $ p $ .
If there are multiple solutions, you may output any of them.
Explanation/Hint
In the first test case, the permutation $ p = [2,1,3] $ is suitable since $ p_2 = 1 $ and $ p_3 \oplus 2 = 1 $ .
In the second test case, the permutation $ p = [3,6,2,5,1,4] $ is suitable, as:
- $ p_2 = 6 = 4 \oplus 2 = p_6 \oplus 2 $
- $ p_3 = 2 = 1 \oplus 3 = p_5 \oplus 3 $
- $ p_4 = 5 = 1 \oplus 4 = p_5 \oplus 4 $
- $ p_5 = 1 = 4 \oplus 5 = p_6 \oplus 5 $