AT_arc217_a [ARC217A] Min of Sum of XOR

You are given a positive integer $ N $ . Find one permutation $ P=(P_1,P_2,\ldots,P_N) $ of $ (1,2,\ldots,N) $ that minimizes $ \displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j $ . Here, $ \displaystyle \bigoplus_{1\le j\le i} P_j $ is defined as the bitwise $ \mathrm{XOR} $ of $ P_1,P_2,\ldots,P_i $ . You are given $ T $ test cases; solve each of them. What is bitwise $ \mathrm{XOR} $ ? The bitwise $ \mathrm{XOR} $ of non-negative integers $ A $ and $ B $ , $ A \oplus B $ , is defined as follows. - In the binary representation of $ A \oplus B $ , the digit at the $ 2^k $ ( $ k \geq 0 $ ) place is $ 1 $ if exactly one of the digits at the $ 2^k $ place in the binary representations of $ A $ and $ B $ is $ 1 $ , and $ 0 $ otherwise. For example, $ 3 \oplus 5 = 6 $ (in binary: $ 011 \oplus 101 = 110 $ ). In general, the bitwise $ \mathrm{XOR} $ of $ k $ non-negative integers $ p_1, p_2, p_3, \dots, p_k $ is defined as $ (\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k) $ , and it can be proved that this does not depend on the order of $ p_1, p_2, p_3, \dots, p_k $ .

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ N $

Output the answers for the test cases in order, separated by newlines. For each test case, output a permutation $ P=(P_1,P_2,\ldots,P_N) $ of $ (1,2,\ldots,N) $ that minimizes $ \displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j $ , separated by spaces. If there are multiple permutations $ P $ that achieve the minimum, any of them will be accepted.

### Sample Explanation 1 Consider the first test case. If $ P=(1,3,2) $ , then $ \displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j=1 + (1 \oplus 3) + (1 \oplus 3 \oplus 2) = 1+2+0=3 $ . The value of $ \displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j $ cannot be made less than $ 3 $ , so outputting $ P=(1,3,2) $ is correct. Outputting $ P=(2,3,1) $ is also correct. ### Constraints - $ 1\le T\le 10^3 $ - $ 1\le N $ - The sum of $ N $ over all test cases is at most $ 2\times 10^5 $ . - All input values are integers.