CF1338C Perfect Triples

Consider the infinite sequence $ s $ of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers $ (a, b, c) $ such that - $ a \oplus b \oplus c = 0 $ , where $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). - $ a $ , $ b $ , $ c $ are not in $ s $ . Here triple of integers $ (a_1, b_1, c_1) $ is considered to be lexicographically smaller than triple $ (a_2, b_2, c_2) $ if sequence $ [a_1, b_1, c_1] $ is lexicographically smaller than sequence $ [a_2, b_2, c_2] $ . 2. Append $ a $ , $ b $ , $ c $ to $ s $ in this order. 3. Go back to the first step. You have integer $ n $ . Find the $ n $ -th element of $ s $ . You have to answer $ t $ independent test cases. A sequence $ a $ is lexicographically smaller than a sequence $ b $ if in the first position where $ a $ and $ b $ differ, the sequence $ a $ has a smaller element than the corresponding element in $ b $ .

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The first elements of $ s $ are $ 1, 2, 3, 4, 8, 12, 5, 10, 15, \dots $