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.
   • $$$a$$$, $$$b$$$, $$$c$$$ 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 $$$b$$$.