30178번 - Perfect Triples 다국어

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 $b$.

The first line contains a single integer $t$ ($1 \le t \le 10^5$) --- the number of test cases.

Each of the next $t$ lines contains a single integer $n$ ($1\le n \le 10^{16}$) --- the position of the element you want to know.

In each of the $t$ lines, output the answer to the corresponding test case.

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