A13432. 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 $b$ .

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 $