Perfect Triples
题意翻译
### 题目描述
通过如下方式构造一个无穷数列 $S$:
1. 选择一个字典序最小的有序三元组 $(a,b,c)$ ,且满足 $a,b,c \notin S~, a \oplus b\oplus c=0$。
2. 将 $a,b,c$ 依次加入数列 $S$。
给出一个数 $n$ ,求数列 $S$ 的第 $n$ 项。
### 数据范围
$1\le n\le 10^{16}$
题目描述
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 $ .
输入输出格式
输入格式
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.
输出格式
In each of the $ t $ lines, output the answer to the corresponding test case.
输入输出样例
输入样例 #1
9
1
2
3
4
5
6
7
8
9
输出样例 #1
1
2
3
4
8
12
5
10
15
说明
The first elements of $ s $ are $ 1, 2, 3, 4, 8, 12, 5, 10, 15, \dots $