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 $

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 $1\le n\le 10^{16}$