CF1338C.Perfect Triples

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

Consider the infinite sequence $s$ of positive integers, created by repeating the following steps:

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 $b$ .

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#1
```
9
1
2
3
4
5
6
7
8
9
```
输出#1
```
1
2
3
4
8
12
5
10
15
```

说明/提示

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

首页