Junk Problem - المسألة

#2072. Junk Problem

الإحصائيات

This problem is prepared by bulijiojiodibuliduo .

浏览维基百科并阅读一些随机参考资料是编写题目的最佳方式。

寻找一个子集 $S \in \{1, 2, \dots, n\}$，使得：

对于所有满足 $a, b \in S$ 且 $a < b$ 的数对 $(a, b)$，其按位异或（bitwise XOR）的结果必须互不相同。
$|S| \geq \sqrt{0.5n}$。

输入格式

第一行包含一个整数 $n$ ($1 \leq n \leq 10^7$)。

输出格式

第一行包含一个整数 $m$：集合 $S$ 的大小。第二行包含 $m$ 个从 $1$ 到 $n$ 的不同整数：集合 $S$ 中的元素，顺序不限。

样例

输入 1

输出 1

4
1 2 3 4

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