Question 89
Let $M \subseteq \{1, 2, \dots, 2011\}$ be a subset satisfying the following condition: For any three elements in $M$, there exist two of them $a$ and $b$, such that $a \mid b$ or $b \mid a$. Determine, with proof, the maximum value of $|M|$, where $|M|$ denotes the number of elements of $M$. (posed by Feng Zhigang)