4984. Sets

Amuzi is going to play a game with sets.

Firstly, he has a set $A=1,2,3,\dots ,n$ and 2 empty sets $B$ and $C$. He will put some elements in $A$ into $B$ (Note that each element in $A$ will be chosen no more than once). After that, for $\mathrm{\forall }x,y\in B$ , he will put $(x-y)$ into $C$.

Amuzi doesn’t like the number $5$ and $8$, so he doesn’t want these two numbers to be in $C$.

Now Amuzi wants to maximize the size of $B$, can you tell him the maximum size of $B$?