Q50

There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that

$$x*x=y*y=x*y*x*y=y*x*y*x=e$$

where $e$ is the identity element. The maximum number of elements in such a group is ____.