Let $S$ be the square in the coordinate plane with vertices $(0,0),(1,0),(1,1),$ and $(0,1)$. Consider the following five isometries of the plane: rotations of $90^{\circ },180^{\circ },$ and $270^{\circ }$ counterclockwise around the origin, reflection across the $x$-axis, and reflection across the $y$-axis. How many of the $25$ sequences of two of these transformations (not necessarily distinct) will return $S$ to its original position?