Let $T$ be the triangle in the coordinate plane with vertices $(0,0),(4,0),$ and $(0,3)$. Consider the following five isometries of the plane: rotations of $90^{\circ },180^{\circ },$ and $270^{\circ }$ counterclockwise around the origin, reflection across the line $y=x$, and reflection across the line $y=-x$. How many of the $125$ sequences of three of these transformations (not necessarily distinct) will return $T$ to its original position?