Two mirrors (represented by line segments in the plane) each have length 1 meter. They are joined such that one endpoint of one mirror coincides with one endpoint of the other mirror at the point $$A$$ and such that the angle between the mirrors is 1 degree. Let points $$B$$ and $$C$$ be the remaining two endpoints which are not joined. A light source that emits light in all directions is placed at point $$P$$ within triangle $$ABC$$. Find the maximum number of times a light ray can bounce off of $$AB$$ and/or $$AC$$ before intersecting $$BC$$. (For example, one such light ray can bounce off of $$AB$$, then $$AC$$, then $$AB$$ again, then $$AC$$ again, then $$AB$$ again, and touch $$BC$$; this light ray would have bounced off of $$AB$$ and/or $$AC$$ 5 times.)