A circle of radius 1 is randomly placed in a 15-by-36 rectangle $$ABCD$$ so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal $$AC$$ is $$m/n,$$ where $$m$$ and $$n$$ are relatively prime positive integers, find $$m + n.$$

(第二十二届AIME1 2004 第10题)