While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of $$x$$ for which the sine of $$x$$ degrees is the same as the sine of $$x$$ radians are $$\frac{m\pi}{n-\pi}$$ and $$\frac{p\pi}{q+\pi}$$, where $$m$$, $$n$$, $$p$$, and $$q$$ are positive integers. Find $$m+n+p+q$$.

(第二十届AIME2 2002 第10题)