Consider the parallelogram with vertices $$(10,45),$$ $$(10,114),$$ $$(28,153),$$ and $$(28,84).$$ A line through the origin cuts this figure into two congruent polygons. The slope of the line is $$m/n,$$ where $$m_{}$$ and $$n_{}$$ are relatively prime positive integers. Find $$m+n.$$

(第十七届AIME1999 第2题)