In isosceles triangle $$ABC$$, $$A$$ is located at the origin and $$B$$ is located at (20,0). Point $$C$$ is in the first quadrant with $$AC = BC$$ and angle $$BAC = 75^{\circ}$$. If triangle $$ABC$$ is rotated counterclockwise about point $$A$$ until the image of $$C$$ lies on the positive $$y$$-axis, the area of the region common to the original and the rotated triangle is in the form $$p\sqrt{2} + q\sqrt{3} + r\sqrt{6} + s$$, where $$p,q,r,s$$ are integers. Find $$(p-q+r-s)/2$$.

(第二十五届AIME1 2007 第12题)