An equilateral triangle is inscribed in the ellipse whose equation is $$x^2+4y^2=4$$. One vertex of the triangle is $$(0,1)$$, one altitude is contained in the y-axis, and the length of each side is $$\sqrt{\frac mn}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

(第十九届AIME1 2001 第5题)