Consider the shape formed from taking equilateral triangle A B C with side length 6 and tracing out the arc B C with center A. Set the shape down on line l so that segment A B is perpendicular to l, and B touches l. Beginning from arc B C touching l, We roll A B C along l until both points A and C are on the line. The area traced out by the roll can be written in the form n \pi, where n is an integer. Find n.