A circle with radius 1 and center (0,1) lies on the coordinate plane. Ariel stands at the origin and rolls a ball of paint at an angle of 35 degrees relative to the positive x-axis (counting degrees counterclockwise). The ball repeatedly bounces off the circle and leaves behind a trail of paint where it rolled. After the ball of paint returns to the origin, the paint has traced out a star with n points on the circle. What is n?