# Good Triangles In a Convex 2014 Sided Polygon

Consider a convex polygon $$P$$ with 2014 sides no four of whose vertices lie on a circle. A triangle with its vertices among the vertices of $$P$$ is said to be good if all remaining 2011 vertices lie outside the circumcircle of that triangle. Find the number of good triangles.

Note: This problem is not original.

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