The SET game is a deck with $81$ unique cards that vary in four features across three possibilities for each kind of feature: shape (oval, squiggle or diamond), color (red, green or purple), number of shapes (one, two or three) and shading (solid, striped or open). A $\textbf{set}$ consists in three cards whose characteristics, when considered individually, are the same on each card or different on all of them. All features have to satisfy this rule. In other words: the shape must be the same on all three cards or different on all them, the color must be the same on the three cards or different on all them, and so on. Ana and Bárbara divided among themselves the $81$ SET cards. Ana got $40$ cards and Bárbara got $41$. Each girl counted the number of ways she could form a three-card $\textbf{set}$ with her cards. What are the possible values of the sum of these two numbers?