\begin{gather*} |A| = | \{ (1,3),(2,2),(3,1),(1,4),(2,3),(3,2),(4,1) \}| = 7\\ |S| = | \{ (1,1),...,(1,6),(2,1),...,(2,6),...,(6,1),...,(6,6) \}| = 36 \end{gather*}