2019 AMC 10A Problem 24

Let p, q, and r be the distinct roots of the polynomial x^3 - 22x^2 + 80x - 67. It is given that there exist real numbers A, B, and C such that \dfrac{1}{s^3 - 22s^2 + 80s - 67} = \dfrac{A}{s-p} + \dfrac{B}{s-q} + \frac{C}{s-r}for all s\notin\{p,q,r\}. What is \tfrac1A+\tfrac1B+\tfrac1C?

\textbf{(A) }243\qquad\textbf{(B) }244\qquad\textbf{(C) }245\qquad\textbf{(D) }246\qquad\textbf{(E) } 247

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.