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Let $p$ , $q$ , and $r$ be the distinct roots of the polynomial $x^{3} - 20 x^{2} + 90 x - 100$ . It is given that there exist real numbers $A$ , $B$ , and $C$ such that

\frac{1}{s ^{3} - 20 s ^{2} + 90 s - 100} = \frac{A}{s - p} + \frac{B}{s - q} + \frac{C}{s - r}

for all $so t \in p, q, r$ . What is $\frac{1}{A} + \frac{1}{B} + \frac{1}{C}$ ?