# Intersection points, part 2

Algebra Level 5

$f(x)=-\frac{1}{10}\left(x^3+3x^2+4x-18\right)$

Given that the graphs of $$f$$ and its inverse $$f^{-1}$$ intersect at 5 points, denoted as $$(a_i,b_i)$$ for $$i=1,2,3,4,5$$.

Let $$\displaystyle S=\sum_{i=1}^{5} |a_i|$$. Find $$\displaystyle \left \lfloor 1000S\right \rfloor$$.

 Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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