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$\large S= \dfrac{2^2+1}{2^2-1}+\dfrac{3^2+1}{3^2-1}+ \ldots + \dfrac{2016^2+1}{2016^2-1}$

If $S$ denotes the value of the above expression, then find the value of $\lfloor S \rfloor + 2016$ .

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