# 2016? Nah I Choose 4016!

$a+\dfrac{1}{b+\dfrac{1}{c}} = \frac{4016}{2007} , \qquad \dfrac{1}{c+\dfrac{1}{b+\dfrac{1}{a}}} = \dfrac{p}{q}$

Positive integers $$a,b,c,p$$ and $$q$$ satisfy the system of equations above. If $$p$$ and $$q$$ are coprime, submit your answer as $$p+q$$.

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