Algebra Level 3

Find the least positive integer value of $$n$$ such that for any $$n$$ positive reals $$a_{1},a_{2},\ldots,a_{n}$$, we have

$\dfrac{a_{1}^2+1}{a_{1}}+\dfrac{a_{2}^2+1}{a_{2}}+\cdots +\dfrac{a_{n}^2+1}{a_{n}} \geq 2016.$

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