Use your inequalities!

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

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