Round-up and round-down

\[ \large f(n)=\left\lfloor\dfrac{n}{\left\lfloor \sqrt{n}\right\rfloor}\right\rfloor \qquad, \qquad g(n)=\left\lceil\dfrac{n}{\left\lceil \sqrt{n}\right\rceil}\right\rceil\]

For positive integer \(n\), define functions \(f\) and \(g\) as above.

How many positive integers \(n\) less than 2015 such that \(f(n)\neq g(n)\)?

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