Now generalize this

Algebra Level 4

\[\large\left\lceil\sqrt2\right\rceil\times\left\lceil\sqrt3\right\rceil\times\left\lceil\sqrt4\right\rceil\times\cdots\times\left\lceil\sqrt{99}\right\rceil\]

Find the largest non-negative integer \(n\) such that \(2^n\) is a factor of the number above.


Inspiration.

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