Now generalize this

Algebra Level 4

2×3×4××99\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 nn such that 2n2^n is a factor of the number above.


Inspiration.

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