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Find the largest non-negative integer nnn such that 2n2^n2n is a factor ⌊2⌋×⌊3⌋×⌊4⌋×⋯×⌊99⌋\left\lfloor\sqrt2\right\rfloor\times\left\lfloor\sqrt3\right\rfloor\times\left\lfloor\sqrt4\right\rfloor\times\cdots\times\left\lfloor\sqrt{99}\right\rfloor⌊2⌋×⌊3⌋×⌊4⌋×⋯×⌊99⌋
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