Only real roots!

Algebra Level 3

k=1999(x247x+k)=(x247x+1)(x247x+2)(x247x+999)\prod_{k=1}^{999} (x^2-47x+k) = (x^2-47x+1)(x^2-47x+2)\dots(x^2-47x+999)

If the product of all real roots of the polynomial above can be expressed in the form n!n!, what is the value of nn?

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