Algebra Level 5

$x^{2016} + (2016!+1!)x^{2015} + (2015!+2!)x^{2014} + \cdots + (1!+2016!) = 0$

Find the number of integer solutions to the equation above.

Notation: $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$.

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