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

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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