The number is so cute

\[\large N = \color{red}{1!} \cdot \color{orange}{2!} \cdot \color{yellow}{3!} \cdot \color{green}{4!} \cdot \color{blue}{5!} \cdots \color{magenta}{2015!} \cdot \color{purple}{2016!} \cdot \color{black}{2017!}\]

How many trailing number of zeros does \(N\) have?

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

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