Lucky Number 17!

Find the remainder when the number below is divided by 17.

\[ \large 1^{1!} + 2^{2!} + 3^{3!} + 4^{4!} + \cdots + 17^{17!} \]

Notation:
\(!\) denotes the factorial notation. For example, \(10! = 1\times2\times3\times\cdots\times10 \).

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