Lucky Number 17!

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

11!+22!+33!+44!++1717! \large 1^{1!} + 2^{2!} + 3^{3!} + 4^{4!} + \cdots + 17^{17!}

Notation:
!! denotes the factorial notation. For example, 10!=1×2×3××1010! = 1\times2\times3\times\cdots\times10 .

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