2016 and factorial 2

Number Theory Level 4

Find the sum of all of perfect squares that can be expressed as form $$\displaystyle \left(\sum_{i=1}^m i! \right)+2016$$.

If you think that no perfect square satisfies this condition, or there are infinitely many perfect squares that satisfy this condition, submit your answer as 999.

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

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