What is the units digit of $\sum\limits_{n=1}^{1337} (n!)^4$?

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What is the units digit of $\sum\limits_{n=1}^{1337}(n!)^4$ ? I find 9 but I am not sure.

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Hint

In mod $10$ we have $n!=0$ for $n\ge5$.

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Hint: consider $\pmod{10}$. What is $5! \pmod{10}$?