Really Really Troublesome

Number Theory Level pending

Find the unit's place of the following expression:

\[11^{1! + 2! + ... + 10!} + 12^{1! + 2! + ... + 10!} + \cdots + 19^{1! + 2! + ... + 10!} + 20^{1! + 2! + ... + 10!} \]

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