Let \( \gamma = \alpha \times \beta \) where \[ \alpha = \underbrace{999 \cdots 9}_{2010 \text{ '9's}} \] and \[ \beta = \underbrace{444 \cdots 4}_{2010 \text{ '4's}} \] Find the sum of digits of \( \gamma \).

Let's think step by step and output the final answer within \boxed{}.
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