Do I Know a Number Other Than 4?

When (4444)4444(4444)^{4444} is written in decimal notation, the sum of its digits is AA. Let BB be the sum of the digits of AA. Find the digital sum of B.B.

(Note: A digital sum means you take the sum of the digits, and then if more than one digit remains, take the sum again, and keep repeating until only one digit remains.)

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