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Omni-MATH / When 4444⁴⁴⁴⁴ is written in decimal notation, the sum of its digits is A. Let B be the sum of the digits of A. Find the sum of the digits of B. (A and B are written in decimal nota…

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problem

When 444444444444^{4444} is written in decimal notation, the sum of its digits is A. A. Let BB be the sum of the digits of A.A. Find the sum of the digits of B. B. (AA and BB are written in decimal notation.)
Plain-text mathematical notation (without MathML)
When 4444⁴⁴⁴⁴ is written in decimal notation, the sum of its digits is A. Let B be the sum of the digits of A. Find the sum of the digits of B. (A and B are written in decimal notation.)
Original LaTeX notation
When $4444^{4444}$ is written in decimal notation, the sum of its digits is $ A.$ Let $B$ be the sum of the digits of $A.$ Find the sum of the digits of $ B.$ ($A$ and $B$ are written in decimal notation.)

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