When is written in decimal notation, the sum of its digits is Let be the sum of the digits of Find the sum of the digits of ( and are written in decimal notation.)
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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.)
Izvor: Međunarodna matematička olimpijada, shortlist 1975
Školjka 
is written in decimal notation, the sum of its digits is 
Let 
be the sum of the digits of 
(
and