# Recursive Digit Sums

Let $$A$$ be a number with 2001 digits such that $$A$$ is a multiple of $$10!$$ Let $$B$$ be the digit sum of $$A$$, $$C$$ be the digit sum of $$B$$, and $$D$$ be the digit sum of $$C$$. What is the unit’s digit of $$D$$?

Details and assumptions

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is $$1 + 1 + 2 + 3 = 7$$.

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