# Sum of sum

The function $$f(x)$$ is the sum of digits of $$x$$; for example: $$f(24)=6$$, $$f(78)=15$$, and $$f(144)=9$$ (note that $$f(99)=18$$ and not $$1+8=9$$).

Find $$f(1)+f(2)+f(3)+ \cdots + f(1000)$$.

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