# $$\frac{1000}{1}$$! Oops

Algebra Level 4

Let $$s_n$$ be the sum of the digits of a natural number $$n$$. If $$\dfrac ab$$ satisfies the condition of the smallest value of $$\dfrac n{s_n}$$, where $$n$$ is a four-digit number, find $$a+b$$.

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