For natural number $n$, define the function $f(n)$ to be the number you get by adding the digits of the number $n$. For example, $f(16) = 7$, $f(f(78)) = 6$, and $f(f(f(5978))) = 2$. Find the least natural number $n$ such that $f(f(f(n)))$ is not a one-digit number.

Source: Purple Comet Math Meet, High School Round, 2008

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