# I bet you can't solve this

Algebra Level 5

The function $$f : \mathbb{N} \to \mathbb{N}$$ satisfies the condition $$f(m+n) \ge f(m)+f(f(n))-1$$ for all $$m,n \in \mathbb{N}$$. Find the sum of all possible values of $$f(2007)$$.

Let this sum be $$k$$. Submit your answer as the sum of digits of $$k$$.

Assumption: $$\mathbb{N}$$ is the set of all positive integers.

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