Let $f$ be a function defined on the set of positive integers, with values in the same set, which satisfies:

- $f(n + f(n)) = 1$ for all $n \ge 1$.
- $f(1998) = 2$

Find the lowest possible value of the sum $f(1) + f(2) + \ldots + f(1999)$, and find the formula of $f$ for which this minimum is satisfied.

Let's think step by step and output the final answer within \boxed{}.
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