The function $f: \mathbb{N} \to \mathbb{N}_0$ is defined such that:
- $f(2) = 0$
- $f(3) > 0$
- $f(6042) = 2014$
- For all $m, n \in \mathbb{N}$, $f(m + n) - f(m) - f(n) \in \{0, 1\}$

Determine $f(2014)$.

Note: $\mathbb{N}_0 = \{0, 1, 2, \ldots\}$

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