HMMT 2016 C8

Let $X$ be the collection of all functions $f:\{0,1, \ldots, 2016\} \rightarrow\{0,1, \ldots, 2016\}$. Compute the number of functions $f \in X$ such that

$$\max _{g \in X}\left(\min _{0 \leq i \leq 2016}(\max (f(i), g(i)))-\max _{0 \leq i \leq 2016}(\min (f(i), g(i)))\right)=2015 .$$