Let $f$ be a function from all pairs of elements in $\{1,\dots ,n\}$ to $\{1,\dots ,n\}$ such that $f(x,y)\ne x$ and $\ne y$ for all $x,y$. We call $X\subseteq \{1,\dots ,n\}$ independent if whenever $x,y\in X$ we have $f(x,y)\notin X$.Let $g(n)$ be such that, in every function $f$, there is an independent set of size at least $g(n)$. Estimate $g(n)$.