Monroe has designed an algorithm for determining the correct sequence of actions necessary to earn a flummox in the competitive board game gottenlieb. Through a bit of analysis, he has determined the algorithm requires $10n$ moves to solve certain initial board states, $5n+2n^2$ moves to solve other initial board states, and $3n+n^2$ move to solve the remaining initial board states. What is the time complexity of his algorithm $($i$.$e$.$ what is $O(n)?$ Why?