Give an algorithm that takes as input a binary tree $($or root of such a tree$)$ T$,$ and outputs the root node of the largest $($by total number of nodes$)$ binary search tree S$,$ such that S is a subtree of T$.$ If multiple such trees exist, return the left$-$most such root. What is the runtime of your algorithm? $[$Hint: Write a recursive function that returns multiple values.$]$