In a $2-3-4$ tree $,$ a node can have $2$ keys, $3$ keys $($full node$),$ and $4$ keys. In addition, it is a self$-$balanced tree. To solve the problem, consider how each split changes the potential. How does an insert operation change the potential?You may start with defining a potential function as $,$ where denotes the the number of nodes in with three keys and denotes the number of nodes in with two keys. The potential function is initially $0$ and is always nonnegative. Note that the presentation contains the true cost and the change in potential. Think of "cost" as "number of splits".Perform a split on a full node $.$ Analyze the potential by $(1)$ if $\text{'}$s parent has $0$ keys $($i$.$e$.,$ is the root$)(2)$ if $\text{'}$s parent has $1$ key $(2)$ if $\text{'}$s parent has $2$ keys.Perform an insert operation on and the actual number of splits is $.$