A tree in a Fibonacci heap is $$path$-$like$$ if all of its nodes lie on a single, downward path from the root. Similarly, a Fibonacci heap is $$path$-$like$$ if and only if it contains exactly one tree and that tree is considered $$path$-$like.$$ For this question, you can assume that the keys associated with the Fibonacci heap are arbitrary integers.

Let H be an i$-$node path$-$like Fibonacci heap, where i $>=2.$ Exhibit a sequence of six Fibonacci heap operations that transforms H into an $($i $+1)-$node path$-$like Fibonacci heap. Be sure to explain and$/$or draw the state of the heap after each step.

NOTE: Inserting elements to a fibonacci heap is LAZY. Simply adding them will not create a path$-$like structure.