Assume the complete binary tree numbering scheme used by Heapsort and apply the Heapsort algorithm to the following key sequence $(4,12,5,9,6,2,6).$ Answer the following questions:

$($a$)$ What value is in the root node of the INITIAL STRUCTURE $($NOT HEAP!$)?$

$($b$)$ What value is in location $4$ of the initial HEAP $($The root is at location $1)?$

$($c$)$ After a single deletion $($of the parameter at the heap root$)$ and tree restructuring, what value is in location $4$ of the new HEAP?

$**$ I've seen many questions here of this same problem all with a different answer. ChatGPT has also given me multiple different answers. Please only answer this if you are absolutely sure you have the correct answer, cand an prove your findings. Thank you!