Given the following file:

$$

$24,8,77,2,61,12,57,13,49,18$

$$

Sort this file by hand using Heapsort and answer the following questions:

$($a$)$ Draw the initial COMPLETE tree representation of the file BEFORE the HEAP is created.

$($b$)$ Draw the initial heap.

$($c$)$ Continue with the sort for two iterations PAST the initial heap $$ i$.$e$.,$ you pop off $77$ and $61$ from the root. NOW RESTRUCTURE THE HEAP AFTER $61$ is popped $$ what is the NEW ROOT?