Problem $1$:

$($a$)(12$ pts$)$ The values $16,25,32,19,106,59,12,3,99,42,6,27$ are to be inserted into a MAXheap $($initially empty$).$ Insert the values in the listed order.

Demonstrate the process by drawing the Binary Heap $($tree$)$ after each insertion and verify that the final binary heap will be like this:

$($b$)(3$ pts$)$ List the contents of the Vector that represents the final MAX$-$heap in $($a$).$