The problems below are to be solved by paper$-$and$-$pencil. This is not a programming assignment. Your work will likely spread over a good number of pages; use as much of your own paper as needed and submit a scan of your pages.

Problem $1$:

$($a$)(12$ pts$)$ The values $\backslash (16,25,32,19,106,59,12,3,99,42,6,27\backslash )$ 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$).$