$(12$ points$)$ Suppose that we have the following series of key values: $7,16,49,82,5,31,6.$

$($a$)(7$ pts$.)$ Write out the min heap after each value is inserted into the heap.

$($b$)(3$ pts$.)$ Write out the min heap after each of the three numbers are deleted.

$($c$)(2$ pts$.)$ Write out the binary search tree with all the threads after each value is inserted into the

tree.