A $3-$max$-$heap is a like a max heap, except that all of the non$-$leaf children have $3$ children

$($except possibly for the right most node on the second to last level$).$

a$)$ Give an efficient REMOVE algorithm for $3-$max$-$heaps, and analyze it's running time.

b$)$ Write an efficient algorithm to convert a $3-$max$-$heap to a max heap, and analyze it's running

time

c$)$ If we use a $3-$max$-$heap to define a sorting algorithm, what is the big$-$O efficiency? Explain if

this is better, worse, or equivalent to regular heap sort.