$3.$ A three$-$heap with $\backslash ($ n $\backslash )$ elements can be stored in an array A$,$ where $\backslash (\backslash$underline$\{$A$\}[0]\backslash )$ contains the root of the tree.

a$.$ Draw the three$-$heap that results from inserting $\backslash (5,2,8,3,6,4,9,7,1\backslash )$ in that order into an initially empty three$-$heap. You do not need to show the array representation of the heap. You are only required to show the final tree, although you draw intermediate trees.

b$.$ Assuming that elements are placed in the array starting at location A$[0],$ give expressions to calculate the left, middle, and right children of the element stored in $\backslash (\backslash$mathrm$\{$A$\}[$i$]$: $\backslash )$

Left child:

Middle child:

Right child:

c$.$ Draw the array representation of your heap from part b$.$