$(30$ pts$)$ Sort the following lists by heapsort by using the array representation of heaps. You should provided a similar diagram shown in Figure $6\mathrm{.}14,$

a$.1,2,3,4,5($in increasing order$)$

b$.5,4,3,2,1($in increasing order$)$

c$.$ S$,$ O$,$ R$,$ T$,$ I, N$,$ G $($in alphabetical order$)$