$(45$ pts$)$ Construct a heap for the list $7,8,10,13,15,6,20,3,17$ by the bottom$-$up algorithm we learned in the class. Suppose that the elements are stored in an array. That is$,$ initial values of the array, $A,$ is filled up as follows in the beginning:

$A[0]=7,A[1]=8,A[2]=10,A[3]=13,A[4]=15,A[5]=6,A[6]=20,A[7]=3,A[8]=17.$

Find out the array values after you apply the heapify algorithm.

$($a$)A[0]=$

$($b$)A[1]=$

$($c$)A[2]=$

$($d$)A[3]=$

$($e$)A[4]=$

$($f$)A[5]=$

$($g$)A[6]=$

$($h$)A[7]=$

$($i$)A[8]=$