Problem $3.$ In this problem we focus on the BUILD$-$MAX$-$HEAP operation.

Illustrate the operation of BUILD$-$MAX$-$HEAP on the array $A=[6,3,12,9,25,17,4,22,8,5].$

Prove that the running time of the BUILD$-$MAX$-$HEAP operation is $O(nlgn).$ Note, this is not a tight bound.