$=(6,8,10,9,7,5,4,13,23,1,5,7,12,4)$ Heap$-$Sort $(3$ points$)$: Run the HEAP$-$Sort Algorithm on the above array and count up the total number of exchanges $($You can assume the array has already been built as a heap$)$ Write down the initial Max$-$heap array $$ Write down the array after each key exchange in the HEAP$-$Sort. $$ Write down the total number of key exchanges in the HEAP$-$Sort algorithm. $$ No need to illustrate all your steps. Note: Number of exchanges is the number of times that you swap the position of two keys $($Values of the array$)$ until it is a sorted array