Given an array A $=<7,6,5,4,3,2,1>,$ apply the bottom$-$up heap construction algorithm buildMinHeap$($A$,7)$ to transform it into a min$-$heap. Please show the updated array after each swap made during the downHeap procedure.

Follow the pseudocode provided from M$6$ slides:

buildMinHeap$($A$,$ n$)$

for i $=($n$/2-1)$ down to $0$

downHeap$($A$,$ i$)$

downHeap$($A$,$ i$)$

smallest $=$ index of the smallest element among

A$[$i$]$ and its two children

if smallest $!=$ i

swap A$[$i$]$ with A$[$smallest$]$

downHeap$($A$,$ smallest$)$