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Argue the correctness of HEAPSORT using the following loop invariant:

At the start of each iteration of the for loop of lines $2–5$,the subarray $A[1..i]$ is a max-heap containing the $i$ smallest elements of $A[1..n] $, and the subarray $A[i+1..n]$ contains the $n- i$ largest elements of $A[1..n]$, sorted.