HEAPSORT (A) 1 BUILD-MAX-HEAP(A) 2 for i -A.length downto 2 3 exchange A1] vith ACi] 4 A.heap-size -A.heap-size 1 MAX-HEAPIFY(A,1) 4 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[i..i] is a max-heap containing the i smallest elements of A[1. . n] and the subarray Ali+1..1] contains the n-i largest elements of A[1..n] sorted