Below are three different methods for building a max$-$heap. Suppose that A$[1,2,...,$ n$]$ initially contains n elements, which are not necessarily in heap format. You may assume that the value of A$.$heapsize $=$ n$.$ For each method, justify whether the method correctly. builds a max$-$heap. If so$,$ justify your answer. If not, provide an example showing it doesn$$t work. METHOD $1$: Initial call: Make$-$Heap$1($A$,$ n$)$ Make$-$Heap$1($A$,$ i$)$ If i $>1$ Bubble$-$up$($A$,$i$)$ Make$-$Heap$1($A$,$i $1)$ METHOD $2$: Initial call: Make$-$Heap$2($A$,$ n$)$ Make$-$Heap$2($A$,$ i$)$ If i $1$ Bubble$-$down$($A$,$i$)$ Make$-$Heap$2($A$,$i $1)$ METHOD $3$: Initial call: Make$-$Heap$3($A$,1)$ Make$-$Heap$3($A$,$ i$)$ If i $$ A$.$heapsize Bubble$-$up$($A$,$i$)$ Make$-$Heap$3($A$,$i $+1)$