$1.[3$ points$]$ Put the letters C A H N M R B in a binary search tree, without balancing, and show the result.

$2.[4$ points$]$ Put the letters C A H N M R B in an AVL binary and show the result.

$3.[3$ points$]$ Put the letters C A H M M B in a min$-$heap using up$-$heap bubbling and show the result.

$4.[3$ points$]$ Put the letters Z B Q L R C in this max$-$heap $($Figure $1)$ and show the result.

Figure $1$

$5.[4$ points$]$ Remove the top letter in this max$-$heap $($Figure $1)$ and show each step of heapify$().$

$6.[3$ points$]$ Transpose this max$-$heap $($Figure $2)$ into array storage.

Figure $2$