Figure $1$: a binary tree $3.$ Consider the binary tree in Fig. $1$

$-$ Is it a binary search tree, and why? $(5$ points$)$

$-$ What's the in$-$order traversal sequDence of the binary tree? $(10$ pts$)$

$-$ Remove nodes $\text{'}4\text{'}$ and $\text{'}8\text{'}$ from the binary tree. After removal, can this binary tree represent the structure of a heap? If not, perform heapify and visualize the process to make it a max$-$heap. $(20$ points$)$

Figure $2$: A binary tree

$4.$ Consider the binary tree in Fig. $2$

$-$ Is it a balanced binary tree, and why? $(5$ points$)$

$-$ If the binary tree is not balanced, balance it using rotation operations. Draw the binary tree structure after rotation. $(15$ points$)$