$($a$)$ Draw the binary search tree created if the following numbers are inserted in the tree in the given order. $(4$ marks$)$

$\backslash [$

$1561837172024139$

$\backslash ]$

$($b$)$ Is it a balanced tree? $(1$ mark$)$ Why? $(1$ mark$)$

$($c$)$ Write down the post$-$order traversal of the tree. $(3$ marks$)$

$($d$)$ Write down the in$-$order traversal of the tree. $(3$ marks$)$

$($e$)$ Show in steps, how to delete node $13,$ and the delete node $15$ of the tree. $(3$ marks$)$

$($f$)$ With pseudocode, construct an algorithm for searching the maximum value of the tree. $(5$ marks$)$