a$)(3$ marks$)$ Successively insert the values $50,80,30,60,70$ and $40$ into an initially emply binary search tree. Show the resultant tree after each insertion.b$)(3$ marks$)$ Delete $50$ from the final tree in part a$)$ and show the two possible resultant trees.c$)(3$ marks$)$ The method to insert an item into a binary search tree is given below. Complete the code where indicated $(...)$ to permit duplicate insertions of an item.private Node Add$($I item, Node node$)$if $($node $==$ null$)$return new Node $($item$)$ ;elseif $($item$.$ CompareTo $($node$.$Item$)0)\{$node$.$ Left $=$ Add $($item$,$ node.Left$)$ ;return node;$\}$elseif $($item$.$ CompareTo $($node$.$Item$)>0)\{$node$.$Right $=$ Add $($item$,$ node.Right$)$ ;return node;$\}$else$\}$d$)(2$ marks$)$ Using your algorithm in part c$),$ successively insert the values $50,40,60,50$ and $50$ into an initially empty binary search tree. Show the resultant tree after each insertion.