$(10$ points$)$ Recall that a comparison$-$based sorting algorithm can be repre$-$

sented in the $($binary$)$ decision tree model. Following the worked example

of Tutorial SS$13($refer to the collection of exercises and solutions on the

tutorial page on canvas$),$ the figure below shows part of the decision tree

for mergesort operating on a list of $4$ numbers, $a_1,a_2,a_3,a_4.$ Please

expand subtree $T_1,$ i$.$e$.,$ draw and label all of the edges, internal $($compar$-$

ison$)$ nodes and leaves in subtree $T_1.$ Edges in the tree must be labelled

with $$ or $>$ and leaves must show the final sorted order.