Below is an algorithm which will take any tree and convert it into a number sequence. We will call this number sequence the Tree Code. INPUT: a tree T with vertex set $\{1,...,$ n$\}$ where n $>2$ OUTPUT: a sequence of numbers $($the Tree Code$)$ which represents T$..($step $1)$ i $=1($step $2)$ j $=$ smallest leaf of T$,$ and suppose the incident edge is e $=$ jk $($step $3)$ si $=$ k and T :$=$ T with e and j removed. $($step $4)$ if i $=$ n $2,$ output $($s$1,...,$ sn$2)$ and STOP; otherwise i :$=$ i $+1$ and go to step $2.($a$)$ If a Tree Code consists of k elements, how many vertices does its tree have? $($b$)$ Run the algorithm on the tree below to generate the Tree Code which represents it$.$ Show the outcome of each step of the algorithm.