a$)$ Construct a suffix tree for the following string aagcagga$\backslash$$$.$ Show the individual steps of construction $(9$ steps in total$).$

b$)$ Search the following patterns in the suffix tree you created in part $($a$).$ Show your search steps. You may either provide written explanations of the search steps without redrawing the suffix tree you created in part $($a$),$ or you may show your steps visually by redrawing the suffix tree. If the pattern is found, indicate the number of occurences of the pattern and show the places of occurrence.

i$)$ Search pattern ag$.$

ii$)$ Search pattern gac.