Question $3$: Hash Tree for Candidate Support Counting $(10$ points$)$ Given the following candidate $3-$itemsets: $\{1,4,5\},\{1,2,4\},\{4,5,7\},\{1,2,5\},\{4,5,8\},\{1,3,6\},\{2,4,6\},\{1,5,9\},\{3,5,6\},\{3,6,7\},\{5,6,7\},\{3,6,9\},\{6,8,9\},\{4,7,9\},\{2,5,8\}1.$ Construct a hash tree with the following rules: o Use the hash function: x mod $3,$ where x is the item in the itemset $($e$.$g$.,$ at depth $1,$ x is the first item in the itemset, at depth $2,$ it will be the second item in the itemset and so on$...).$ o The max leaf size is $3.$ If the number of candidate itemsets in a leaf node exceeds this limit$,$ split the node using the next item in the candidate set. $2.$ Insert the candidate itemsets into the tree according to the hash function. $3.$ Draw the resulting hash tree structure.