In a divide and conquer based algorithm, the recursive calls form a tree structure as shown in the following figure. The size of subproblems is $\frac{1}{4}$ of upper$-$level problems when generating a new level of subproblems. And the branching factor is $3$ which means one problem is divided into $3$ subproblems every time. For tackling a problem of size $n,$ the time to divide the problem into $3$ subproblems and combine results of the $3$ subproblems is linear to $n($the size of the problem$),$ i$.$e$.,T(n)=3T(\frac{n}{4})+O(n).$ The same is true for tackling a subproblem. For example, the time to divide a subproblem of size $\frac{n}{4}$ into $3$ subproblems further and combine their results is linear to $\frac{n}{4}.$ Please answer the following questions $({15}^9)$

How many levels of subproblems in the tree? $(3($:$3^{\text{'}}$