Given a set $S$ of size $n = 2^{2^m}$, where $m \in \mathbb{Z}^+$, we use the following algorithm to perform clustering and labeling:

F(S)
1  If |S| == 2 then return;
2  Apply a clustering algorithm with a time complexity of Θ(lg n) to divide the set S
   into three clusters, S1, S2, and S3, and label them where |S| = n, |S1| = |S2| = √n,
   and |S3| = n − 2√n.
3  Call F(S1)
4  Call F(S2)

Let $T(n)$ represent the time required to use this algorithm to cluster and label a set of size $n$. Provide an asymptotic tight bound ($\Theta$) for $T(n)$, assuming that $T(n)$ is a constant for sufficiently small $n$.