$B_i$ and $C_i$ in $I$ with a partition of $B_i \cup C_i$ into $\frac{t}{2} + 1$ sets. Each of the resulting new sets can be split naturally into a collection of pairs and a collection of triples of which at most one is empty. This results in $$\left (\frac t 2+1\right )+(4-1)=\frac t 2 +4$$ collections of pairs and triples, respectively. Now, for each $B_\ell$ and $C_\ell$ with $\ell\in\{1,2,\ldots,\frac t 2+4\}$, construct two rooted binary phylogenetic trees as described in the definition of the set of intermezzo trees associated with $I$. This yields $$2\left (\frac {t} 2 +4\right )=t+8=m$$ pairwise non-isomorphic trees. Second, suppose that $t$ is odd. Replace $B_i$ and $C_i$ in $I$ with a partition of $B_i \cup C_i$ into $\frac{t-1}{2} + 1$ sets. Additionally, add $B_*=\emptyset$ and $C_*=\emptyset$. Analogous to the first case, this results in $$\left (\frac {t-1} 2+1+1\right )+(4-1)=\frac {t-1} 2 +5$$ collections of pairs and triples, respectively. Again, for each $B_\ell$ and $C_\ell$ with $\ell\in\{1,2,\ldots,\frac {t-1} 2+5\}$ construct two rooted binary phylogenetic trees as described in the definition of the set of intermezzo trees associated with $I$. Noting that the two trees for $B_*$ and $C_*$ are isomorphic, it follows that the construction yields 