 &= \max \bigl\{ \sum_{i=0}^d \frac{0}{{|{\mathcal{I}}_i|}} ({\boldsymbol{0}}^{{\sf T}}\bar{\theta}_{{\mathcal{I}}_i})^0 :~ ({\mathcal{I}}_0,\cdots,{\mathcal{I}}_d)\in{\bar{\texttt{P}}}(k,d) \bigr\} \