For diagram number 8, we compute
$$ \begin{align} \chi_{i}^{l}\equiv -{1\over 2} \sum_{kcd} \langle kl\vert V\vert cd\rangle t_{ik}^{cd} \tag{32} \end{align} $$at a cost of \( A^3 n_u^2 \), and then compute
$$ \begin{align} -P(ij) \sum_l \chi_i^l t_{lj}^{ab} \tag{33} \end{align} $$at the cost of \( A^3 n_u^2 \).