(10%) Given a sequence $K = \langle k_1, k_2, k_3, k_4, k_5 \rangle$ of five distinct keys in sorted order (so that $k_1 < k_2 < k_3 < k_4 < k_5$) and six dummy keys $d_0, d_1, d_2, d_3, d_4, d_5$ representing values not in $K$, we have a probability $p_i$ for $k_i$ and a probability $q_i$ for $d_i$. Determine the cost of an optimal binary search tree for $K$ with the following probabilities: