We offer $n$ courses where each course $i$ has a start time $s_i$, a finish time $f_i$, and a weight $w_i$. Two courses are considered compatible if their time intervals do not overlap. For simplicity, we can assume that the courses are sorted in non-decreasing order of their finish times, denoted as $f_1 \le f_2 \le \cdots \le f_n$. Additionally, let $p(j)$ for a course $j$ represent the largest index $i < j$ such that courses $i$ and $j$ are disjoint. We define $p(j) = 0$ if no course $i < j$ is disjoint from $j$. Our goal is to find a set $S \subseteq \{1, \ldots, n\}$ of mutually compatible courses such that the total weight of the courses in $S$ is maximized. We have designed a recursive algorithm for this purpose, but we have omitted an essential part. Please assist us in completing the missing portion. Hint: This algorithm returns the value of the optimal solution to the problem consisting of courses $\{1, \ldots, i\}$.

F(i)
    If i = 0 return 0
    return ______