$\begin{aligned} &&(1 \times 2 \times 3) + (1 \times 2 \times 4) + \ldots + (1 \times 2 \times 100) \\ &+& (1 \times 3 \times 4) + (1 \times 3 \times 5) + \ldots + (1 \times 3 \times 100) \\ &+& (1 \times 4 \times 5) + (1 \times 4 \times 6) + \ldots + (1 \times 4 \times 100) \\ &+& \ldots \\ &+& (98 \times 99 \times 100) \end{aligned}$

Let $S$ denote the value of the sum above. What is the last two digits of $S$?