Question 9
Let $N$ be the number of ordered sixtuples of integers $(a, b, c, d, e, f)$ such as $a^{3}+b^{3}+c^{3}+d^{3}+e^{3}+f^{3}=168$ and $-202120212021^{9}\lt a b c d e f\lt 202120212021^{9}$, where $abcdef$ is the product of you are whole. Which of the following is the rest of $N$ in division by 6?