2. Let $n$ be a three-digit positive integer that does not contain the digit 0. If any permutation of the units, tens, and hundreds digits of $n$ does not form a three-digit number that is a multiple of 4, find the number of such $n$.
(54th Ukrainian Mathematical Olympiad)
Hint: Classify by the number of even digits (i.e., $2,4,6,8$) appearing in the three-digit code of $n$. It is known from the discussion that the number of $n$ satisfying the condition is $125+150+0+8=283$.

