Question 12
Given a function $f$ for which $$
\begin{aligned} f(x) &= f(398 - x) \\ &= f(2158 - x) \\ &= f(3214 - x) \end{aligned}
$$ holds for all real $x,$ what is the largest number of different values that can appear in the list $f(0),$ $f(1),$ $f(2),$ $\ldots,$ $f(999)?$
\begin{aligned} f(x) &= f(398 - x) \\ &= f(2158 - x) \\ &= f(3214 - x) \end{aligned}
$$ holds for all real $x,$ what is the largest number of different values that can appear in the list $f(0),$ $f(1),$ $f(2),$ $\ldots,$ $f(999)?$