Given a function $f$ for which  
$f(x) = f(398 - x) = f(2158 - x) = f(3214 - x)$  
holds for all real $x,$ what is the largest number of different values that can appear in the list $f(0),f(1),f(2),\cdots,f(999)?$

Let's think step by step and output the final answer within \boxed{}.
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