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\documentclass{article}
\begin{document}
$$ f_a, f^a, f_a^a, f^a_a $$
$ {}_a$, ${}^a $
\[ \mathop{A}\limits_B\limits^C \qquad
\mathop{A}\limits^C \limits_B \qquad
\mathop{A}\nolimits_B\limits^C \qquad
\mathop{A}\nolimits^C \limits_B
\]
\[ \mathop{A}\limits_B\nolimits^C \qquad
\mathop{A}\limits^C \nolimits_B \qquad
\mathop{A}\nolimits_B\nolimits^C\qquad
\mathop{A}\nolimits^C\nolimits_B
\]
\[ \mathop{\mathop{A}\limits_B}\limits^C \qquad
\mathop{\mathop{A}\nolimits_B}\limits^C \qquad
\mathop{\mathop{A}\limits_B}\nolimits^C \qquad
\mathop{\mathop{A}\nolimits_B}\nolimits^C
\]
\[
\stackrel{C}{{\stackrel{B}{A}}}
\]
\end{document}
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