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\(\newcommand{\cycle}[1]{\arraycolsep 5 pt \left(\begin{array}#1\end{array}\right)} \newcommand{\importantarrow}{\Rightarrow} \newcommand{\qchoose}[2]{\left[{#1\atop#2}\right]_q} \def\neg1choose#1#2{\left[{#1\atop#2}\right]_{-1}} \newcommand{\bp}{ \begin{enumerate}{\setcounter{enumi}{\value{problemnumber}}}} \newcommand{\ep}{\setcounter{problemnumber}{\value{enumi}} \end{enumerate}} \newcommand{\ignore}[1]{} \renewcommand{\bottomfraction}{.8} \renewcommand{\topfraction}{.8} \newcommand{\apple}{\text{๐ŸŽ}} \newcommand{\ap}{\apple} \newcommand{\banana}{\text{๐ŸŒ}} \newcommand{\ba}{\banana} \newcommand{\pear}{\text{๐Ÿ}} \newcommand{\pe}{\pear} \DeclareMathOperator{\Fix}{Fix} \DeclareMathOperator{\Orb}{Orb} \newcommand{\F}{\mathcal{F}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)