\(\require{tikz}\require{graphicx}\DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Perm}{Perm} \DeclareMathOperator{\Stab}{Stab} \DeclareMathOperator{\Orb}{Orb} \DeclareMathOperator{\Rot}{Rot} \DeclareMathOperator{\re}{Re} \DeclareMathOperator{\im}{Im} \DeclareMathOperator{\conj}{conj} \DeclareMathOperator{\Id}{Id} \newcommand{\C}{\mathbb{C}} \newcommand{\Quat}{\mathbb{H}} \newcommand{\extC}{\hat{\C}} \newcommand{\R}{\mathbb{R}} \newcommand{\extR}{\hat{\R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\F}{\mathbb{F}} \newcommand{\Proj}{\mathbb{P}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\M}{{\rm \bf M}} \newcommand{\H}{{\rm \bf H}} \newcommand{\HU}{\H_{\U}} \newcommand{\S}{{\rm \bf S}} \newcommand{\D}{\mathbb{D}} \newcommand{\closedD}{\hat{\D}} \newcommand{\U}{\mathbb{U}} \newcommand{\spacer}{\rule[0cm]{0cm}{0cm}} \newcommand{\MOD}{\mathbin{\text{MOD}}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)