$$ \def\Forall{\enskip \forall} \def\forthat{\;\bigm|\;} \def\hateq{\mathrel{\widehat{=}}} \def\hint#1{\quad\color{maroon}{\small\textit{#1}}} \def\stx#1{\small\textrm{#1}} \def\guide#1{\quad{\stx{#1}}} \def\ol#1{\overline{#1}} \def\lraq{ \quad\leftrightarrow\quad } \def\Lraq{ \quad\Leftrightarrow\quad } \def\ra{ \,\rightarrow\, } \def\raq{ \quad\rightarrow\quad } \def\Ra{ \,\Rightarrow\, } \def\Raq{ \quad\Rightarrow\quad } \def\ux#1{\;\textrm{#1}} \newcommand\m[1][]{#1\ux{m}} \newcommand\mm[1][]{#1\ux{mm}} \newcommand\cm[1][]{#1\ux{cm}} \newcommand\km[1][]{#1\ux{km}} \newcommand\qm[1][]{#1\ux{m}^2} \newcommand\cel[1][]{#1\,^\circ\textrm{C}} \newcommand\deg[1][]{#1\,^\circ} \newcommand\eur[1][]{#1\ux{€}} \newcommand\pct[1][]{#1\,\%} \newcommand\prm[1][]{#1\,{}^\text{o}\mkern-5mu/\mkern-3mu_\text{oo}} $$