\(\newcommand{\vheart}{\textcolor{red}{\varheart}} \newcommand{\vdia}{\textcolor{red}{\vardiamond}} \newcommand{\Mod}[1]{\ \left(\mathrm{mod}\ #1\right)} \newcommand{\mmod}[1]{\ \mathrm{\bf mod}\ #1} \newcommand{\st}{ {\mbox{ s.t. }} } \newcommand{\pow}[1]{ \mathcal{P}\left(#1\right) } \newcommand{\diff}[2]{ \frac{\mathrm{d}#1}{\mathrm{d}#2}} \newcommand{\bdiff}[2]{ \frac{\mathrm{d}}{\mathrm{d}#2} \left( #1 \right)} \newcommand{\ddiff}[3]{ \frac{\mathrm{d}^#1#2}{\mathrm{d}{#3}^#1}} \newcommand{\limp}{ {\;\Rightarrow\;} } \newcommand{\nimp}{ {\;\not\Rightarrow\;} } \newcommand{\liff}{ {\;\Leftrightarrow\;} } \newcommand{\niff}{ {\;\not\Leftrightarrow\;} } \newcommand{\arccsc}{\mathop{\mathrm{arccsc}}} \newcommand{\arcsec}{\mathop{\mathrm{arcsec}}} \newcommand{\arccot}{\mathop{\mathrm{arccot}}} \renewcommand{\textcolor}[2]{{\color{#1}{#2}}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)