\(\renewcommand{\P}{\mathcal{P}} \newcommand{\B}{\mathcal{B}} \newcommand{\C}{\mathcal{C}} \newcommand{\E}{\mathcal{E}} \newcommand{\R}{\mathcal{R}} \newcommand{\Z}{\mathcal{Z}} \newcommand{\lt}{ < } \newcommand{\gt}{ > } \newcommand{\amp}{ & } \)