\(\newcommand{\abs}[1]{\left\lvert #1 \right\rvert} \newcommand{\set}[1]{\left\{ #1 \right\}} \renewcommand{\neg}{\sim} \newcommand{\brac}[1]{\left( #1 \right)} \newcommand{\eval}[1]{\left. #1 \right|} \newcommand{\floor}[1]{\lfloor #1 \rfloor} \newcommand{\ceil}[1]{\lceil #1 \rceil} \newcommand{\nCr}[2]{_{#1}C_{#2}} \newcommand{\nPr}[2]{_{#1}P_{#2}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)