$\require{bbm} \newcommand{\N}{\mathbbm{N}} \newcommand{\Z}{\mathbbm{Z}} \newcommand{\D}{\mathbbm{D}} \newcommand{\Q}{\mathbbm{Q}} \newcommand{\R}{\mathbbm{R}} \newcommand{\C}{\mathbbm{C}} \newcommand{\ec}{\operatorname{e}}% \newcommand{\expo}[1]{\operatorname{e}^{#1}} \newcommand{\integ}[3]{\int_{#1}^{#2}#3\,\dup} \newcommand{\dup}{\operatorname{d}} $