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\usepackage{lipsum}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[USenglish]{babel}
\usepackage[stretch=10,shrink=10]{microtype}
\usepackage[left=1.3in,
right=1.3in,
top=1in,
bottom=1in,
footskip=.5in]{geometry}
\setlength{\columnsep}{0.4in}
\renewcommand{\rmdefault}{zpltlf}
\usepackage{newpxtext}
% will mess up embeded symbols
% \usepackage{newpxmath}
\title{The hard mode}
\author{krasjet}
\date{}
\begin{document}
\begin{multicols}{2}
[
\maketitle
]
\section{Section One}
\lipsum[2-3]
\section{Section $1 + 1 = 2$}
\lipsum[2-1]
\begin{align*}
x^2 + 2 = 4
\end{align*}
\lipsum[2-1]
\subsection{Subsection Two.One}
\lipsum[2-5]
\section*{$\mathrm{e}^{\ln(3)}$}
\setcounter{section}{3}
\setcounter{subsection}{0}
\lipsum[1-2]
\subsection{Subsection $\mathrm{e}^{\ln(3)}$.1, with looo\-ooooooooong title}
\lipsum[2-5]
\subsection{$\mathbb{S}$ubsection Three.Two, another long title}
\lipsum[1-1]
\subsection{Subsection Three.Three}
\lipsum[2-3]
\section{The $x \to \infty$ End}
\lipsum[2-2]
\end{multicols}
\end{document}
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