\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{environ}
\usepackage{etoolbox}
\usepackage{mathrsfs}
\usepackage{mathtools}
\usepackage{tcolorbox}
\usepackage{tikz}
\usepackage{xcolor}
\tcbuselibrary{breakable}
\tcbuselibrary{skins}

% A pretty color palette taken from https://flatuicolors.com/palette/defo. To
% see a preview of the different colors, use the \showcolors command below.
\definecolor{flatdarkgray}{HTML}{7F8C8D}
\definecolor{flatgray}{HTML}{BDC3C7}
\definecolor{flatred}{HTML}{C0392B}
\definecolor{flatorange}{HTML}{D35400}
\definecolor{flatyellow}{HTML}{F39C12}
\definecolor{flatdenim}{HTML}{2C3E50}
\definecolor{flatpurple}{HTML}{8E44AD}
\definecolor{flatblue}{HTML}{2980B9}
\definecolor{flatgreen}{HTML}{27AE60}
\definecolor{flatcyan}{HTML}{16A085}
\definecolor{flatdarkgrayalt}{HTML}{95A5A6}
\definecolor{flatgrayalt}{HTML}{ECF0F1}
\definecolor{flatredalt}{HTML}{E74C3C}
\definecolor{flatorangealt}{HTML}{E67E22}
\definecolor{flatyellowalt}{HTML}{F1C40F}
\definecolor{flatdenimalt}{HTML}{34495E}
\definecolor{flatpurplealt}{HTML}{9B59B6}
\definecolor{flatbluealt}{HTML}{3498DB}
\definecolor{flatgreenalt}{HTML}{2ECC71}
\definecolor{flatcyanalt}{HTML}{1ABC9C}
\definecolor{flatbrown}{HTML}{836953}

\newcommand{\showcolors}{%
  \begin{center}
    \begin{tikzpicture}
      \tikzstyle{swatch}=[minimum width=3cm, minimum height=0.5cm, y=0.5cm]
      \node[swatch, fill=flatdarkgray]    at (0, 9) {\texttt{flatdarkgray}};
      \node[swatch, fill=flatgray]        at (0, 8) {\texttt{flatgray}};
      \node[swatch, fill=flatred]         at (0, 7) {\texttt{flatred}};
      \node[swatch, fill=flatorange]      at (0, 6) {\texttt{flatorange}};
      \node[swatch, fill=flatyellow]      at (0, 5) {\texttt{flatyellow}};
      \node[swatch, fill=flatdenim]       at (0, 4) {\texttt{flatdenim}};
      \node[swatch, fill=flatpurple]      at (0, 3) {\texttt{flatpurple}};
      \node[swatch, fill=flatblue]        at (0, 2) {\texttt{flatblue}};
      \node[swatch, fill=flatgreen]       at (0, 1) {\texttt{flatgreen}};
      \node[swatch, fill=flatcyan]        at (0, 0) {\texttt{flatcyan}};
      \node[swatch, fill=flatdarkgrayalt] at (3, 9) {\texttt{flatdarkgrayalt}};
      \node[swatch, fill=flatgrayalt]     at (3, 8) {\texttt{flatgrayalt}};
      \node[swatch, fill=flatredalt]      at (3, 7) {\texttt{flatredalt}};
      \node[swatch, fill=flatorangealt]   at (3, 6) {\texttt{flatorangealt}};
      \node[swatch, fill=flatyellowalt]   at (3, 5) {\texttt{flatyellowalt}};
      \node[swatch, fill=flatdenimalt]    at (3, 4) {\texttt{flatdenimalt}};
      \node[swatch, fill=flatpurplealt]   at (3, 3) {\texttt{flatpurplealt}};
      \node[swatch, fill=flatbluealt]     at (3, 2) {\texttt{flatbluealt}};
      \node[swatch, fill=flatgreenalt]    at (3, 1) {\texttt{flatgreenalt}};
      \node[swatch, fill=flatcyanalt]     at (3, 0) {\texttt{flatcyanalt}};
    \end{tikzpicture}
  \end{center}
}

% New theorem environments.
\newtheorem{theorem}{Theorem}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{benchmark}{Benchmark}
\newtheorem{example}{Example}
\newtheorem{invariant}{Invariant}

% Toggleable TODOs.
\newtoggle{showtodos}
\toggletrue{showtodos}
% \togglefalse{showtodos}
\newcommand{\TODO}[2][]{%
  \iftoggle{showtodos}{{\textcolor{blue}{\textbf{TODO(#1): #2}}}}{}%
}

% Toggleable notes.
\newtoggle{shownotes}
\toggletrue{shownotes}
% \togglefalse{shownotes}
\newcommand{\NOTE}[2][]{%
  \iftoggle{shownotes}{{\textcolor{red}{NOTE(#1): #2}}}{}%
}

% Labels and references. To label a figure use the \figlabel command, to label
% a lemma, use the \lemlabel command, etc. Similarly, use the \figref, lemref,
% etc. commands to reference these labels. For example:
%
%     \begin{figure}
%       % ...
%       \caption{A nice figure}\figlabel{MyNiceFigure}
%     \end{figure}
%
%     Refer to \figref{MyNiceFigure} for a nice figure.
%
% Toggle showlabels to show or hide all labels.
\newtoggle{showlabels}
% \toggletrue{showlabels}
\togglefalse{showlabels}
\newcommand{\genericlabel}[2]{%
  \label{#1:#2}%
  \iftoggle{showlabels}{\textcolor{flatdarkgray}{\texttt{[#2]}}}{}%
}
\newcommand{\algolabel}[1]{\genericlabel{alg}{#1}}
\newcommand{\algoref}[1]{Algorithm~\ref{alg:#1}}
\newcommand{\applabel}[1]{\genericlabel{app}{#1}}
\newcommand{\appref}[1]{Appendix~\ref{app:#1}}
\newcommand{\benchlabel}[1]{\genericlabel{bench}{#1}}
\newcommand{\benchref}[1]{Benchmark~\ref{bench:#1}}
\newcommand{\clmlabel}[1]{\genericlabel{clm}{#1}}
\newcommand{\clmref}[1]{Claim~\ref{clm:#1}}
\newcommand{\eqnlabel}[1]{\genericlabel{eqn}{#1}}
\newcommand{\eqnref}[1]{\eqref{eqn:#1}}
\newcommand{\invlabel}[1]{\genericlabel{inv}{#1}}
\newcommand{\invref}[1]{Invariant~\ref{inv:#1}}
\newcommand{\examplelabel}[1]{\genericlabel{exa}{#1}}
\newcommand{\exampleref}[1]{Example~\ref{exa:#1}}
\newcommand{\figlabel}[1]{\genericlabel{fig}{#1}}
\newcommand{\figref}[1]{Figure~\ref{fig:#1}}
\newcommand{\lemlabel}[1]{\genericlabel{lem}{#1}}
\newcommand{\lemref}[1]{Lemma~\ref{lem:#1}}
\newcommand{\linelabel}[1]{\genericlabel{line}{#1}}
\newcommand{\lineref}[1]{line~\ref{line:#1}}
\newcommand{\Lineref}[1]{Line~\ref{line:#1}}
\newcommand{\lstlabel}[1]{\genericlabel{lst}{#1}}
\newcommand{\lstref}[1]{Listing~\ref{lst:#1}}
\newcommand{\seclabel}[1]{\genericlabel{sec}{#1}}
\newcommand{\secref}[1]{Section~\ref{sec:#1}}
\newcommand{\appendixlabel}[1]{\genericlabel{appendix}{#1}}
\newcommand{\appendixref}[1]{Appendix~\ref{appendix:#1}}
\newcommand{\tablabel}[1]{\genericlabel{tab}{#1}}
\newcommand{\tabref}[1]{Table~\ref{tab:#1}}
\newcommand{\thmlabel}[1]{\genericlabel{thm}{#1}}
\newcommand{\thmref}[1]{Theorem~\ref{thm:#1}}

% Surrounding symbols.
\DeclarePairedDelimiter{\parens}{(}{)}
\DeclarePairedDelimiter{\set}{\{}{\}}
\DeclarePairedDelimiterX{\setst}[2]{\{}{\}}{#1 \,\delimsize|\, #2}
\DeclarePairedDelimiter{\brackets}{[}{]}
\DeclarePairedDelimiterX{\pfrac}[2]{(}{)}{\frac{#1}{#2}}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}

% Symbols and abbreviations.
\newcommand{\nats}{\mathbb{N}}
\newcommand{\ints}{\mathbb{Z}}
\newcommand{\rats}{\mathbb{Q}}
\newcommand{\reals}{\mathbb{R}}
\newcommand{\complexes}{\mathbb{C}}
\newcommand{\partialto}{\rightharpoonup}
% https://tex.stackexchange.com/a/74132
\newcommand{\defeq}{\stackrel{\mathclap{\mbox{\normalfont \tiny def}}}{=}}


% Misc.
\newcommand{\defword}[1]{\textbf{\textcolor{flatdenim}{#1}}}

% Tech report environment.
%
% If you're writing a paper and there's too much content, you might want to
% move some content out of the paper and into the technical report version of
% the paper. To do this, you can put the content in the techreport environment
% like this:
%
%   This text will appear in the paper and tech report.
%   \begin{techreport}
%     This text will only appear in the tech report.
%   \end{techreport}
%
% When the techreportenabled toggle is enabled, the tech report content will be
% shown. When the toggle is disabled, the tech report content will be hidden.
% Moreover, when the toggle is enabled, the tech report content will be shown
% with a red bar on its left margin to make it easier for readers to figure out
% what is new in the tech report.
\newtoggle{techreportenabled}
\toggletrue{techreportenabled}
\togglefalse{techreportenabled}