\usepackage{xcolor}

\usepackage{fontspec}

\usepackage[sc]{mathpazo}

\usepackage{fontspec}

\setmainfont[Ligatures=TeX]{Palatino Linotype}

\usepackage{amssymb}

\usepackage{amsmath}

\usepackage{menukeys}

\definecolor{darkblue}{rgb}{0,0,0.6}

\usepackage[colorlinks=true,urlcolor=darkblue,linkcolor=darkblue]{hyperref}

%%% for trees

%% http://anorien.csc.warwick.ac.uk/mirrors/CTAN/graphics/pgf/contrib/forest/forest.pdf

\newcommand\grid[1]{%

\begin{tikzpicture}[baseline=(char.base)]

  \path[use as bounding box]

    (0,0) rectangle (1em,1em);

  \draw[red!50, fill=red!20]

    (0,0) rectangle (1em,1em);

  \node[inner sep=1pt,anchor=base west]

    (char) at (0em,\gridraiseamount) {#1};

\end{tikzpicture}}

\newcommand\gridraiseamount{0.12em}

\makeatletter

\newcommand\Grid[1]{%

  \@tfor\z:=#1\do{\grid{\z}}}

\makeatother	

\newcommand\Vspace[1][.3em]{%

  \mbox{\kern.06em\vrule height.3ex}%

  \vbox{\hrule width#1}%

  \hbox{\vrule height.3ex}}

\def\VS{\Vspace[0.6em]}

\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}

\newcommand{\defn}[1]{\textit{\textbf{#1}}}

\newcommand{\dq}[1]{\mbox{\tt{"}}#1\mbox{\tt{"}}}

\definecolor{codegray}{gray}{0.9}

\newcommand{\HEADER}{{\bf Please submit your solutions via email. Please submit 

only ASCII text or PDFs. Every solution should be preceeded by the corresponding 

question, like:

\begin{center}

\begin{tabular}{ll}

Q$n$: & \ldots a difficult question from me\ldots\\

A:    & \ldots an answer from you \ldots\\

Q$n+1$ & \ldots another difficult question\ldots\\

A:     & \ldots another brilliant answer from you\ldots

\end{tabular}

\end{center}

\noindent Solutions will only be accepted until 30th December! Please send only

one homework per email.}\bigskip}