\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \usepackage{tikz, pgfplots} \usetikzlibrary{positioning,matrix,arrows} \usetikzlibrary{shapes,decorations,shadows,fadings,patterns} \usetikzlibrary{decorations.markings}