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\def\d{\displaystyle}
\def\N{\mathbb N}
\def\B{\mathbf B}
\def\Z{\mathbb Z}
\def\Q{\mathbb Q}
\def\R{\mathbb R}
\def\C{\mathbb C}
\def\U{\mathcal U}
\def\x{\mathbf{x}}
\def\y{\mathbf{y}}
\def\X{\mathcal{X}}
\def\Y{\mathcal{Y}}
\def\pow{\mathcal P}
\def\inv{^{-1}}
\def\st{:}
\def\iff{\leftrightarrow}
\def\Iff{\Leftrightarrow}
\def\imp{\rightarrow}
\def\Imp{\Rightarrow}
\def\isom{\cong}
\def\bar{\overline}
\def\card#1{\left| #1 \right|}
\def\twoline#1#2{\begin{pmatrix}#1 \\ #2 \end{pmatrix}}
\def\mchoose#1#2{
\left.\mathchoice
{\left(\kern-0.48em\binom{#1}{#2}\kern-0.48em\right)}
{\big(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\big)}
{\left(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
{\left(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
\right.}
\def\o{\circ}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
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