\(
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\id}{\mathrm{id}}
\newcommand{\symdiff}{\mathbin{\triangle}}
\newcommand{\inv}[1]{{#1}^\leftarrow}
\DeclareMathOperator{\powset}{\mathcal{P}}
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\syt}{syt}
\)