$$
\newcommand{\seq}[2]{{#1}_{1},{#1}_{2},\cdots,{#1}_{#2}}
\newcommand{\num}[1]{1,2,\cdots,#1}
\newcommand{\stra}[2]{\begin{bmatrix}#1 \\ #2\end{bmatrix}}
\newcommand{\strb}[2]{\begin{Bmatrix}#1 \\ #2\end{Bmatrix}}
\newcommand{\dw}[1]{\underline{#1}}
\newcommand{\up}[1]{\overline{#1}}
$$
