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