I need help with writing a permutation in Cauchy's two-line notation that has many columns please. Because there are so many columns, it extends outside the horizontal box. I have decided that the best thing to do is to split it over two lines.
Below is a MWE. The first produces the notation exactly how I would like it if it didn't extend outside the horizontal box. The second is an attempt to split it over two lines so it is within the horizontal box. I am more or less happy with the second one, except for how it treats the parentheses. I want the left parenthesis to take the first two lines and the right parenthesis to take the last two lines.
\documentclass{article}
\usepackage{amsmath}
\usepackage{multirow}
\begin{document}
\begin{align*}
\sigma=\left(\begin{array}{cccccccccccccc}
1 & 2 & 3 & 4 & \ldots{} & \frac{n}{2}-1 & \frac{n}{2} & \frac{n}{2}+1 & \frac{n}{2}+2 & \ldots{} & n-3 & n-2 & n-1 & n \\
1 & \frac{n}{2}+1 & 3 & \frac{n}{2}+3 & \ldots{} & \frac{n}{2}-1 & n-1 & \frac{n}{2} & \frac{n}{2}+2 & \ldots{} & 4 & n-2 & 2 & n \\
\end{array}\right).
\end{align*}
\begin{align*}
\begin{tabular}{ccccccccc}
\multirow{2}{*}{$\sigma=($} & $1$ & $2$ & $3$ & $4$ & \ldots{} & $\frac{n}{2}-1$ & $\frac{n}{2}$ & \\
& $1$ & $\frac{n}{2}+1$ & $3$ & $\frac{n}{2}+3$ & \ldots{} & $\frac{n}{2}-1$ & $n-1$ & \\
& $\frac{n}{2}+1$ & $\frac{n}{2}+2$ & \ldots{} & $n-3$ & $n-2$ & $n-1$ & $n$ & \multirow{2}{*}{)} \\
& $\frac{n}{2}$ & $\frac{n}{2}+2$ & \ldots{} & $4$ & $n-2$ & $2$ & $n$ & \\
\end{tabular}.
\end{align*}
\end{document}
Cauchy's two-line notation is essentially just a matrix with two rows, so a solution using matrices would be fine too. Any other suggestions to make the notation take less space are welcome too.
Thank you.