Let $A = \{ 1,2 , \ldots , n \}$. For a permutation $P = ( P ( 1 ) , P ( 2 ) , \cdots , P ( n ) )$ of the elements of $A$, let $P ( 1 )$ denote the first element of $P$. Find the number of all such permutations $P$ so that for all $i , j \in A$:

\begin{itemize}
  \item if $i < j < P ( 1 )$, then $j$ appears before $i$ in $P$; and
  \item if $P ( 1 ) < i < j$, then $i$ appears before $j$ in $P$.
\end{itemize}