\begin{algorithm}
\caption{Randomize in Place - Modified for Proof}
\begin{algorithmic}
\INPUT An array $A$ of size $n$
\OUTPUT A uniform randomized permutation of $A$
\STATE swap $A[1]$ with $A[$ \CALL{Random}{$1, n$} $]$
\FOR{$i = 2$ \TO $n$}
\STATE swap $A[i]$ with $A[$ \CALL{Random}{$i, n$} $]$
\ENDFOR
\end{algorithmic}
\end{algorithm}