Suppose we have N \geq 3 cards C_{1}, C_{2}, \ldots, C_{N} lined up in a row, and we want to shuffle the deck so that it is equally likely to see any possible outcome. We have devised the following algorithm to perform this task:
\textbf{Data}: the cards C_{1}, C_{2}, \ldots, C_{N}
\textbf{Result}: a uniformly random permutation of C_{1}, C_{2}, \ldots, C_{N}
\textbf{for} i=1,2, \ldots, N do
\quad j \leftarrow \mathbf{D}(N)
\quad swap the positions of C_{i} and C_{j}
\textbf{end}
Prove that this algorithm is incorrect, i.e., it does not properly shuffle the cards.