Can't get table border lines to meet in the corners

\documentclass[border=10pt]{standalone}

\begin{document}

\begin{tabular} { | r | p{2cm} | p{2cm} | }
\hline
\# & One & Two \\
\hline
1 & alpha & bravo \\
2 & apple & banana \\
\hline
\end{tabular}

\end{document}

Edit 3

If you are a perfectionist, please consider the following defects at the intersection of horizontal and vertical lines.

Maybe you hate them even though they are small enough to be visible at a glance.

Edit 3.1

Based on Ulrike's comment below, we need to use array package to remove such a bad feature.

\documentclass[border=10pt]{standalone}

\usepackage{array}
\begin{document}

\begin{tabular} {|r|p{2cm}|p{2cm}|}
\hline
\# & One & Two \\
\hline
1 & alpha & bravo \\
2 & apple & banana \\
\hline
\end{tabular}

\end{document}