Summing The Triangle

\[ \begin{array}{c} 1 \end{array} \\ \begin{array}{cc} 1 & 1 \end{array} \\ \begin{array}{ccc} 1 & 2 & 1 \end{array} \\ \begin{array}{cccc} 1 & 3 & 3 & 1\end{array} \\ \begin{array}{ccccc} 1 & 4 & 6 & 4 & 1\end{array} \\ \begin{array}{cccccc} \vdots & \hphantom{\vdots} & \vdots & \hphantom{\vdots} & \vdots \end{array} \\ \]

Pascal's Triangle is shown above for the \(0^\text{th}\) row through the \(4^\text{th}\) row.

What is the sum of all the elements in the \(12^\text{th}\) row?

Note: The topmost row in Pascal's Triangle is the \(0^\text{th}\) row. Then, the next row down is the \(1^\text{st}\) row, and so on.

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