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A $12$-hour unit hydrograph (of $\text{1 cm}$ excess rainfall) of a catchment is of a triangular shape with a base width of $144$ hour and a peak discharge of $23\text{ m}^3\text{/s}$. The area of the catchment (in $\text{km}^2, \textit{round off to the nearest integer}$) is _____________
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