Let $ABC$ be a triangle with $AB = 26$, $BC = 51$, and $CA = 73$. Let $O$ be an arbitrary point in the interior of $\triangle ABC$. Lines $\ell_1$, $\ell_2$, and $\ell_3$ pass through $O$ and are parallel to $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$, respectively. The intersections of $\ell_1$, $\ell_2$, and $\ell_3$ with the sides of $\triangle ABC$ form a hexagon whose area is $A$. Compute the minimum value of $A$.

Let's think step by step and output the final answer within \boxed{}.
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