A triangle $$ABC$$ with $$AC=20$$ is inscribed in a circle $$\omega$$. A tangent $$t$$ to $$\omega$$ is drawn through $$B$$. The distance of $$t$$ from $$A$$ is $$25$$ and that from $$C$$ is $$16$$. If $$S$$ denotes the area of the triangle $$ABC$$, find the largest integer not exceeding $$S/20$$.