Geometry Level 5

In a triangle $$ABC$$, points $$D$$ and $$E$$ are on $$BC$$ such that $$| BD | : | DE | : | EC | = 1 : 1:1$$, and points $$F$$ and $$G$$ are on $$AC$$ such that $$| AF | : | FG | : |GC | = 1 : 3 : 1$$.

The quadrilateral $$PQRS$$ is formed by the intersection of segments $$BF, BG, AD$$ and $$AE$$.

If the area of the triangle $$ABC$$ is 1001 square units, what is the area of quadrilateral $$PQRS$$?

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