If the tangent at a point $P$ on the parabola $y^2=3 x$ is parallel to the line $x+2 y=1$ and the tangents at the points $Q$ and $R$ on the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ are perpendicular to the line $x-y=2$, then the area of the triangle $P Q R$ is:
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