308. Given a number $a$. Find the minimum value of the area of a rectangle with sides parallel to the coordinate axes $O x$ and $O y$ and containing the figure defined by the system of inequalities

$$
\left\{\begin{array}{l}
y \leqslant -x^{2} \\
y \geqslant x^{2}-2 x+a
\end{array}\right.
$$
308. Answer: $S=(1-a) \sqrt{1-a}$ for $a \leqslant 0$; $S=1-2a$ for $0<a<1/2$; $S=0$ for $a \geqslant 1/2$.