Let the area of the region enclosed by the curve y= min { sin x, cos x} and the x axis between x=-π to x=π be A. Then A^2 is equal to ____.

Let the area of the region enclosed by the curve $\displaystyle y=\min \{\sin x, \cos x\}$ and the $\displaystyle x$ axis between $\displaystyle x=-\pi$ to $\displaystyle x=\pi$ be $\displaystyle A$. Then $\displaystyle A^2$ is equal to $\displaystyle \_\_\_\_$.