Area between sine and cosine

Let $S=\{(x,y)\in\mathbb{R}^{2}:0\le x\le\pi, \min\{\sin x,\cos x\}\le y\le\max\{\sin x,\cos x\}\}$. If $\alpha$ is the area of $S$, then the value of $2\sqrt{2}\alpha$ is equal to __________.