If the area of the region $\left\{(x, y): 1-2 x \leq y \leq 4-x^2, x \geq 0, y \geq 0\right\}$ is $\frac{\alpha}{\beta}, \alpha, \beta \in \mathbf{N}, \operatorname{gcd}(\alpha, \beta)=1$, then the value of $(\alpha+\beta)$ is :
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