If the area of the region {(x, y):|4-x^2| ≤ y ≤ x^2, y ≤ 4, x ≥ 0} is ((80 √ 2)/(α)-β), α, β ∈ N, then α+β is equal to ____.

If the area of the region $\displaystyle \left\{(x, y):\left|4-x^2\right| \leq y \leq x^2, y \leq 4, x \geq 0\right\}$ is $\displaystyle \left(\frac{80 \sqrt{2}}{\alpha}-\beta\right), \alpha, \beta \in \mathbf{N}$, then $\displaystyle \alpha+\beta$ is equal to $\displaystyle \_\_\_\_$.