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If the area of the region $$S = \{(x,y): 2y - y^2 \le x^2 \le 2y, x \ge y\}$$ is equal to $$\dfrac{n+2}{n+1} - \dfrac{\pi}{n-1}$$, then the natural number $$n$$ is equal to ______.
Correct Answer: 5
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