Two pi or not two pi

Calculus Level 5

This closed curve satisfies the equation $\sqrt{1-|x|} + \sqrt{1-|y|} = 1.$ It looks much like the unit circle but is a little bulgier. Not surprisingly, the circumference $$C$$ of this curve is slightly greater than that of the unit circle.

By what percent is this circumference greater than that of the unit circle? In other words, what is $\frac{ C - 2\pi}{2\pi} \times 100?$

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