# Let's circulate again

Calculus Level 5

How many real numbers $$I$$ are there such that $I=\oint_{C}\frac{y}{x^2+y^2}dx-\frac{x}{x^2+y^2}dy$

for some simple closed curve $$C$$ that does not run through the origin?

If you come to the conclusion that there are infinitely many such $$I$$, enter 666.

Special Case

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