How many possible values are there for the following integral-

\(\displaystyle \oint_{C}\frac{dz}{(z-z_1)(z-z_2)..(z-z_n)}\)

(I'm guessing the answer is not n, but don't see why)

Should also add that C is a closed contour that does not go through any of the points \(\displaystyle z_i\)