I am wondering how to manipulate contours to solve the following double complex integral: $$ \left( \oint_a dy \oint_a dz- \oint_a dz \oint_a dy \right) f(y)g(z) = \left( \oint_a dy \oint_y dz \right) f(y)g(z) $$ where $a$, $y$ and $ z$ are complex, $f$ and $g$ are general complex functions, and $\oint_a$ means integration around point $a$.
Does anyone have an idea?
I am aware of techniques used in manipulating contours with one complex variable $\ldots$