Vector Calculus · Superchallenge problem

Let $f(x,y) = x^4 - 6x^2y^2 + y^4 + x^2 + y^2$ and let $C$ be the cardioid $r = 1 + \cos\theta$ with outward unit normal $\mathbf n$. Evaluate the normal-derivative flux $\displaystyle\oint_C \nabla f\cdot\mathbf n\,ds$. Give your answer in terms of $\pi$.