IMO Team Selection Contest I

Let ${\mathbb{R}}^{+}$ be the set of positive real numbers. Determine all functions $f:{\mathbb{R}}^{+}\to {\mathbb{R}}^{+}$ satisfying the equation $$xf(x^2)f(f(y))+f(yf(x))=f(xy)(f(f(x^2))+f(f(y^2))).$$ for all $x,y\in {\mathbb{R}}^{+}$.