Find all functions $f:\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R}$ that satisfied the functional equation
$\displaystyle f\left(\frac{x+y+z}{3},\frac{a+b+c}{3}\right)=f(x,a)f(y,b)f(z,c)$
for every real number $x,y,z,a,b,c$ that $az+bx+cy\neq ay+bz+cx$
I don't know how to solve it. This question was awarded as the best problem in the competition.