KZ-MO 2008 Problem 3

Let $f(x,y,z)$ be the polynomial with integer coefficients. Suppose that for all reals $x,y,z$ the following equation holds: $$f(x,y,z) = - f(x,z,y) = - f(y,x,z) = - f(z,y,x)$$ Prove that if $a,b,c\in\mathbb{Z}$ then $f(a,b,c)$ takes an even value