AT-OEMO-REG 2015 Problem 2

Let $x$ , $y$ , and $z$ be positive real numbers with $x+y+z = 3$ . Prove that at least one of the three numbers $$x(x+y-z)$$ $$y(y+z-x)$$ $$z(z+x-y)$$ is less or equal $1$ .

(Karl Czakler)