CH-SMO 2010 Problem 4

Let $x$ , $y$ , $z \in\mathbb{R}^+$ satisfying $xyz = 1$ . Prove that $$\frac {(x + y - 1)^2}{z} + \frac {(y + z - 1)^2}{x} + \frac {(z + x - 1)^2}{y}\geqslant x + y + z\text{.}$$