International Mathematical Olympiad 2000 — Official contest Question 2

Let $a$, $b$, $c$ be positive real numbers with $abc = 1$. Show that $$
\left( a - 1 + \frac 1b \right)
\left( b - 1 + \frac 1c \right)
\left( c - 1 + \frac 1a \right)
\le 1.
$$