SMO 2013 Junior Round 1 Question 2

Real numbers $a,b,c$ satisfy $|a-b|=1$, $|b-c|=1$, $|c-a|=2$ and $abc=60$. Find
$$\frac a{bc}+\frac b{ca}+\frac c{ab}-\frac1a-\frac1b-\frac1c.$$