HMMT 2005 A4

If $a, b, c>0$, what is the smallest possible value of $\left\lfloor\frac{a+b}{c}\right\rfloor+\left\lfloor\frac{b+c}{a}\right\rfloor+\left\lfloor\frac{c+a}{b}\right\rfloor$ ? (Note that $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.)