Cauchy distribution & tail estimate

Let $\displaystyle \xi_1$, $\displaystyle \xi_2$... be independent identically distributed random variables with the Cauchy distribution. How do you prove that:

$\displaystyle \liminf_{n\rightarrow\infty}\mathbb{P}(\max(\xi_1, ...,\xi_n)> xn) \geq \exp(-\pi x)$

for any $\displaystyle x\geq 0$ ?

The Cauchy distribution is given by the density:

$\displaystyle f(u)=\frac{1}{\pi (1+u^2)}$ , $\displaystyle u \in\mathbb{R}$

And has no expectation or variance defined.

Thanks for any help.