4. Given $n(n \geqslant 3)$ real numbers $x_{1}, x_{2}, \cdots, x_{n}$ satisfying $\left\{\begin{array}{l}x_{1}+x_{2}+\cdots+x_{n}=n \\ x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=n\end{array}\right.$, then
$$
\frac{x_{1} x_{2}+x_{2} x_{3}+\cdots+x_{n-1} x_{n}+x_{n} x_{1}}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdots+\frac{1}{x_{n}}}=
$$
$1$