RU-ALLRUSSIAN 2023 Problem 108

Given is a real number $a \in (0,1)$ and positive reals $x_0, x_1, \ldots, x_n$ such that $\sum x_i=n+a$ and $\sum \frac{1}{x_i}=n+\frac{1}{a}$ . Find the minimal value of $\sum x_i^2$ .