Školjka

%V0 Find all solutions of the following system of $n$ equations in $n$ variables: $$$\begin{align*} x_{1}|x_{1}|-(x_{1}-a)&|x_{1}-a| = x_{2}|x_{2}|, \\ x_{2}|x_{2}|-(x_{2}-a)&|x_{2}-a| = x_{3}|x_{3}|, \\ &\vdots \\ x_{n}|x_{n}|-(x_{n}-a)&|x_{n}-a| = x_{1}|x_{1}| \\ \end{align*}$$$ where $a$ is a given number.