Find all solutions of the following system of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
equations in
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
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*}](/media/m/f/7/7/f77f4383084efd3594c472e11b4005b8.png)
where
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
is a given number.
%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.