BALTIC-WAY 2018 Problem 4

Find all functions $f:[0,+\infty) \rightarrow[0,+\infty)$, such that for any positive integer $n$ and for any non-negative real numbers $x_{1}, \ldots, x_{n}$

$$f\left(x_{1}^{2}+\cdots+x_{n}^{2}\right)=f\left(x_{1}\right)^{2}+\cdots+f\left(x_{n}\right)^{2} .$$