IR-TST 2019 Problem 5

Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all $x,y\in \mathbb{R}$ : $$f\left(f(x)^2-y^2\right)^2+f(2xy)^2=f\left(x^2+y^2\right)^2$$ Proposed by Ali Behrouz - Mojtaba Zare Bidaki