Functional equation $f(x+f(xy))=f(x+f(x)f(y))=f(x)+xf(y)$

Find all functions $f : mathbb{R}to mathbb{R}$ such that $$f(x+f(xy))=f(x+f(x)f(y))=f(x)+xf(y)$$ for any $x, yin mathbb{R}$.