functional equations - Find all $f: mathbb{R} rightarrow mathbb{R}$ such that $forall x,y in mathbb{R}$:$f(f(f(x)+y)+y)=x+y+f(y)$

Find all $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $\forall x,y \in \mathbb{R}$:
$f(f(f(x)+y)+y)=x+y+f(y)$

I got the following:

(1)$f$ is injective
(2) $f(0)=0$

(3)$f(f(f(x)))=x$

But then how to proceed?