Determine all functions with the property that holds for all .
(Croatia)
Determine all functions $f:\mathbb{Z}\rightarrow\mathbb{Z}$ with the property that \[f(x-f(y))=f(f(x))-f(y)-1\]holds for all $x,y\in\mathbb{Z}$.
\begin{flushright}\emph{(Croatia)}\end{flushright}
Školjka 
with the property that 
holds for all 
.