Each vertex $v$ and each edge $e$ of a graph $G$ are assigned numbers $f(v)\in\{1,2\}$ and $f(e)\in\{1,2,3\}$, respectively. Let $S(v)$ be the sum of numbers assigned to the edges incident to $v$ plus the number $f(v)$. We say that an assignment $f$ is cool if $S(u) \ne S(v)$ for every pair $(u,v)$ of adjacent (i.e. connected by an edge) vertices in $G$. Prove that for every graph there exists a cool assignment.