Consider the standard version of Dijkstra's algorithm on directed graphs. Assume it is known that the input digraph $G = (V, E)$ has the following property: for all $v \in V$ the weight of all outgoing edges $vu$ is the same. 

How can one modify Dijkstra's algorithm so that _exactly one relaxation_ is done for every vertex $v \in V$? (i. e. decreasing of current minimal path length $d_{v}$ is done exactly once for every $v$).