Graph Algorithms · Hard problem

A project's activities are arcs in a directed network from start event $1$ to finish event $7$: $1\to2{:}4, 1\to3{:}2, 2\to4{:}5, 3\to4{:}3, 3\to5{:}6, 4\to6{:}2, 5\to6{:}4, 6\to7{:}3$ (days). Every activity leaving an event can start only once ALL activities entering that event are finished. What is the minimum number of days to complete the whole project?