Directed Graphs and Network Flows · Challenge problem

A digraph has vertices $1,\dots,8$ with arcs $1\to2$, $2\to3$, $3\to4$, $4\to1$ (a $4$-cycle), $5\to6$, $6\to7$, $7\to5$ (a $3$-cycle), and also $4\to5$, $5\to1$, $7\to8$. What is the size of the largest strongly connected component?