  We show that the number of labelled $P_7$-free bipartite graphs with $n$
vertices grows as $n^{\Theta(n)}$. This resolves an open problem posed by Allen
[P. Allen, Forbidden induced bipartite graphs. J. Graph Theory 60 (2009), no.
3, 219--241.], and completes the description of speeds of monogenic classes of
bipartite graphs. Our solution is based on a new decomposition scheme of
bipartite graphs, which is of independent interest.
