  Globular clusters (GCs) formed when the Milky Way experienced a phase of
rapid assembly. We use the wealth of information contained in the Galactic GC
population to quantify the properties of the satellite galaxies from which the
Milky Way assembled. To achieve this, we train an artificial neural network on
the E-MOSAICS cosmological simulations of the co-formation and co-evolution of
GCs and their host galaxies. The network uses the ages, metallicities, and
orbital properties of GCs that formed in the same progenitor galaxies to
predict the stellar masses and accretion redshifts of these progenitors. We
apply the network to Galactic GCs associated with five progenitors: {\it
Gaia}-Enceladus, the Helmi streams, Sequoia, Sagittarius, and the recently
discovered, `low-energy' GCs, which provide an excellent match to the predicted
properties of the enigmatic galaxy `Kraken'. The five galaxies cover a narrow
stellar mass range [$M_\star=(0.6{-}4.6)\times10^8~{\rm M}_\odot$], but have
widely different accretion redshifts ($z_{\rm acc}=0.57{-}2.65$). All accretion
events represent minor mergers, but Kraken likely represents the most major
merger ever experienced by the Milky Way, with stellar and virial mass ratios
of $r_{M_\star}=1$:$31^{+34}_{-16}$ and $r_{M_{\rm h}}=1$:$7^{+4}_{-2}$,
respectively. The progenitors match the $z=0$ relation between GC number and
halo virial mass, but have elevated specific frequencies, suggesting an
evolution with redshift. Even though these progenitors likely were the Milky
Way's most massive accretion events, they contributed a total mass of only
$\log{(M_{\rm \star,tot}/{\rm M}_\odot)}=9.0\pm0.1$, similar to the stellar
halo. This implies that the Milky Way grew its stellar mass mostly by in-situ
star formation. We conclude by organising these accretion events into the most
detailed reconstruction to date of the Milky Way's merger tree.
