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We use the astrometric and photometric data from Gaia Data Release 2 and line-of-sight velocities from various other surveys to study the 3d structure and kinematics of the Sagittarius dwarf galaxy. The combination of photometric and astrometric data makes it possible to obtain a very clean separation of Sgr member stars from the Milky Way foreground; our final catalogue contains ~2.6e5 candidate members with magnitudes G<18, more than half of them being red clump stars. We construct and analyze maps of the mean proper motion and its dispersion over the region ~30x12 degrees, which show a number of interesting features. The intrinsic 3d density distribution (orientation, thickness) is strongly constrained by kinematics; we find that the remnant is a prolate structure with the major axis pointing at 45deg from the orbital velocity and extending up to ~5 kpc, where it transitions into the stream. We perform a large suite of N-body simulations of a disrupting Sgr galaxy as it orbits the Milky Way over the past 2.5 Gyr, which are tailored to reproduce the observed properties of the remnant (not the stream). The richness of available constraints means that only a narrow range of parameters produce a final state consistent with observations. The total mass of the remnant is ~4e8 Msun, of which roughly a quarter resides in stars. The galaxy is significantly out of equilibrium, and even its central density is below the limit required to withstand tidal forces. We conclude that the Sgr galaxy will likely be disrupted over the next Gyr.