Collapsed limits of compact Heisenberg manifolds with sub-Riemannian metrics

We show that every collapsed Gromov-Hausdorff limit of compact Heisenberg manifolds endowed with left-invariant Riemannian/sub-Riemannian metrics is isometric to a flat torus.We say that a sequence of sub-Riemannian manifolds collapses if their total measure with respect to Popp's volume converges to zero.