  In this short article, we prove the existence of ancient solutions of the
mean curvature flow that for t -> 0 collapse to a round point, but for t ->
-infinity become more and more oval: near the center they have asymptotic
shrinkers modeled on round cylinders S^j x R^n-j and near the tips they have
asymptotic translators modeled on Bowl^j+1 x R^n-j-1. We also give a
characterization of the round shrinking sphere among ancient alpha-Andrews
flows. Our proofs are based on the recent estimates of Haslhofer-Kleiner.
