  We construct closed, embedded, ancient mean curvature flows in each dimension
$n\ge 2$ with the topology of $S^1 \times S^{n-1}$. These examples are not mean
convex and not solitons. They are constructed by analyzing perturbations of the
self-shrinking doughnuts constructed by Drugan and Nguyen (or, alternatively,
Angenent's self shrinking torus when $n =2$)
