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We provide formal matched asymptotic expansions for ancient convex  solutions to MCF. The formal analysis leading to the solutions is  analogous to that for the generic MCF neck pinch in  [1].  For any $p, q$ with $p+q=n$, $p\geq1$, $q\geq2$ we find a formal ancient  solution which is a small perturbation of an ellipsoid. For  $t\to-\infty$ the solution becomes increasingly astigmatic: $q$ of its  major axes have length $\approx\sqrt{2(q-1)(-t)}$, while the other $p$ axes  have length $\approx \sqrt{-2t\log(-t)}$.  We conjecture that an analysis similar to that in [2] will  lead to a rigorous construction of ancient solutions to MCF with the  asymptotics described in this paper.

Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow