  For each $n\ge 3$, we construct an $O(2)\times O(n-1)$-invariant ancient
Ricci flow on the $n$-sphere $S^n$ with positive curvature operator and bounded
"girth". As time approaches minus infinity, it decomposes into a flat cylinder
$S^1\times \mathbb{R}^{n-1}$ in the "waist" region and an $(n-2)$-plane of
cigar solitons around any point in the "tip" region (both of which are of the
same scale). This solution appears to be new, even in dimension three.
