  We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all
pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We
do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same
running time, thereby improving on the recent bound of $\tilde{O}(n^{2.5})$ by
Abboud et al. (STOC 2021). Our running time is nearly optimal as a function of
$n$.
