  We classify all positive n-particle N^kMHV Yangian invariants in N=4
Yang-Mills theory with n=5k, which we call extremal because none exist for
n>5k. We show that this problem is equivalent to that of enumerating plane
cactus graphs with k pentagons. We use the known solution of that problem to
provide an exact expression for the number of cyclic classes of such invariants
for any k, and a simple rule for writing them down explicitly. As a byproduct,
we provide an alternative (but equivalent) classification by showing that a
product of k five-brackets with disjoint sets of indices is a positive Yangian
invariant if and only if the sets are all weakly separated.
