  We construct invariants for any closed semipositive symplectic manifold which
count rational curves satisfying tangency constraints to a local divisor. More
generally, we introduce invariants involving multibranched local tangency
constraints. We give a formula describing how these invariants arise as point
constraints are pushed together in dimension four, and we use this to
recursively compute all of these invariants in terms of Gromov--Witten
invariants of blowups. As a key tool, we study analogous invariants which count
punctured curves with negative ends on a small skinny ellipsoid.
