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A direct search for new heavy neutral Higgs bosons A and H in the t (t) over barZ channel is presented, targeting the process pp -> A -> ZH with H -> t (t) over bar. For the first time, the channel with decays of the Z boson to muons or electrons in association with all-hadronic decays of the t (t) over bar system is targeted. The analysis uses proton-proton collision data collected at the CERN LHC with the CMS experiment at root s = 13 TeV, which correspond to an integrated luminosity of 138 fb(-1). No signal is observed. Upper limits on the product of the cross section and branching fractions are derived for narrow resonances A and H with masses up to 2100 and 2000GeV, respectively, assuming A boson production through gluon fusion. The results are also interpreted within two-Higgs-doublet models, where A and H are CP-odd and CP-even states, respectively, complementing and substantially extending the reach of previous searches.