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The Future Circular Collider (FCC-hh) is a proposed successor of the Large Hadron Collider (LHC). FCC-hh would push both the energy and intensity frontiers of searches for new physics particles. In particular, due to higher energy and luminosity than at the LHC, at FCC-hh there would be produced around times larger amount of mesons and times of bosons, which then may decay into feebly interacting particles. In this paper we demonstrate the potential of FCC-hh by studying its sensitivity to heavy neutral leptons (HNLs) with masses $m_{N} Journal version