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Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\\approx2\\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\\approx 50\\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\\approx1.8\\%$. 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