Na(+)/H(+) antiporter that extrudes sodium in exchange for external protons. Might be able to function at relatively high concentrations of Na(+) ions. Has also Li(+)/H(+) antiport activity under K(+)-rich conditions, but it might not have any physiological relevance. Belongs to the monovalent cation:proton antiporter 1 (CPA1) transporter (TC 2.A.36) family.