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Computing the nonperturbative running of the coupling in the range from $0.2\\,$GeV to $70\\,$GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain $\\Lambda_{\\overline{\\rm MS}}^{(3)}=341(12)\\,$MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. 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