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The bounds on the light quark masses are obtained by fitting the squares of pseudoscalar meson masses $m^2_\pi$ and $m^2_K$ to second order in $1/N_c$ expansion. It is shown that the values of the quark mass ratios $x=m_u/m_d$ and $y=m_s/m_d$ belong to the third order algebraic curve $f(x,y)=0$. Two parameters of the curve are fractional linear functions of the squared masses of $\pi$ and $K$ mesons and, when Dashen's theorem is satisfied, coincide with the values $x_W=0.56$ and $y_W=20.18$ obtained by Weinberg from the current algebra. The curve is stable, i.e. it does not change when taking into account chiral corrections in the mass formulas of pseudoscalars, and is universal: any two independent fractional linear functions lead to the same curve. A part of the curve corresponding to the physical values of the quark masses can be distinguished if we use the ratio $m_s/m_{ud}=27.23(10)$ known from calculations on the lattice, which gives $m_u/m_d=0.455(8)$, $m_s/m_d=19.81(10)$. The value of the low-energy constant $B_0(2\, GeV)=2.682(36)(39)\,GeV$ (also known from lattice simulations) allows us to obtain absolute values of the light quark masses: $m_u=2.14(7)\, MeV$, $m_d=4.70(12)\, MeV$, $m_s=93.13(2.25)\, MeV$ (all values refer to the $\overline{MS}$ scheme at the $2\, GeV$ scale).
