Chemical freeze-outs of strange and non-strange particles and residual chemical non-equilibrium

We propose an elaborate version of the hadron resonance gas model with the combined treatment of separate chemical freeze-outs for strange and non-strange hadrons and with an additional \gamma_{s} factor which accounts for the remaining strange particle non-equilibration. Two sets of chemical freeze-outs parameters are connected by the conservation laws of entropy, baryonic charge, isospin projection and strangeness. The developed approach enables us to perform a high-quality fit of the hadron multiplicity ratios for AGS, SPS and RHIC energies with total \chi^2/dof \simeq 1.05. A special attention is paid to a complete description of the Strangeness Horn. A well-known \bar p, \bar \Lambda and \bar \Xi selective suppression problem is also discussed.