  Analysis of directed flow ($v_1$) of protons, antiprotons and pions in
heavy-ion collisions is performed in the range of incident energies
$\sqrt{s_{NN}}$ = 2.7--27 GeV. Simulations have been done within a three-fluid
model employing a purely hadronic equation of state (EoS) and two versions of
the EoS involving deconfinement transitions: a first-order phase transition and
a smooth crossover transition. High sensitivity of the directed flow,
especially the proton one, to the EoS is found. The crossover EoS is favored by
the most part of considered experimental data. A strong wiggle in the
excitation function of the proton $v_1$ slope at the midrapidity obtained with
the first-order-phase-transition EoS and a smooth proton $v_1$ with positive
midrapidity slope, within the hadronic EoS unambiguously disagree with the
data. The pion and antiproton $v_1$ also definitely testify in favor of the
crossover EoS. The results obtained with deconfinement EoS's apparently
indicate that these EoS's in the quark-gluon sector should be stiffer at high
baryon densities than those used in the calculation.
