  We show, in a model-independent manner, that the QCD critical point can
appear only inside the pion condensation phase of the phase-quenched QCD as
long as the contribution of flavor-disconnected diagrams is negligible. The
sign problem is known to be maximally severe in this region, implying that the
QCD critical point is reachable by the present lattice QCD techniques only if
there is an enhancement of the flavor-disconnected contribution at finite
baryon chemical potential.
