  For a birational log Fano contraction, it is conjectured an inequality
between the dimension of its exceptional locus and the minimal log discrepancy
over the locus. The conjecture follows from the existence of the flip for the
contraction and another conjecture about the maximum of minimal log discripancy
in given dimension; in particular, it holds in small dimensions (up to 4), and
some special cases. It is illustrated by some examples.
