  We propose two systems of "intrinsic" signs for counting such curves. In both
cases the result acquires an exceptionally strong invariance property: it does
not depend on the choice of a surface. One of our counts includes all divisor
classes of canonical degree 2 and gives in total 30. The other one excludes the
class $-2K$, but adds up the results of counting for a pair of real structures
that differ by Bertini involution. This count gives 96.
