Blow up points on real projective plane

Question

What is the genus of the blow-up at $3$ non-colinear points of $\mathbb{R} \mathbb{P}^2$? This question occurred to me as I was trying to eliminate the sigular points at the vertices of a given triangle when performing the isogonal conjugate. I hope this change of background surface would not ruin too many features of conics and cubics with respect to the triangle.